-DOCSTART-	_	_	O

Cautious	_	_	O
Asset	_	_	O
Investment	_	_	O
has	_	_	O
a	_	_	O
total	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
150,000	_	_	B-LIMIT
to	_	_	O
manage	_	_	O
and	_	_	O
decides	_	_	O
to	_	_	O
invest	_	_	O
it	_	_	O
in	_	_	O
money	_	_	B-VAR
market	_	_	I-VAR
fund	_	_	I-VAR
,	_	_	O
which	_	_	O
yields	_	_	O
a	_	_	O
2	_	_	B-PARAM
%	_	_	I-PARAM
return	_	_	B-OBJ_NAME
as	_	_	O
well	_	_	O
as	_	_	O
in	_	_	O
foreign	_	_	B-VAR
bonds	_	_	I-VAR
,	_	_	O
which	_	_	O
gives	_	_	O
and	_	_	O
average	_	_	O
rate	_	_	O
of	_	_	O
return	_	_	B-OBJ_NAME
of	_	_	O
10.2	_	_	B-PARAM
%	_	_	O
.	_	_	O
Internal	_	_	O
policies	_	_	O
require	_	_	O
PAI	_	_	O
to	_	_	O
diversify	_	_	O
the	_	_	O
asset	_	_	O
allocation	_	_	O
so	_	_	O
that	_	_	O
the	_	_	O
minimum	_	_	B-CONST_DIR
investment	_	_	O
in	_	_	O
money	_	_	B-VAR
market	_	_	I-VAR
fund	_	_	I-VAR
is	_	_	O
40	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
total	_	_	O
investment	_	_	O
.	_	_	O
Due	_	_	O
to	_	_	O
the	_	_	O
risk	_	_	O
of	_	_	O
default	_	_	O
of	_	_	O
foreign	_	_	O
countries	_	_	O
,	_	_	O
no	_	_	B-CONST_DIR
more	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
40	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
total	_	_	O
investment	_	_	O
should	_	_	O
be	_	_	O
allocated	_	_	O
to	_	_	O
foreign	_	_	B-VAR
bonds	_	_	I-VAR
.	_	_	O
How	_	_	O
much	_	_	O
should	_	_	O
the	_	_	O
Cautious	_	_	O
Asset	_	_	O
Investment	_	_	O
allocate	_	_	O
in	_	_	O
each	_	_	O
asset	_	_	O
so	_	_	O
as	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
its	_	_	O
average	_	_	B-OBJ_NAME
return	_	_	I-OBJ_NAME
?	_	_	O

The	_	_	O
Notorious	_	_	O
Desk	_	_	O
company	_	_	O
wants	_	_	O
to	_	_	O
promote	_	_	O
a	_	_	O
new	_	_	O
brand	_	_	O
of	_	_	O
wine	_	_	O
and	_	_	O
wants	_	_	O
to	_	_	O
market	_	_	O
it	_	_	O
using	_	_	O
a	_	_	O
total	_	_	O
market	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
87,000	_	_	B-LIMIT
.	_	_	O
To	_	_	O
do	_	_	O
so	_	_	O
,	_	_	O
the	_	_	O
company	_	_	O
needs	_	_	O
to	_	_	O
decide	_	_	O
how	_	_	O
much	_	_	O
to	_	_	O
allocate	_	_	O
on	_	_	O
each	_	_	O
of	_	_	O
its	_	_	O
two	_	_	O
advertising	_	_	O
channels	_	_	O
:	_	_	O
(	_	_	O
1	_	_	O
)	_	_	O
morning	_	_	B-VAR
TV	_	_	I-VAR
show	_	_	I-VAR
and	_	_	O
(	_	_	O
2	_	_	O
)	_	_	O
social	_	_	B-VAR
media	_	_	I-VAR
.	_	_	O
Each	_	_	O
day	_	_	O
,	_	_	O
it	_	_	O
costs	_	_	O
the	_	_	O
company	_	_	O
$	_	_	O
1,000	_	_	B-PARAM
and	_	_	O
$	_	_	O
2000	_	_	B-PARAM
to	_	_	O
run	_	_	O
advertisement	_	_	O
spots	_	_	O
on	_	_	O
morning	_	_	B-VAR
TV	_	_	I-VAR
show	_	_	O
and	_	_	O
social	_	_	B-VAR
media	_	_	I-VAR
respectively	_	_	O
.	_	_	O
The	_	_	O
expected	_	_	O
daily	_	_	O
reach	_	_	B-OBJ_NAME
,	_	_	O
based	_	_	O
on	_	_	O
past	_	_	O
ratings	_	_	O
,	_	_	O
is	_	_	O
15,000	_	_	B-PARAM
viewers	_	_	O
for	_	_	O
each	_	_	O
morning	_	_	B-VAR
show	_	_	I-VAR
spot	_	_	O
and	_	_	O
30,000	_	_	B-PARAM
internet	_	_	O
users	_	_	O
for	_	_	O
a	_	_	O
social	_	_	B-VAR
media	_	_	I-VAR
spot	_	_	I-VAR
.	_	_	O
The	_	_	O
chief	_	_	O
marketer	_	_	O
knows	_	_	O
from	_	_	O
her	_	_	O
experience	_	_	O
that	_	_	O
both	_	_	O
channels	_	_	O
are	_	_	O
key	_	_	O
to	_	_	O
the	_	_	O
success	_	_	O
of	_	_	O
the	_	_	O
product	_	_	O
launch	_	_	O
.	_	_	O
She	_	_	O
wants	_	_	O
to	_	_	O
plan	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
4	_	_	B-LIMIT
but	_	_	O
no	_	_	B-CONST_DIR
more	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
7	_	_	B-LIMIT
morning	_	_	B-VAR
show	_	_	I-VAR
spots	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
the	_	_	O
social	_	_	B-VAR
media	_	_	I-VAR
spots	_	_	I-VAR
needs	_	_	O
to	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
due	_	_	O
to	_	_	O
pricing	_	_	O
tier	_	_	O
policy	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
times	_	_	O
should	_	_	O
each	_	_	O
of	_	_	O
the	_	_	O
media	_	_	O
channels	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
reach	_	_	B-OBJ_NAME
of	_	_	O
the	_	_	O
campaign	_	_	O
?	_	_	O

An	_	_	O
consumer	_	_	O
electronics	_	_	O
business	_	_	O
needs	_	_	O
to	_	_	O
determine	_	_	O
the	_	_	O
level	_	_	O
of	_	_	O
production	_	_	O
of	_	_	O
its	_	_	O
two	_	_	O
hottest	_	_	O
video	_	_	O
game	_	_	O
consoles	_	_	O
,	_	_	O
which	_	_	O
are	_	_	O
the	_	_	O
PX7	_	_	B-VAR
and	_	_	O
Silent	_	_	B-VAR
X	_	_	I-VAR
,	_	_	O
ahead	_	_	O
of	_	_	O
the	_	_	O
holiday	_	_	O
season	_	_	O
.	_	_	O
Making	_	_	O
one	_	_	O
PX7	_	_	B-VAR
console	_	_	O
requires	_	_	O
3	_	_	B-PARAM
hours	_	_	O
of	_	_	O
labor	_	_	O
and	_	_	O
yields	_	_	O
a	_	_	O
$	_	_	O
40	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
.	_	_	O
On	_	_	O
the	_	_	O
other	_	_	O
hand	_	_	O
,	_	_	O
one	_	_	O
Silent	_	_	B-VAR
X	_	_	I-VAR
console	_	_	O
can	_	_	O
be	_	_	O
produced	_	_	O
in	_	_	O
7	_	_	B-PARAM
hours	_	_	O
and	_	_	O
offers	_	_	O
a	_	_	O
greater	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
75	_	_	B-PARAM
.	_	_	O
Given	_	_	O
the	_	_	O
demand	_	_	O
forecast	_	_	O
,	_	_	O
the	_	_	O
business	_	_	O
decides	_	_	O
to	_	_	O
produce	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-PARAM
as	_	_	O
many	_	_	O
PX7	_	_	B-VAR
consoles	_	_	O
as	_	_	O
Silent	_	_	B-VAR
X	_	_	I-VAR
ones	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
it	_	_	O
can	_	_	O
spend	_	_	O
up	_	_	B-CONST_DIR
to	_	_	I-CONST_DIR
48	_	_	B-LIMIT
hours	_	_	O
a	_	_	O
week	_	_	O
to	_	_	O
manufacture	_	_	O
these	_	_	O
consoles	_	_	O
.	_	_	O
Can	_	_	O
you	_	_	O
help	_	_	O
the	_	_	O
business	_	_	O
determine	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
each	_	_	O
console	_	_	O
to	_	_	O
produced	_	_	O
each	_	_	O
week	_	_	O
to	_	_	O
obtain	_	_	O
the	_	_	O
maximum	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Matter	_	_	O
Auto	_	_	O
manufactures	_	_	O
EV	_	_	O
cars	_	_	O
and	_	_	O
hybrid	_	_	O
trucks	_	_	O
that	_	_	O
are	_	_	O
targeted	_	_	O
for	_	_	O
baby	_	_	O
boomers	_	_	O
and	_	_	O
millennials	_	_	O
.	_	_	O
To	_	_	O
market	_	_	O
these	_	_	O
two	_	_	O
products	_	_	O
,	_	_	O
Matter	_	_	O
Auto	_	_	O
has	_	_	O
launched	_	_	O
a	_	_	O
boisterous	_	_	O
ads	_	_	O
campaign	_	_	O
and	_	_	O
has	_	_	O
decided	_	_	O
to	_	_	O
purchase	_	_	O
TV	_	_	O
commercial	_	_	O
spots	_	_	O
on	_	_	O
two	_	_	O
channels	_	_	O
:	_	_	O
TV	_	_	B-VAR
shows	_	_	I-VAR
and	_	_	O
sports	_	_	B-VAR
programs	_	_	I-VAR
.	_	_	O
Each	_	_	O
sports	_	_	B-VAR
ad	_	_	I-VAR
is	_	_	O
seen	_	_	O
by	_	_	O
4	_	_	B-PARAM
million	_	_	O
baby	_	_	O
boomers	_	_	O
and	_	_	O
18	_	_	B-PARAM
million	_	_	O
millennials	_	_	O
and	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
90,000	_	_	B-PARAM
.	_	_	O
Each	_	_	O
TV	_	_	B-VAR
show	_	_	I-VAR
commercial	_	_	O
is	_	_	O
watched	_	_	O
by	_	_	O
12	_	_	B-PARAM
million	_	_	O
baby	_	_	O
boomers	_	_	O
and	_	_	O
5	_	_	B-PARAM
million	_	_	O
millennials	_	_	O
,	_	_	O
and	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
20,000	_	_	B-PARAM
.	_	_	O
Matter	_	_	O
Auto	_	_	O
would	_	_	O
like	_	_	O
to	_	_	O
reach	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
40	_	_	B-LIMIT
million	_	_	O
baby	_	_	O
boomers	_	_	O
and	_	_	O
25	_	_	B-LIMIT
million	_	_	O
millennials	_	_	O
.	_	_	O
Determine	_	_	O
how	_	_	O
Matter	_	_	O
Auto	_	_	O
can	_	_	O
meet	_	_	O
its	_	_	O
advertising	_	_	O
requirements	_	_	O
at	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
food	_	_	O
truck	_	_	O
sells	_	_	O
and	_	_	O
delivers	_	_	O
rice	_	_	B-VAR
bowls	_	_	I-VAR
and	_	_	O
quesadillas	_	_	B-VAR
during	_	_	O
the	_	_	O
pandemic	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
on	_	_	O
a	_	_	O
rice	_	_	B-VAR
bowl	_	_	I-VAR
is	_	_	O
3	_	_	B-PARAM
$	_	_	O
,	_	_	O
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
on	_	_	O
a	_	_	O
quesadilla	_	_	B-VAR
is	_	_	O
2$.	_	_	B-PARAM
In	_	_	O
order	_	_	O
to	_	_	O
thrive	_	_	O
,	_	_	O
it	_	_	O
must	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
40	_	_	B-LIMIT
rice	_	_	B-VAR
bowls	_	_	I-VAR
but	_	_	O
can	_	_	O
make	_	_	B-CONST_DIR
only	_	_	I-CONST_DIR
up	_	_	I-CONST_DIR
to	_	_	I-CONST_DIR
70	_	_	B-LIMIT
in	_	_	O
a	_	_	O
day	_	_	O
.	_	_	O
It	_	_	O
must	_	_	O
also	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
quesadillas	_	_	B-VAR
due	_	_	O
to	_	_	O
its	_	_	O
high	_	_	O
demand	_	_	O
,	_	_	O
but	_	_	O
can	_	_	O
not	_	_	B-CONST_DIR
prepare	_	_	I-CONST_DIR
more	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
80	_	_	B-LIMIT
a	_	_	O
day	_	_	O
.	_	_	O
Due	_	_	O
to	_	_	O
staff	_	_	O
shortage	_	_	O
,	_	_	O
the	_	_	O
food	_	_	O
truck	_	_	O
can	_	_	O
only	_	_	O
prepare	_	_	O
up	_	_	O
to	_	_	O
100	_	_	B-LIMIT
items	_	_	O
in	_	_	B-CONST_DIR
total	_	_	I-CONST_DIR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
food	_	_	O
item	_	_	O
should	_	_	O
it	_	_	O
prepare	_	_	O
to	_	_	O
satisfy	_	_	O
its	_	_	O
customers	_	_	O
and	_	_	O
maximize	_	_	B-OBJ_DIR
its	_	_	O
daily	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

GameShop	_	_	O
would	_	_	O
like	_	_	O
to	_	_	O
attract	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
200	_	_	B-LIMIT
customers	_	_	O
into	_	_	O
its	_	_	O
store	_	_	O
daily	_	_	O
.	_	_	O
Therefore	_	_	O
,	_	_	O
it	_	_	O
decides	_	_	O
to	_	_	O
sell	_	_	O
two	_	_	O
popular	_	_	O
video	_	_	O
games	_	_	O
,	_	_	O
Kommand	_	_	B-VAR
and	_	_	O
Kontrol	_	_	B-VAR
,	_	_	O
at	_	_	O
steep	_	_	O
discount	_	_	O
to	_	_	O
attract	_	_	O
foot	_	_	O
traffic	_	_	O
.	_	_	O
The	_	_	O
GameShop	_	_	O
owner	_	_	O
pays	_	_	O
$	_	_	O
14	_	_	B-PARAM
and	_	_	O
$	_	_	O
8	_	_	B-PARAM
for	_	_	O
each	_	_	O
unit	_	_	O
of	_	_	O
Kommand	_	_	B-VAR
and	_	_	O
Kontrol	_	_	B-VAR
respectively	_	_	O
and	_	_	O
has	_	_	O
at	_	_	O
its	_	_	O
disposition	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
daily	_	_	I-CONST_DIR
budget	_	_	I-CONST_DIR
of	_	_	O
$	_	_	O
500	_	_	B-LIMIT
for	_	_	O
this	_	_	O
sales	_	_	O
campaign	_	_	O
.	_	_	O
For	_	_	O
each	_	_	O
unit	_	_	O
of	_	_	O
Kommand	_	_	B-VAR
game	_	_	O
sold	_	_	O
,	_	_	O
GameShop	_	_	O
incurs	_	_	O
an	_	_	O
cost	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
11	_	_	B-PARAM
and	_	_	O
attracts	_	_	O
20	_	_	B-PARAM
fans	_	_	O
into	_	_	O
its	_	_	O
store	_	_	O
in	_	_	O
average	_	_	O
.	_	_	O
In	_	_	O
comparison	_	_	O
,	_	_	O
each	_	_	O
unit	_	_	O
of	_	_	O
Kontrol	_	_	B-VAR
incurs	_	_	O
a	_	_	O
lower	_	_	O
cost	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
3	_	_	B-PARAM
but	_	_	O
only	_	_	O
attracts	_	_	O
5	_	_	B-PARAM
fans	_	_	O
in	_	_	O
average	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
units	_	_	O
of	_	_	O
each	_	_	O
video	_	_	O
game	_	_	O
should	_	_	O
be	_	_	O
stocked	_	_	O
daily	_	_	O
to	_	_	O
meet	_	_	O
his	_	_	O
campaign	_	_	O
while	_	_	O
minimizing	_	_	B-OBJ_DIR
its	_	_	O
cost	_	_	B-OBJ_NAME
?	_	_	O

Cacaotier	_	_	O
has	_	_	O
30,000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
cocoa	_	_	O
available	_	_	B-CONST_DIR
to	_	_	O
make	_	_	O
gourmet	_	_	B-VAR
truffles	_	_	I-VAR
and	_	_	O
chocolate	_	_	B-VAR
bars	_	_	I-VAR
.	_	_	O
Consumer	_	_	O
research	_	_	O
determines	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-PARAM
the	_	_	O
amount	_	_	O
of	_	_	O
the	_	_	O
chocolate	_	_	B-VAR
bars	_	_	I-VAR
are	_	_	O
needed	_	_	O
than	_	_	O
the	_	_	O
gourmet	_	_	B-VAR
truffles	_	_	I-VAR
and	_	_	O
there	_	_	O
needs	_	_	O
to	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
gourmet	_	_	B-VAR
truffles	_	_	I-VAR
made	_	_	O
.	_	_	O
Each	_	_	O
gourmet	_	_	B-VAR
truffle	_	_	I-VAR
weighs	_	_	O
700	_	_	B-PARAM
grams	_	_	O
and	_	_	O
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
7	_	_	B-PARAM
.	_	_	O
In	_	_	O
contrast	_	_	O
,	_	_	O
a	_	_	O
chocolate	_	_	B-VAR
bar	_	_	I-VAR
weighs	_	_	O
300	_	_	B-PARAM
grams	_	_	O
each	_	_	O
and	_	_	O
sells	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
3	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
product	_	_	O
should	_	_	O
Cacaotier	_	_	O
prepare	_	_	O
to	_	_	O
obtain	_	_	O
the	_	_	O
maximum	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Young	_	_	O
Bucks	_	_	O
needs	_	_	O
to	_	_	O
allocate	_	_	O
resources	_	_	O
at	_	_	O
its	_	_	O
two	_	_	O
plants	_	_	O
Alpha	_	_	B-VAR
and	_	_	O
Beta	_	_	B-VAR
to	_	_	O
produce	_	_	O
two	_	_	O
products	_	_	O
:	_	_	O
cement	_	_	O
and	_	_	O
stucco	_	_	O
.	_	_	O
To	_	_	O
meet	_	_	O
customer	_	_	O
demands	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
tons	_	_	O
of	_	_	O
cement	_	_	O
and	_	_	O
80	_	_	B-LIMIT
tons	_	_	O
of	_	_	O
stucco	_	_	O
must	_	_	O
be	_	_	O
produced	_	_	O
daily	_	_	O
.	_	_	O
Running	_	_	O
the	_	_	O
plant	_	_	B-VAR
Alpha	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
40	_	_	B-PARAM
per	_	_	O
hour	_	_	O
and	_	_	O
yields	_	_	O
3	_	_	B-PARAM
tons	_	_	O
of	_	_	O
cement	_	_	O
and	_	_	O
2	_	_	B-PARAM
ton	_	_	O
of	_	_	O
stucco	_	_	O
.	_	_	O
Running	_	_	O
the	_	_	O
plant	_	_	B-VAR
Beta	_	_	I-VAR
for	_	_	O
an	_	_	O
hour	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
100	_	_	B-PARAM
and	_	_	O
produces	_	_	O
5	_	_	B-PARAM
tons	_	_	O
of	_	_	O
cement	_	_	O
and	_	_	O
4	_	_	B-PARAM
tons	_	_	O
of	_	_	O
stucco	_	_	O
.	_	_	O
Determine	_	_	O
the	_	_	O
daily	_	_	O
production	_	_	O
plan	_	_	O
at	_	_	O
its	_	_	O
plants	_	_	O
that	_	_	O
will	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
cost	_	_	B-OBJ_NAME
of	_	_	O
meeting	_	_	O
the	_	_	O
demands	_	_	O
.	_	_	O

A	_	_	O
chemical	_	_	O
plant	_	_	O
produces	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
compounds	_	_	O
,	_	_	O
Alnolyte	_	_	B-VAR
and	_	_	O
Blenzoate	_	_	B-VAR
.	_	_	O
To	_	_	O
produce	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
compound	_	_	O
,	_	_	O
we	_	_	O
need	_	_	O
to	_	_	O
use	_	_	O
both	_	_	O
an	_	_	O
automatic	_	_	O
device	_	_	O
and	_	_	O
a	_	_	O
human	_	_	O
-	_	_	O
operated	_	_	O
device	_	_	O
.	_	_	O
On	_	_	O
a	_	_	O
given	_	_	O
day	_	_	O
,	_	_	O
each	_	_	O
processing	_	_	O
device	_	_	O
is	_	_	O
available	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
500	_	_	B-LIMIT
minutes	_	_	O
.	_	_	O
To	_	_	O
extract	_	_	O
a	_	_	O
package	_	_	O
of	_	_	O
Alnolyte	_	_	B-VAR
,	_	_	O
it	_	_	O
takes	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
processing	_	_	O
on	_	_	O
the	_	_	O
automatic	_	_	O
device	_	_	O
and	_	_	O
4	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
human	_	_	O
-	_	_	O
operated	_	_	O
device	_	_	O
.	_	_	O
To	_	_	O
extract	_	_	O
a	_	_	O
package	_	_	O
of	_	_	O
Blenzoate	_	_	B-VAR
,	_	_	O
the	_	_	O
automatic	_	_	O
device	_	_	O
needs	_	_	O
to	_	_	O
be	_	_	O
run	_	_	O
for	_	_	O
7	_	_	B-PARAM
minutes	_	_	O
and	_	_	O
the	_	_	O
human	_	_	O
-	_	_	O
operated	_	_	O
device	_	_	O
for	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
.	_	_	O
The	_	_	O
manufacturer	_	_	O
can	_	_	O
sell	_	_	O
a	_	_	O
package	_	_	O
of	_	_	O
Alnolyte	_	_	B-VAR
for	_	_	O
a	_	_	O
revenue	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
7	_	_	B-PARAM
and	_	_	O
Blenzoate	_	_	B-VAR
for	_	_	O
a	_	_	O
revenue	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
10	_	_	B-PARAM
.	_	_	O
Assuming	_	_	O
that	_	_	O
the	_	_	O
plant	_	_	O
can	_	_	O
sell	_	_	O
all	_	_	O
the	_	_	O
compounds	_	_	O
it	_	_	O
produces	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
packages	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
be	_	_	O
produced	_	_	O
daily	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
revenue	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
furniture	_	_	O
maker	_	_	O
creates	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
tables	_	_	O
,	_	_	O
standing	_	_	B-VAR
table	_	_	I-VAR
and	_	_	O
dining	_	_	B-VAR
table	_	_	I-VAR
.	_	_	O
It	_	_	O
takes	_	_	O
2	_	_	B-PARAM
hours	_	_	O
to	_	_	O
produce	_	_	O
the	_	_	O
parts	_	_	O
of	_	_	O
a	_	_	O
standing	_	_	B-VAR
table	_	_	I-VAR
and	_	_	O
4	_	_	B-PARAM
hours	_	_	O
for	_	_	O
those	_	_	O
of	_	_	O
a	_	_	O
dining	_	_	B-VAR
table	_	_	I-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
it	_	_	O
takes	_	_	O
1	_	_	B-PARAM
hour	_	_	O
and	_	_	O
2.5	_	_	B-PARAM
hours	_	_	O
to	_	_	O
assemble	_	_	O
a	_	_	O
dining	_	_	B-VAR
table	_	_	I-VAR
and	_	_	O
standing	_	_	B-VAR
table	_	_	I-VAR
respectively	_	_	O
.	_	_	O
Finally	_	_	O
,	_	_	O
polishing	_	_	O
a	_	_	O
dining	_	_	B-VAR
table	_	_	I-VAR
takes	_	_	O
1.5	_	_	B-PARAM
hours	_	_	O
whereas	_	_	O
polishing	_	_	O
a	_	_	O
standing	_	_	B-VAR
table	_	_	I-VAR
requires	_	_	O
2	_	_	B-PARAM
hours	_	_	O
.	_	_	O
Every	_	_	O
month	_	_	O
,	_	_	O
there	_	_	O
are	_	_	O
a	_	_	O
total	_	_	O
of	_	_	O
6000	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
producing	_	_	O
the	_	_	O
parts	_	_	O
,	_	_	O
3000	_	_	B-LIMIT
hours	_	_	O
for	_	_	O
assembling	_	_	O
the	_	_	O
parts	_	_	O
,	_	_	O
and	_	_	O
4500	_	_	B-LIMIT
hours	_	_	O
for	_	_	O
polishing	_	_	O
the	_	_	O
tables	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
made	_	_	O
on	_	_	O
a	_	_	O
standing	_	_	B-VAR
table	_	_	I-VAR
is	_	_	O
$	_	_	O
45	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
on	_	_	O
a	_	_	O
dining	_	_	B-VAR
table	_	_	I-VAR
$	_	_	O
95	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
tables	_	_	O
should	_	_	O
be	_	_	O
manufactured	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
monthly	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
flower	_	_	O
grower	_	_	O
has	_	_	B-CONST_DIR
120	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
agricultural	_	_	O
land	_	_	O
in	_	_	O
which	_	_	O
he	_	_	O
wants	_	_	O
to	_	_	O
plant	_	_	O
tulips	_	_	B-VAR
and	_	_	O
orchids	_	_	B-VAR
.	_	_	O
The	_	_	O
seed	_	_	O
for	_	_	O
tulips	_	_	B-VAR
costs	_	_	O
$	_	_	O
15	_	_	B-PARAM
per	_	_	O
acre	_	_	O
whereas	_	_	O
the	_	_	O
seed	_	_	O
for	_	_	O
orchids	_	_	B-VAR
costs	_	_	O
$	_	_	O
40	_	_	B-PARAM
per	_	_	O
acre	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
tulips	_	_	B-VAR
is	_	_	O
$	_	_	O
75	_	_	B-PARAM
whereas	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
for	_	_	O
orchids	_	_	B-VAR
is	_	_	O
$	_	_	O
105	_	_	B-PARAM
an	_	_	O
acre	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
grower	_	_	O
has	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
budget	_	_	I-CONST_DIR
of	_	_	O
$	_	_	O
1200	_	_	B-LIMIT
to	_	_	O
spend	_	_	O
on	_	_	O
seeds	_	_	O
,	_	_	O
determine	_	_	O
how	_	_	O
many	_	_	O
tulips	_	_	B-VAR
and	_	_	O
orchids	_	_	B-VAR
he	_	_	O
needs	_	_	O
to	_	_	O
plant	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
profit	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
beauty	_	_	O
and	_	_	O
health	_	_	O
company	_	_	O
makes	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
dish	_	_	O
detergents	_	_	O
Fruity	_	_	B-VAR
Loop	_	_	I-VAR
and	_	_	O
Passion	_	_	B-VAR
Cook	_	_	I-VAR
.	_	_	O
Fruity	_	_	B-VAR
Loop	_	_	I-VAR
consists	_	_	O
of	_	_	O
10	_	_	B-PARAM
%	_	_	I-PARAM
soap	_	_	O
and	_	_	O
6	_	_	B-PARAM
%	_	_	I-PARAM
citric	_	_	O
acid	_	_	O
and	_	_	O
Passion	_	_	B-VAR
Cook	_	_	I-VAR
consists	_	_	O
of	_	_	O
5	_	_	B-PARAM
%	_	_	I-PARAM
soap	_	_	O
and	_	_	O
10	_	_	B-PARAM
%	_	_	I-PARAM
citric	_	_	O
acid	_	_	O
.	_	_	O
After	_	_	O
doing	_	_	O
some	_	_	O
research	_	_	O
,	_	_	O
the	_	_	O
company	_	_	O
realizes	_	_	O
that	_	_	O
it	_	_	O
needs	_	_	O
to	_	_	O
use	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
soap	_	_	O
and	_	_	O
15	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
citric	_	_	O
acid	_	_	O
.	_	_	O
If	_	_	O
Fruity	_	_	B-VAR
Loop	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
6	_	_	B-PARAM
per	_	_	O
kg	_	_	O
and	_	_	O
Passion	_	_	B-VAR
Cook	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
5	_	_	B-PARAM
per	_	_	O
kg	_	_	O
,	_	_	O
determine	_	_	O
how	_	_	O
much	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
detergents	_	_	O
should	_	_	O
be	_	_	O
produced	_	_	O
so	_	_	O
that	_	_	O
nutrient	_	_	O
requirements	_	_	O
are	_	_	O
met	_	_	O
at	_	_	O
a	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
.	_	_	O

East	_	_	O
Oak	_	_	O
Designs	_	_	O
are	_	_	O
famous	_	_	O
for	_	_	O
its	_	_	O
high	_	_	O
-	_	_	O
end	_	_	O
furniture	_	_	O
.	_	_	O
Each	_	_	O
sofa	_	_	B-VAR
produced	_	_	O
by	_	_	O
East	_	_	O
Oak	_	_	O
Designs	_	_	O
nets	_	_	O
the	_	_	O
company	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
400	_	_	B-PARAM
.	_	_	O
Each	_	_	O
kitchen	_	_	B-VAR
cabinet	_	_	I-VAR
yields	_	_	O
a	_	_	O
$	_	_	O
1200	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
.	_	_	O
Every	_	_	O
week	_	_	O
,	_	_	O
100	_	_	B-LIMIT
gallons	_	_	O
of	_	_	O
lacquer	_	_	O
and	_	_	O
300	_	_	B-LIMIT
lengths	_	_	O
of	_	_	O
high	_	_	O
-	_	_	O
quality	_	_	O
oak	_	_	O
are	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
Each	_	_	O
sofa	_	_	B-VAR
requires	_	_	O
approximately	_	_	O
3	_	_	B-PARAM
gallon	_	_	O
of	_	_	O
lacquer	_	_	O
and	_	_	O
10	_	_	B-PARAM
length	_	_	O
of	_	_	O
oak	_	_	O
.	_	_	O
Each	_	_	O
kitchen	_	_	B-VAR
cabinet	_	_	I-VAR
takes	_	_	O
10	_	_	B-PARAM
gallon	_	_	O
of	_	_	O
lacquer	_	_	O
and	_	_	O
24	_	_	B-PARAM
lengths	_	_	O
of	_	_	O
wood	_	_	O
.	_	_	O
What	_	_	O
should	_	_	O
the	_	_	O
production	_	_	O
plan	_	_	O
for	_	_	O
East	_	_	O
Oak	_	_	O
Designs	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
maximum	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
wood	_	_	O
artist	_	_	O
manufactures	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
decors	_	_	O
made	_	_	O
of	_	_	O
rosewood	_	_	O
.	_	_	O
The	_	_	O
first	_	_	O
product	_	_	O
,	_	_	O
a	_	_	O
vase	_	_	B-VAR
décor	_	_	I-VAR
,	_	_	O
requires	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
each	_	_	O
for	_	_	O
carving	_	_	O
and	_	_	O
14	_	_	B-PARAM
minutes	_	_	O
each	_	_	O
for	_	_	O
polishing	_	_	O
.	_	_	O
The	_	_	O
second	_	_	O
décor	_	_	O
is	_	_	O
a	_	_	O
wood	_	_	B-VAR
canvas	_	_	I-VAR
and	_	_	O
it	_	_	O
requires	_	_	O
18	_	_	B-PARAM
minutes	_	_	O
each	_	_	O
for	_	_	O
carving	_	_	O
and	_	_	O
8	_	_	B-PARAM
minutes	_	_	O
each	_	_	O
for	_	_	O
polishing	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
400	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
carving	_	_	O
and	_	_	O
640	_	_	B-LIMIT
for	_	_	O
polishing	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
each	_	_	O
for	_	_	O
vase	_	_	B-VAR
décor	_	_	I-VAR
and	_	_	O
$	_	_	O
85	_	_	B-PARAM
for	_	_	O
each	_	_	O
wood	_	_	B-VAR
canvas	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
decors	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
the	_	_	O
artist	_	_	O
creates	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
her	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

Linda	_	_	O
owns	_	_	O
a	_	_	O
bakery	_	_	O
and	_	_	O
sells	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
cookies	_	_	O
:	_	_	O
chocolate	_	_	B-VAR
chip	_	_	I-VAR
and	_	_	O
oatmeal	_	_	B-VAR
.	_	_	O
Each	_	_	O
chocolate	_	_	B-VAR
chip	_	_	I-VAR
cookie	_	_	I-VAR
requires	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
mixing	_	_	O
and	_	_	O
1	_	_	B-PARAM
table	_	_	O
spoon	_	_	O
of	_	_	O
vanilla	_	_	O
extract	_	_	O
.	_	_	O
Each	_	_	O
oatmeal	_	_	B-VAR
cookie	_	_	I-VAR
requires	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
mixing	_	_	O
and	_	_	O
2	_	_	B-PARAM
table	_	_	O
spoons	_	_	O
of	_	_	O
vanilla	_	_	O
extract	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
360	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
mixing	_	_	O
time	_	_	O
available	_	_	B-CONST_DIR
and	_	_	O
50	_	_	B-LIMIT
table	_	_	O
spoons	_	_	O
of	_	_	O
vanilla	_	_	O
extract	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
Each	_	_	O
chocolate	_	_	B-VAR
chip	_	_	I-VAR
cookie	_	_	O
can	_	_	O
be	_	_	O
sold	_	_	B-OBJ_NAME
for	_	_	O
$	_	_	O
4	_	_	B-PARAM
and	_	_	O
each	_	_	O
oatmeal	_	_	B-VAR
cookie	_	_	I-VAR
can	_	_	O
be	_	_	O
sold	_	_	B-OBJ_NAME
for	_	_	O
$	_	_	O
3	_	_	B-PARAM
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
Linda	_	_	O
's	_	_	O
revenue	_	_	B-OBJ_NAME
,	_	_	O
then	_	_	O
graphically	_	_	O
solve	_	_	O
the	_	_	O
LP	_	_	O
.	_	_	O
(	_	_	O
A	_	_	O
fractional	_	_	O
number	_	_	O
of	_	_	O
cookies	_	_	O
is	_	_	O
okay	_	_	O
)	_	_	O

A	_	_	O
clothing	_	_	O
company	_	_	O
wants	_	_	O
to	_	_	O
add	_	_	O
t	_	_	B-VAR
-	_	_	I-VAR
shirts	_	_	I-VAR
and	_	_	O
hoodies	_	_	B-VAR
,	_	_	O
both	_	_	O
with	_	_	O
printed	_	_	O
designs	_	_	O
,	_	_	O
to	_	_	O
its	_	_	O
collection	_	_	O
.	_	_	O
Both	_	_	O
t	_	_	B-VAR
-	_	_	I-VAR
shirts	_	_	I-VAR
and	_	_	O
hoodies	_	_	B-VAR
require	_	_	O
designing	_	_	O
and	_	_	O
printing	_	_	O
.	_	_	O
T	_	_	B-VAR
-	_	_	I-VAR
shirts	_	_	I-VAR
require	_	_	O
1	_	_	B-PARAM
hour	_	_	O
of	_	_	O
designing	_	_	O
time	_	_	O
and	_	_	O
2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
printing	_	_	O
time	_	_	O
.	_	_	O
Hoodies	_	_	B-VAR
require	_	_	O
2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
designing	_	_	O
time	_	_	O
and	_	_	O
3	_	_	B-PARAM
hours	_	_	O
of	_	_	O
printing	_	_	O
time	_	_	O
.	_	_	O
The	_	_	O
designers	_	_	O
are	_	_	O
available	_	_	B-CONST_DIR
40	_	_	B-LIMIT
hours	_	_	O
a	_	_	O
week	_	_	O
and	_	_	O
the	_	_	O
printing	_	_	O
machine	_	_	O
is	_	_	O
available	_	_	B-CONST_DIR
60	_	_	B-LIMIT
hours	_	_	O
per	_	_	O
week	_	_	O
.	_	_	O
Each	_	_	O
t	_	_	B-VAR
-	_	_	I-VAR
shirt	_	_	I-VAR
nets	_	_	O
the	_	_	O
company	_	_	O
$	_	_	O
10	_	_	B-PARAM
in	_	_	O
profit	_	_	B-OBJ_NAME
,	_	_	O
and	_	_	O
each	_	_	O
hoodie	_	_	B-VAR
nets	_	_	O
$	_	_	O
15	_	_	B-PARAM
in	_	_	O
profit	_	_	B-OBJ_NAME
.	_	_	O
What	_	_	O
ratio	_	_	O
of	_	_	O
t	_	_	B-VAR
-	_	_	I-VAR
shirts	_	_	I-VAR
and	_	_	O
hoodies	_	_	B-VAR
will	_	_	O
produce	_	_	O
the	_	_	O
most	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
within	_	_	O
the	_	_	O
constraints	_	_	O
?	_	_	O

A	_	_	O
weight	_	_	O
loss	_	_	O
program	_	_	O
needs	_	_	O
to	_	_	O
include	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
200	_	_	B-LIMIT
units	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
50	_	_	B-LIMIT
units	_	_	O
of	_	_	O
carbs	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
two	_	_	O
cuisine	_	_	O
options	_	_	O
available	_	_	O
:	_	_	O
Indian	_	_	B-VAR
and	_	_	O
Thai	_	_	B-VAR
.	_	_	O
One	_	_	O
plate	_	_	O
of	_	_	O
Indian	_	_	B-VAR
food	_	_	I-VAR
contains	_	_	O
13	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
23	_	_	B-PARAM
units	_	_	O
of	_	_	O
carbs	_	_	O
.	_	_	O
One	_	_	O
plate	_	_	O
of	_	_	O
Thai	_	_	B-VAR
food	_	_	I-VAR
contains	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
carbs	_	_	O
.	_	_	O
Indian	_	_	B-VAR
food	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
12	_	_	B-PARAM
per	_	_	O
plate	_	_	O
food	_	_	O
and	_	_	O
Thai	_	_	B-VAR
food	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
15	_	_	B-PARAM
per	_	_	O
plate	_	_	O
.	_	_	O
Find	_	_	O
the	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
for	_	_	O
the	_	_	O
program	_	_	O
that	_	_	O
can	_	_	O
consist	_	_	O
of	_	_	O
a	_	_	O
mixture	_	_	O
of	_	_	O
the	_	_	O
cuisines	_	_	O
and	_	_	O
at	_	_	O
the	_	_	O
same	_	_	O
time	_	_	O
meet	_	_	O
the	_	_	O
minimal	_	_	O
protein	_	_	O
and	_	_	O
carb	_	_	O
requirements	_	_	O
.	_	_	O

Bob	_	_	O
has	_	_	O
a	_	_	O
small	_	_	O
coffee	_	_	O
shop	_	_	O
.	_	_	O
He	_	_	O
mainly	_	_	O
sells	_	_	O
cups	_	_	O
of	_	_	O
coffee	_	_	B-VAR
and	_	_	O
tea	_	_	B-VAR
.	_	_	O
It	_	_	O
takes	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
cup	_	_	O
of	_	_	O
coffee	_	_	B-VAR
and	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
cup	_	_	O
of	_	_	O
tea	_	_	B-VAR
.	_	_	O
Bob	_	_	O
only	_	_	B-CONST_DIR
has	_	_	O
500	_	_	B-LIMIT
minutes	_	_	O
a	_	_	O
week	_	_	O
to	_	_	O
make	_	_	O
drinks	_	_	O
(	_	_	O
coffee	_	_	B-VAR
and	_	_	O
tea	_	_	B-VAR
)	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
Bob	_	_	O
only	_	_	B-CONST_DIR
has	_	_	O
enough	_	_	O
product	_	_	O
to	_	_	O
make	_	_	O
300	_	_	B-LIMIT
total	_	_	O
cups	_	_	O
per	_	_	O
week	_	_	O
.	_	_	O
He	_	_	O
makes	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
1	_	_	B-PARAM
on	_	_	O
each	_	_	O
cup	_	_	O
of	_	_	O
coffee	_	_	B-VAR
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
2	_	_	B-PARAM
on	_	_	O
each	_	_	O
cup	_	_	O
of	_	_	O
tea	_	_	B-VAR
.	_	_	O
How	_	_	O
many	_	_	O
cups	_	_	O
of	_	_	O
coffee	_	_	B-VAR
and	_	_	O
tea	_	_	B-VAR
should	_	_	O
Bob	_	_	O
make	_	_	O
each	_	_	O
week	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
,	_	_	O
assuming	_	_	O
he	_	_	O
sells	_	_	O
all	_	_	O
his	_	_	O
cups	_	_	O
?	_	_	O

You	_	_	O
have	_	_	O
participated	_	_	O
in	_	_	O
a	_	_	O
math	_	_	O
contest	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
problems	_	_	O
to	_	_	O
solve	_	_	O
:	_	_	O
long	_	_	B-VAR
answer	_	_	I-VAR
questions	_	_	I-VAR
and	_	_	O
multiple	_	_	B-VAR
choice	_	_	I-VAR
questions	_	_	I-VAR
.	_	_	O
Long	_	_	B-VAR
answer	_	_	I-VAR
questions	_	_	I-VAR
are	_	_	O
worth	_	_	O
10	_	_	B-PARAM
points	_	_	B-OBJ_NAME
and	_	_	O
multiple	_	_	B-VAR
choice	_	_	I-VAR
questions	_	_	I-VAR
are	_	_	O
worth	_	_	O
2	_	_	B-PARAM
points	_	_	B-OBJ_NAME
.	_	_	O
In	_	_	O
total	_	_	O
,	_	_	O
you	_	_	O
have	_	_	O
enough	_	_	O
time	_	_	O
to	_	_	O
answer	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
15	_	_	B-LIMIT
questions	_	_	O
.	_	_	O
You	_	_	O
need	_	_	O
to	_	_	O
answer	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
long	_	_	B-VAR
answer	_	_	I-VAR
questions	_	_	I-VAR
and	_	_	O
7	_	_	B-LIMIT
multiple	_	_	B-VAR
choice	_	_	I-VAR
questions	_	_	I-VAR
,	_	_	O
but	_	_	O
time	_	_	O
restricts	_	_	O
answering	_	_	O
more	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
11	_	_	B-LIMIT
of	_	_	O
either	_	_	O
type	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
questions	_	_	O
do	_	_	O
you	_	_	O
need	_	_	O
to	_	_	O
answer	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
your	_	_	O
score	_	_	B-OBJ_NAME
?	_	_	O
What	_	_	O
is	_	_	O
your	_	_	O
maximum	_	_	O
score	_	_	O
?	_	_	O
Assume	_	_	O
all	_	_	O
of	_	_	O
your	_	_	O
answers	_	_	O
are	_	_	O
correct	_	_	O
.	_	_	O

To	_	_	O
pay	_	_	O
his	_	_	O
monthly	_	_	O
rent	_	_	O
for	_	_	O
his	_	_	O
beach	_	_	O
house	_	_	O
,	_	_	O
Roy	_	_	O
needs	_	_	O
to	_	_	O
find	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
seashells	_	_	O
and	_	_	O
30	_	_	B-LIMIT
crabs	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
two	_	_	O
beaches	_	_	O
that	_	_	O
Roy	_	_	O
frequents	_	_	O
:	_	_	O
Bonzai	_	_	B-VAR
Beach	_	_	I-VAR
and	_	_	O
Marina	_	_	B-VAR
Beach	_	_	I-VAR
.	_	_	O
Each	_	_	O
day	_	_	O
at	_	_	O
Bonzai	_	_	B-VAR
beach	_	_	I-VAR
,	_	_	O
Roy	_	_	O
finds	_	_	O
3	_	_	B-PARAM
seashells	_	_	O
and	_	_	O
5	_	_	B-PARAM
crabs	_	_	O
.	_	_	O
Each	_	_	O
day	_	_	O
at	_	_	O
Marina	_	_	B-VAR
Beach	_	_	I-VAR
,	_	_	O
Roy	_	_	O
finds	_	_	O
7	_	_	B-PARAM
seashells	_	_	O
and	_	_	O
2	_	_	B-PARAM
crabs	_	_	O
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
to	_	_	O
help	_	_	O
Roy	_	_	O
meet	_	_	O
his	_	_	O
requirements	_	_	O
while	_	_	O
spending	_	_	O
a	_	_	O
minimal	_	_	B-OBJ_DIR
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
time	_	_	I-OBJ_NAME
in	_	_	O
the	_	_	O
mines	_	_	O
.	_	_	O

A	_	_	O
small	_	_	O
wood	_	_	O
shop	_	_	O
that	_	_	O
specializes	_	_	O
in	_	_	O
kitchen	_	_	O
tools	_	_	O
and	_	_	O
can	_	_	O
make	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
30	_	_	B-LIMIT
cutting	_	_	B-VAR
boards	_	_	I-VAR
and	_	_	O
50	_	_	B-LIMIT
knife	_	_	B-VAR
handles	_	_	I-VAR
in	_	_	O
a	_	_	O
week	_	_	O
.	_	_	O
It	_	_	O
takes	_	_	O
a	_	_	O
worker	_	_	O
5	_	_	B-PARAM
hours	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
cutting	_	_	B-VAR
board	_	_	I-VAR
and	_	_	O
10	_	_	B-PARAM
hours	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
knife	_	_	B-VAR
handle	_	_	I-VAR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
on	_	_	O
a	_	_	O
cutting	_	_	B-VAR
board	_	_	I-VAR
is	_	_	O
$	_	_	O
100	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
on	_	_	O
a	_	_	O
knife	_	_	B-VAR
handle	_	_	I-VAR
is	_	_	O
$	_	_	O
250	_	_	B-PARAM
.	_	_	O
The	_	_	O
total	_	_	O
number	_	_	O
of	_	_	O
hours	_	_	O
by	_	_	O
all	_	_	O
of	_	_	O
the	_	_	O
employees	_	_	O
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
200	_	_	B-LIMIT
hours	_	_	O
per	_	_	O
week	_	_	O
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
problem	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
.	_	_	O

Jack	_	_	O
makes	_	_	O
rings	_	_	B-VAR
and	_	_	O
necklaces	_	_	B-VAR
using	_	_	O
gems	_	_	O
,	_	_	O
each	_	_	O
requiring	_	_	O
the	_	_	O
use	_	_	O
of	_	_	O
a	_	_	O
heating	_	_	O
machine	_	_	O
and	_	_	O
a	_	_	O
polishing	_	_	O
machine	_	_	O
.	_	_	O
On	_	_	O
any	_	_	O
day	_	_	O
the	_	_	O
heating	_	_	O
machine	_	_	O
is	_	_	O
available	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
the	_	_	I-CONST_DIR
most	_	_	I-CONST_DIR
15	_	_	B-LIMIT
hours	_	_	O
and	_	_	O
the	_	_	O
polishing	_	_	O
machine	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
the	_	_	I-CONST_DIR
most	_	_	I-CONST_DIR
12	_	_	B-LIMIT
hours	_	_	O
.	_	_	O
It	_	_	O
takes	_	_	O
1	_	_	B-PARAM
hour	_	_	O
on	_	_	O
the	_	_	O
heating	_	_	O
machine	_	_	O
and	_	_	O
2	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
polishing	_	_	O
machine	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
ring	_	_	B-VAR
.	_	_	O
It	_	_	O
takes	_	_	O
3	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
heating	_	_	O
machine	_	_	O
and	_	_	O
4	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
polishing	_	_	O
machine	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
necklace	_	_	B-VAR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
from	_	_	O
the	_	_	O
sale	_	_	O
of	_	_	O
a	_	_	O
ring	_	_	B-VAR
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
from	_	_	O
the	_	_	O
sale	_	_	O
of	_	_	O
a	_	_	O
necklace	_	_	B-VAR
is	_	_	O
$	_	_	O
75	_	_	B-PARAM
.	_	_	O
Assuming	_	_	O
Jack	_	_	O
can	_	_	O
sell	_	_	O
all	_	_	O
the	_	_	O
rings	_	_	B-VAR
and	_	_	O
necklaces	_	_	B-VAR
he	_	_	O
makes	_	_	O
,	_	_	O
how	_	_	O
should	_	_	O
he	_	_	O
schedule	_	_	O
his	_	_	O
daily	_	_	O
production	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
vehicle	_	_	O
company	_	_	O
manufactures	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
vehicles	_	_	O
:	_	_	O
cars	_	_	B-VAR
and	_	_	O
bikes	_	_	B-VAR
.	_	_	O
A	_	_	O
car	_	_	B-VAR
requires	_	_	O
3	_	_	B-PARAM
hours	_	_	O
of	_	_	O
engineering	_	_	O
time	_	_	O
while	_	_	O
a	_	_	O
bike	_	_	B-VAR
requires	_	_	O
1	_	_	B-PARAM
hour	_	_	O
of	_	_	O
engineering	_	_	O
time	_	_	O
.	_	_	O
Both	_	_	O
vehicles	_	_	O
require	_	_	O
30	_	_	B-PARAM
kg	_	_	O
of	_	_	O
steel	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
receives	_	_	B-CONST_DIR
1000	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
steel	_	_	O
each	_	_	O
week	_	_	O
and	_	_	O
a	_	_	O
total	_	_	O
of	_	_	O
400	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
engineering	_	_	O
time	_	_	O
is	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
Each	_	_	O
car	_	_	B-VAR
nets	_	_	O
$	_	_	O
5000	_	_	B-PARAM
in	_	_	O
profit	_	_	B-OBJ_NAME
,	_	_	O
while	_	_	O
each	_	_	O
bike	_	_	B-VAR
nets	_	_	O
$	_	_	O
1000	_	_	B-PARAM
in	_	_	O
profit	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
company	_	_	O
wishes	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
.	_	_	O
Ignoring	_	_	O
the	_	_	O
divisibility	_	_	O
issues	_	_	O
,	_	_	O
construct	_	_	O
a	_	_	O
linear	_	_	O
programming	_	_	O
problem	_	_	O
whose	_	_	O
solution	_	_	O
will	_	_	O
determine	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
vehicle	_	_	O
the	_	_	O
company	_	_	O
should	_	_	O
produce	_	_	O
.	_	_	O

An	_	_	O
oil	_	_	O
company	_	_	O
produces	_	_	O
economical	_	_	B-VAR
,	_	_	O
regular	_	_	B-VAR
and	_	_	O
premium	_	_	B-VAR
grades	_	_	O
of	_	_	O
oil	_	_	O
.	_	_	O
Each	_	_	O
tanker	_	_	O
of	_	_	O
economical	_	_	B-VAR
grade	_	_	I-VAR
oil	_	_	I-VAR
produces	_	_	O
a	_	_	O
net	_	_	B-OBJ_NAME
revenue	_	_	I-OBJ_NAME
of	_	_	O
$	_	_	O
500	_	_	B-PARAM
,	_	_	O
each	_	_	O
tanker	_	_	O
of	_	_	O
regular	_	_	B-VAR
grade	_	_	I-VAR
oil	_	_	I-VAR
produces	_	_	O
a	_	_	O
net	_	_	B-OBJ_NAME
revenue	_	_	I-OBJ_NAME
of	_	_	O
$	_	_	O
1020	_	_	B-PARAM
,	_	_	O
and	_	_	O
each	_	_	O
tanker	_	_	O
of	_	_	O
premium	_	_	B-VAR
grade	_	_	I-VAR
oil	_	_	I-VAR
produces	_	_	O
a	_	_	O
net	_	_	B-OBJ_NAME
revenue	_	_	I-OBJ_NAME
of	_	_	O
$	_	_	O
920	_	_	B-PARAM
.	_	_	O
To	_	_	O
produce	_	_	O
a	_	_	O
tanker	_	_	O
of	_	_	O
economical	_	_	B-VAR
grade	_	_	I-VAR
oil	_	_	I-VAR
,	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
compound	_	_	O
A	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
compound	_	_	O
B	_	_	O
are	_	_	O
required	_	_	O
.	_	_	O
To	_	_	O
produce	_	_	O
a	_	_	O
tanker	_	_	O
of	_	_	O
regular	_	_	B-VAR
grade	_	_	I-VAR
oil	_	_	I-VAR
,	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
compound	_	_	O
A	_	_	O
and	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
compound	_	_	O
B	_	_	O
are	_	_	O
required	_	_	O
.	_	_	O
To	_	_	O
produce	_	_	O
a	_	_	O
tanker	_	_	O
of	_	_	O
premium	_	_	B-VAR
grade	_	_	I-VAR
oil	_	_	I-VAR
,	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
compound	_	_	O
A	_	_	O
and	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
compound	_	_	O
B	_	_	O
are	_	_	O
required	_	_	O
.	_	_	O
Currently	_	_	O
the	_	_	O
company	_	_	O
has	_	_	B-CONST_DIR
200	_	_	B-LIMIT
units	_	_	O
of	_	_	O
compound	_	_	O
A	_	_	O
and	_	_	O
100	_	_	B-LIMIT
units	_	_	O
of	_	_	O
compound	_	_	O
B	_	_	O
to	_	_	O
process	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
full	_	_	O
or	_	_	O
partial	_	_	O
tankers	_	_	O
of	_	_	O
each	_	_	O
oil	_	_	O
grade	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
produce	_	_	O
so	_	_	O
that	_	_	O
net	_	_	B-OBJ_NAME
revenue	_	_	I-OBJ_NAME
is	_	_	O
maximized	_	_	B-OBJ_DIR
?	_	_	O

Bob	_	_	O
's	_	_	O
trainer	_	_	O
has	_	_	O
given	_	_	O
him	_	_	O
a	_	_	O
list	_	_	O
of	_	_	O
available	_	_	O
food	_	_	O
options	_	_	O
as	_	_	O
well	_	_	O
as	_	_	O
the	_	_	O
macro	_	_	O
nutrient	_	_	O
content	_	_	O
and	_	_	O
cost	_	_	O
per	_	_	O
serving	_	_	O
of	_	_	O
each	_	_	O
food	_	_	O
.	_	_	O
A	_	_	O
certain	_	_	O
amount	_	_	O
of	_	_	O
macro	_	_	O
nutrients	_	_	O
is	_	_	O
required	_	_	O
each	_	_	O
day	_	_	O
.	_	_	O
For	_	_	O
example	_	_	O
,	_	_	O
here	_	_	O
is	_	_	O
the	_	_	O
data	_	_	O
corresponding	_	_	O
to	_	_	O
chicken	_	_	B-VAR
and	_	_	O
pork	_	_	B-VAR
and	_	_	O
the	_	_	O
three	_	_	O
macro	_	_	O
nutrients	_	_	O
(	_	_	O
proteins	_	_	O
,	_	_	O
carbs	_	_	O
,	_	_	O
and	_	_	O
fat	_	_	O
)	_	_	O
.	_	_	O
Each	_	_	O
serving	_	_	O
of	_	_	O
chicken	_	_	B-VAR
contains	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
carbs	_	_	O
,	_	_	O
and	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
Each	_	_	O
serving	_	_	O
of	_	_	O
pork	_	_	B-VAR
contains	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
carbs	_	_	O
,	_	_	O
and	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
A	_	_	O
serving	_	_	O
of	_	_	O
chicken	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
10	_	_	B-PARAM
and	_	_	O
a	_	_	O
serving	_	_	O
of	_	_	O
pork	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
15	_	_	B-PARAM
.	_	_	O
Bob	_	_	O
's	_	_	O
trainer	_	_	O
requires	_	_	O
him	_	_	O
to	_	_	O
get	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
units	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
50	_	_	B-LIMIT
units	_	_	O
of	_	_	O
carbs	_	_	O
,	_	_	O
and	_	_	O
30	_	_	B-LIMIT
units	_	_	O
of	_	_	O
fat	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
Find	_	_	O
out	_	_	O
how	_	_	O
many	_	_	O
servings	_	_	O
of	_	_	O
each	_	_	O
meat	_	_	O
to	_	_	O
consume	_	_	O
per	_	_	O
day	_	_	O
to	_	_	O
meet	_	_	O
the	_	_	O
requirements	_	_	O
at	_	_	O
minimal	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
smoothie	_	_	O
store	_	_	O
makes	_	_	O
peanut	_	_	B-VAR
butter	_	_	I-VAR
and	_	_	O
almond	_	_	B-VAR
butter	_	_	I-VAR
smoothies	_	_	I-VAR
.	_	_	O
Both	_	_	O
require	_	_	O
almond	_	_	O
milk	_	_	O
and	_	_	O
protein	_	_	O
powder	_	_	O
.	_	_	O
Each	_	_	O
peanut	_	_	B-VAR
butter	_	_	I-VAR
smoothie	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
almond	_	_	O
milk	_	_	O
and	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
protein	_	_	O
powder	_	_	O
.	_	_	O
Each	_	_	O
almond	_	_	B-VAR
butter	_	_	I-VAR
smoothie	_	_	I-VAR
requires	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
almond	_	_	O
milk	_	_	O
and	_	_	O
1.5	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
powder	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
a	_	_	O
total	_	_	O
of	_	_	O
50	_	_	B-LIMIT
units	_	_	O
of	_	_	O
almond	_	_	O
milk	_	_	O
and	_	_	O
40	_	_	B-LIMIT
units	_	_	O
of	_	_	O
protein	_	_	O
powder	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
peanut	_	_	B-VAR
butter	_	_	I-VAR
smoothie	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
almond	_	_	B-VAR
butter	_	_	I-VAR
smoothie	_	_	I-VAR
is	_	_	O
$	_	_	O
4	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Linda	_	_	O
has	_	_	B-CONST_DIR
300	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
to	_	_	O
grow	_	_	O
spinach	_	_	B-VAR
and	_	_	O
kale	_	_	B-VAR
.	_	_	O
Per	_	_	O
acre	_	_	O
of	_	_	O
land	_	_	O
,	_	_	O
spinach	_	_	B-VAR
costs	_	_	O
$	_	_	O
40	_	_	B-PARAM
for	_	_	O
the	_	_	O
seeds	_	_	O
and	_	_	O
takes	_	_	O
1	_	_	B-PARAM
hour	_	_	O
to	_	_	O
maintain	_	_	O
.	_	_	O
Per	_	_	O
acre	_	_	O
of	_	_	O
land	_	_	O
,	_	_	O
kale	_	_	B-VAR
costs	_	_	O
$	_	_	O
50	_	_	B-PARAM
for	_	_	O
the	_	_	O
seeds	_	_	O
and	_	_	O
takes	_	_	O
2	_	_	B-PARAM
hours	_	_	O
to	_	_	O
maintain	_	_	O
.	_	_	O
Linda	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
14000	_	_	B-LIMIT
for	_	_	O
seeds	_	_	O
and	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
450	_	_	B-LIMIT
hours	_	_	O
for	_	_	O
maintenance	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
spinach	_	_	B-VAR
is	_	_	O
$	_	_	O
20	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
kale	_	_	B-VAR
is	_	_	O
$	_	_	O
30	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
grown	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
video	_	_	O
game	_	_	O
company	_	_	O
makes	_	_	O
a	_	_	O
premium	_	_	B-VAR
and	_	_	O
regular	_	_	B-VAR
version	_	_	O
of	_	_	O
their	_	_	O
console	_	_	O
.	_	_	O
A	_	_	O
premium	_	_	B-VAR
console	_	_	I-VAR
takes	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
testing	_	_	O
and	_	_	O
requires	_	_	O
3	_	_	B-PARAM
IC	_	_	O
chips	_	_	O
to	_	_	O
make	_	_	O
.	_	_	O
A	_	_	O
regular	_	_	B-VAR
console	_	_	I-VAR
takes	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
testing	_	_	O
and	_	_	O
requires	_	_	O
2	_	_	B-PARAM
IC	_	_	O
chips	_	_	O
to	_	_	O
make	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
10000	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
testing	_	_	O
time	_	_	O
and	_	_	O
1500	_	_	B-LIMIT
IC	_	_	O
chips	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
premium	_	_	B-VAR
console	_	_	I-VAR
is	_	_	O
$	_	_	O
100	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
regular	_	_	B-VAR
console	_	_	I-VAR
is	_	_	O
$	_	_	O
75	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
energy	_	_	O
drink	_	_	O
company	_	_	O
wants	_	_	O
to	_	_	O
advertise	_	_	O
their	_	_	O
product	_	_	O
using	_	_	O
commercials	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
three	_	_	O
types	_	_	O
of	_	_	O
commercials	_	_	O
.	_	_	O
Commercials	_	_	B-VAR
with	_	_	I-VAR
famous	_	_	I-VAR
actors	_	_	I-VAR
,	_	_	O
commercials	_	_	B-VAR
with	_	_	I-VAR
regular	_	_	I-VAR
people	_	_	I-VAR
,	_	_	O
and	_	_	O
commercials	_	_	B-VAR
with	_	_	I-VAR
no	_	_	I-VAR
people	_	_	I-VAR
.	_	_	O
The	_	_	O
cost	_	_	O
and	_	_	O
expected	_	_	O
viewership	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
commercial	_	_	O
is	_	_	O
given	_	_	O
.	_	_	O
A	_	_	O
commercial	_	_	B-VAR
with	_	_	I-VAR
a	_	_	I-VAR
famous	_	_	I-VAR
actor	_	_	I-VAR
costs	_	_	O
$	_	_	O
10000	_	_	B-PARAM
and	_	_	O
reaches	_	_	O
50000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
A	_	_	O
commercial	_	_	B-VAR
with	_	_	I-VAR
regular	_	_	I-VAR
people	_	_	I-VAR
costs	_	_	O
$	_	_	O
3000	_	_	B-PARAM
and	_	_	O
reaches	_	_	O
20000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
Finally	_	_	O
,	_	_	O
a	_	_	O
commercial	_	_	B-VAR
with	_	_	I-VAR
no	_	_	I-VAR
people	_	_	I-VAR
costs	_	_	O
$	_	_	O
2000	_	_	B-PARAM
and	_	_	O
reaches	_	_	O
18000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
company	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
3	_	_	B-LIMIT
commercials	_	_	B-VAR
with	_	_	I-VAR
regular	_	_	I-VAR
actors	_	_	I-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
a	_	_	O
third	_	_	B-LIMIT
of	_	_	O
all	_	_	O
commercials	_	_	O
must	_	_	O
be	_	_	O
commercials	_	_	B-VAR
with	_	_	I-VAR
no	_	_	I-VAR
people	_	_	I-VAR
.	_	_	O
Finally	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
commercials	_	_	O
should	_	_	O
be	_	_	O
commercials	_	_	B-VAR
with	_	_	I-VAR
famous	_	_	I-VAR
actors	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
weekly	_	_	O
budget	_	_	B-CONST_DIR
is	_	_	O
$	_	_	O
50000	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
commercial	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
viewership	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
bakery	_	_	O
makes	_	_	O
stuffed	_	_	B-VAR
donuts	_	_	I-VAR
and	_	_	O
pastries	_	_	B-VAR
.	_	_	O
Each	_	_	O
stuffed	_	_	B-VAR
donut	_	_	I-VAR
takes	_	_	O
2	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
baking	_	_	O
machine	_	_	O
and	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
stuffing	_	_	O
machine	_	_	O
.	_	_	O
Each	_	_	O
stuffed	_	_	B-VAR
pastry	_	_	I-VAR
takes	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
baking	_	_	O
machine	_	_	O
and	_	_	O
2	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
stuffing	_	_	O
machine	_	_	O
.	_	_	O
The	_	_	O
baking	_	_	O
machine	_	_	O
is	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
10000	_	_	B-LIMIT
minutes	_	_	O
while	_	_	O
the	_	_	O
stuffing	_	_	O
machine	_	_	O
is	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
7000	_	_	B-LIMIT
minutes	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
donut	_	_	B-VAR
is	_	_	O
$	_	_	O
2	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
pastry	_	_	B-VAR
is	_	_	O
$	_	_	O
4	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
cleaning	_	_	O
company	_	_	O
cleans	_	_	O
houses	_	_	B-VAR
and	_	_	O
apartments	_	_	B-VAR
.	_	_	O
Each	_	_	O
house	_	_	B-VAR
requires	_	_	O
2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
sweeping	_	_	O
and	_	_	O
2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
mopping	_	_	O
.	_	_	O
Each	_	_	O
apartment	_	_	B-VAR
requires	_	_	O
1	_	_	B-PARAM
hour	_	_	O
of	_	_	O
sweeping	_	_	O
and	_	_	O
1.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
mopping	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
600	_	_	B-LIMIT
hours	_	_	O
for	_	_	O
sweeping	_	_	O
and	_	_	O
700	_	_	B-LIMIT
hours	_	_	O
for	_	_	O
mopping	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
house	_	_	B-VAR
cleaned	_	_	O
is	_	_	O
$	_	_	O
300	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
apartment	_	_	B-VAR
cleaned	_	_	O
is	_	_	O
$	_	_	O
250	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
clean	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
breakfast	_	_	O
diner	_	_	O
makes	_	_	O
pancakes	_	_	B-VAR
and	_	_	O
waffles	_	_	B-VAR
.	_	_	O
Each	_	_	O
pancakes	_	_	B-VAR
require	_	_	O
30	_	_	B-PARAM
grams	_	_	O
of	_	_	O
flour	_	_	O
and	_	_	O
10	_	_	B-PARAM
grams	_	_	O
of	_	_	O
butter	_	_	O
.	_	_	O
Each	_	_	O
waffle	_	_	B-VAR
requires	_	_	O
50	_	_	B-PARAM
grams	_	_	O
of	_	_	O
flour	_	_	O
and	_	_	O
15	_	_	B-PARAM
grams	_	_	O
of	_	_	O
butter	_	_	O
.	_	_	O
The	_	_	O
diner	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
5000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
flour	_	_	O
and	_	_	O
2000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
butter	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
pancake	_	_	B-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
waffle	_	_	B-VAR
is	_	_	O
$	_	_	O
7	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
tech	_	_	O
company	_	_	O
makes	_	_	O
laptops	_	_	B-VAR
and	_	_	O
tablets	_	_	B-VAR
.	_	_	O
Each	_	_	O
laptop	_	_	B-VAR
takes	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
manufacturing	_	_	O
time	_	_	O
and	_	_	O
requires	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
silicon	_	_	O
.	_	_	O
Each	_	_	O
tablet	_	_	B-VAR
takes	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
manufacturing	_	_	O
time	_	_	O
and	_	_	O
requires	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
silicon	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
must	_	_	O
makes	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
laptops	_	_	B-VAR
.	_	_	O
They	_	_	O
have	_	_	O
1200	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
manufacturing	_	_	O
time	_	_	O
available	_	_	B-CONST_DIR
and	_	_	O
150	_	_	B-LIMIT
units	_	_	O
of	_	_	O
silicon	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
laptop	_	_	B-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
tablet	_	_	B-VAR
is	_	_	O
$	_	_	O
160	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

John	_	_	O
needs	_	_	O
to	_	_	O
take	_	_	O
supplementation	_	_	O
for	_	_	O
his	_	_	O
calcium	_	_	O
and	_	_	O
iron	_	_	O
deficiency	_	_	O
.	_	_	O
He	_	_	O
needs	_	_	O
to	_	_	O
get	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
15	_	_	B-LIMIT
units	_	_	O
of	_	_	O
calcium	_	_	O
and	_	_	O
20	_	_	B-LIMIT
units	_	_	O
of	_	_	O
iron	_	_	O
everyday	_	_	O
.	_	_	O
In	_	_	O
order	_	_	O
to	_	_	O
do	_	_	O
so	_	_	O
,	_	_	O
he	_	_	O
can	_	_	O
buy	_	_	O
pills	_	_	O
named	_	_	O
SD	_	_	B-VAR
and	_	_	O
LD	_	_	B-VAR
.	_	_	O
Each	_	_	O
SD	_	_	B-VAR
pill	_	_	I-VAR
contains	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
calcium	_	_	O
and	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
iron	_	_	O
.	_	_	O
Each	_	_	O
LD	_	_	B-VAR
pill	_	_	I-VAR
contains	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
calcium	_	_	O
and	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
iron	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
SD	_	_	B-VAR
pill	_	_	I-VAR
is	_	_	O
$	_	_	O
1	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
LD	_	_	B-VAR
pill	_	_	I-VAR
is	_	_	O
$	_	_	O
1.50	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
buy	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
cost	_	_	B-OBJ_NAME
?	_	_	O

Two	_	_	O
different	_	_	O
meals	_	_	O
,	_	_	O
a	_	_	O
vegetarian	_	_	B-VAR
and	_	_	O
meat	_	_	B-VAR
option	_	_	I-VAR
,	_	_	O
are	_	_	O
eaten	_	_	O
everyday	_	_	O
to	_	_	O
get	_	_	O
protein	_	_	O
and	_	_	O
carbs	_	_	O
.	_	_	O
A	_	_	O
vegetarian	_	_	B-VAR
meal	_	_	I-VAR
contains	_	_	O
10	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
20	_	_	B-PARAM
grams	_	_	O
of	_	_	O
carbs	_	_	O
.	_	_	O
A	_	_	O
meat	_	_	B-VAR
meal	_	_	I-VAR
contains	_	_	O
30	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
15	_	_	B-PARAM
grams	_	_	O
of	_	_	O
carbs	_	_	O
.	_	_	O
Daily	_	_	O
requirements	_	_	O
are	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
150	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
carbs	_	_	O
.	_	_	O
If	_	_	O
a	_	_	O
vegetarian	_	_	B-VAR
meal	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
4	_	_	B-PARAM
and	_	_	O
a	_	_	O
meat	_	_	B-VAR
meal	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
6	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
eaten	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
factory	_	_	O
makes	_	_	O
maple	_	_	B-VAR
pecan	_	_	I-VAR
and	_	_	O
mint	_	_	B-VAR
chocolate	_	_	I-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
.	_	_	O
Each	_	_	O
type	_	_	O
of	_	_	O
ice	_	_	O
cream	_	_	O
requires	_	_	O
time	_	_	O
on	_	_	O
a	_	_	O
mixing	_	_	O
machine	_	_	O
and	_	_	O
a	_	_	O
freezing	_	_	O
machine	_	_	O
.	_	_	O
A	_	_	O
batch	_	_	O
of	_	_	O
maple	_	_	B-VAR
pecan	_	_	I-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
requires	_	_	O
50	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
mixing	_	_	O
and	_	_	O
80	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
freezing	_	_	O
.	_	_	O
A	_	_	O
batch	_	_	O
of	_	_	O
mint	_	_	B-VAR
chocolate	_	_	I-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
requires	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
mixing	_	_	O
and	_	_	O
70	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
freezing	_	_	O
.	_	_	O
While	_	_	O
the	_	_	O
mixing	_	_	O
machine	_	_	O
is	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
8000	_	_	B-LIMIT
minutes	_	_	O
per	_	_	O
month	_	_	O
,	_	_	O
the	_	_	O
freezing	_	_	O
machine	_	_	O
is	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
10000	_	_	B-LIMIT
minutes	_	_	O
per	_	_	O
month	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
batch	_	_	O
of	_	_	O
maple	_	_	B-VAR
pecan	_	_	I-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
is	_	_	O
$	_	_	O
400	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
batch	_	_	O
of	_	_	O
mint	_	_	B-VAR
chocolate	_	_	I-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
is	_	_	O
$	_	_	O
250	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
batches	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
maple	_	_	O
farm	_	_	O
makes	_	_	O
maple	_	_	B-VAR
syrup	_	_	I-VAR
and	_	_	O
maple	_	_	B-VAR
candy	_	_	I-VAR
.	_	_	O
They	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
10	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
maple	_	_	B-VAR
syrup	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
12	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
maple	_	_	B-VAR
candy	_	_	I-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
they	_	_	O
must	_	_	O
supply	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
maple	_	_	B-VAR
syrup	_	_	I-VAR
and	_	_	O
5	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
maple	_	_	B-VAR
candy	_	_	I-VAR
per	_	_	O
day	_	_	O
.	_	_	O
Both	_	_	O
require	_	_	O
time	_	_	O
in	_	_	O
a	_	_	O
maple	_	_	O
boiling	_	_	O
station	_	_	O
.	_	_	O
Each	_	_	O
kg	_	_	O
of	_	_	O
maple	_	_	B-VAR
syrup	_	_	I-VAR
and	_	_	O
maple	_	_	B-VAR
candy	_	_	I-VAR
requires	_	_	O
2	_	_	B-PARAM
hours	_	_	O
at	_	_	O
the	_	_	O
boiling	_	_	O
station	_	_	O
.	_	_	O
The	_	_	O
boiling	_	_	O
station	_	_	O
is	_	_	O
available	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
20	_	_	B-LIMIT
hours	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
kg	_	_	O
of	_	_	O
maple	_	_	B-VAR
syrup	_	_	I-VAR
is	_	_	O
$	_	_	O
20	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
kg	_	_	O
of	_	_	O
maple	_	_	B-VAR
candy	_	_	I-VAR
is	_	_	O
$	_	_	O
15	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
kg	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
farmer	_	_	O
has	_	_	B-CONST_DIR
90	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
to	_	_	O
grow	_	_	O
mushrooms	_	_	B-VAR
and	_	_	O
truffles	_	_	B-VAR
.	_	_	O
Each	_	_	O
acre	_	_	O
of	_	_	O
mushrooms	_	_	B-VAR
requires	_	_	O
$	_	_	O
80	_	_	B-PARAM
in	_	_	O
maintenance	_	_	O
and	_	_	O
2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
care	_	_	O
.	_	_	O
Each	_	_	O
acre	_	_	O
of	_	_	O
truffles	_	_	B-VAR
requires	_	_	O
$	_	_	O
200	_	_	B-PARAM
in	_	_	O
maintenance	_	_	O
and	_	_	O
3	_	_	B-PARAM
hours	_	_	O
of	_	_	O
care	_	_	O
.	_	_	O
The	_	_	O
farmer	_	_	O
has	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
13500	_	_	B-LIMIT
to	_	_	O
spend	_	_	O
on	_	_	O
maintenance	_	_	O
and	_	_	O
120	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
time	_	_	O
available	_	_	O
for	_	_	O
care	_	_	O
keeping	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
mushrooms	_	_	B-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
truffles	_	_	B-VAR
is	_	_	O
$	_	_	O
500	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
grown	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
doctor	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
100000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
two	_	_	O
vaccine	_	_	O
companies	_	_	O
,	_	_	O
company	_	_	B-VAR
M	_	_	I-VAR
and	_	_	O
company	_	_	B-VAR
P.	_	_	I-VAR
He	_	_	O
has	_	_	O
decided	_	_	O
to	_	_	O
invest	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	O
as	_	_	O
much	_	_	O
money	_	_	O
in	_	_	O
company	_	_	B-VAR
M	_	_	I-VAR
than	_	_	O
in	_	_	O
company	_	_	B-VAR
P.	_	_	I-VAR
In	_	_	O
addition	_	_	O
he	_	_	O
can	_	_	O
invest	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
80000	_	_	B-LIMIT
in	_	_	O
company	_	_	B-VAR
M.	_	_	I-VAR
If	_	_	O
investments	_	_	O
in	_	_	O
company	_	_	B-VAR
M	_	_	I-VAR
earn	_	_	B-OBJ_NAME
9	_	_	B-PARAM
%	_	_	I-PARAM
and	_	_	O
investments	_	_	O
in	_	_	O
company	_	_	B-VAR
P	_	_	I-VAR
earn	_	_	B-OBJ_NAME
12	_	_	B-PARAM
%	_	_	I-PARAM
,	_	_	O
how	_	_	O
much	_	_	O
should	_	_	O
he	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
earnings	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
wood	_	_	O
shop	_	_	O
makes	_	_	O
canoes	_	_	B-VAR
and	_	_	O
paddles	_	_	B-VAR
.	_	_	O
Each	_	_	O
requires	_	_	O
time	_	_	O
for	_	_	O
cutting	_	_	O
,	_	_	O
woodworking	_	_	O
,	_	_	O
and	_	_	O
sanding	_	_	O
.	_	_	O
Each	_	_	O
canoe	_	_	B-VAR
takes	_	_	O
1	_	_	B-PARAM
hour	_	_	O
of	_	_	O
cutting	_	_	O
,	_	_	O
5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
woodworking	_	_	O
,	_	_	O
and	_	_	O
2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
sanding	_	_	O
.	_	_	O
Each	_	_	O
paddle	_	_	B-VAR
takes	_	_	O
0.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
cutting	_	_	O
,	_	_	O
1	_	_	B-PARAM
hour	_	_	O
of	_	_	O
woodworking	_	_	O
,	_	_	O
and	_	_	O
0.75	_	_	B-PARAM
hours	_	_	O
of	_	_	O
sanding	_	_	O
.	_	_	O
The	_	_	O
wood	_	_	O
shop	_	_	O
has	_	_	O
80	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
cutting	_	_	O
,	_	_	O
100	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
woodworking	_	_	O
,	_	_	O
and	_	_	O
70	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
sanding	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
canoe	_	_	B-VAR
is	_	_	O
$	_	_	O
500	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
paddle	_	_	B-VAR
is	_	_	O
$	_	_	O
75	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
juice	_	_	O
store	_	_	O
sells	_	_	O
two	_	_	O
juices	_	_	O
,	_	_	O
Juice	_	_	B-VAR
A	_	_	I-VAR
and	_	_	O
Juice	_	_	B-VAR
B.	_	_	I-VAR
Each	_	_	O
juice	_	_	O
uses	_	_	O
different	_	_	O
amounts	_	_	O
of	_	_	O
raspberries	_	_	O
,	_	_	O
blueberries	_	_	O
,	_	_	O
and	_	_	O
blackberries	_	_	O
.	_	_	O
Juice	_	_	B-VAR
A	_	_	I-VAR
uses	_	_	O
20	_	_	B-PARAM
g	_	_	O
of	_	_	O
raspberries	_	_	O
,	_	_	O
10	_	_	B-PARAM
g	_	_	O
of	_	_	O
blueberries	_	_	O
,	_	_	O
and	_	_	O
10	_	_	B-PARAM
g	_	_	O
of	_	_	O
blackberries	_	_	O
.	_	_	O
Juice	_	_	B-VAR
B	_	_	I-VAR
uses	_	_	O
15	_	_	B-PARAM
g	_	_	O
of	_	_	O
raspberries	_	_	O
,	_	_	O
15	_	_	B-PARAM
g	_	_	O
of	_	_	O
blueberries	_	_	O
,	_	_	O
and	_	_	O
5	_	_	B-PARAM
g	_	_	O
of	_	_	O
blackberries	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
2000	_	_	B-LIMIT
g	_	_	O
of	_	_	O
raspberries	_	_	O
,	_	_	O
1500	_	_	B-LIMIT
g	_	_	O
of	_	_	O
blueberries	_	_	O
,	_	_	O
and	_	_	O
1400	_	_	B-LIMIT
g	_	_	O
of	_	_	O
blackberries	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
Juice	_	_	B-VAR
A	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
Juice	_	_	B-VAR
B	_	_	I-VAR
is	_	_	O
$	_	_	O
7	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
juice	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
pizza	_	_	O
palace	_	_	O
is	_	_	O
going	_	_	O
to	_	_	O
purchase	_	_	O
pizza	_	_	O
ovens	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
two	_	_	O
models	_	_	O
available	_	_	O
.	_	_	O
Model	_	_	B-VAR
A	_	_	I-VAR
can	_	_	O
make	_	_	O
10	_	_	B-PARAM
pizzas	_	_	O
per	_	_	O
cycle	_	_	O
,	_	_	O
requires	_	_	O
80	_	_	B-PARAM
grams	_	_	O
of	_	_	O
fuel	_	_	O
per	_	_	O
cycle	_	_	O
,	_	_	O
and	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
10000	_	_	B-PARAM
.	_	_	O
Model	_	_	B-VAR
B	_	_	I-VAR
can	_	_	O
make	_	_	O
8	_	_	B-PARAM
pizzas	_	_	O
per	_	_	O
cycle	_	_	O
,	_	_	O
requires	_	_	O
70	_	_	B-PARAM
grams	_	_	O
of	_	_	O
fuel	_	_	O
per	_	_	O
cycle	_	_	O
,	_	_	O
and	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
8000	_	_	B-PARAM
.	_	_	O
The	_	_	O
pizza	_	_	O
palace	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
pizzas	_	_	O
per	_	_	O
cycle	_	_	O
and	_	_	O
use	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
1000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
fuel	_	_	O
per	_	_	O
cycle	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
model	_	_	O
pizza	_	_	O
oven	_	_	O
should	_	_	O
they	_	_	O
purchase	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

Joel	_	_	O
is	_	_	O
on	_	_	O
a	_	_	O
strict	_	_	O
diet	_	_	O
and	_	_	O
insists	_	_	O
on	_	_	O
only	_	_	O
drinking	_	_	O
chocolate	_	_	B-VAR
protein	_	_	I-VAR
shakes	_	_	I-VAR
and	_	_	O
vanilla	_	_	O
meal	_	_	B-VAR
replacement	_	_	I-VAR
smoothies	_	_	I-VAR
.	_	_	O
He	_	_	O
want	_	_	O
to	_	_	O
save	_	_	O
money	_	_	O
and	_	_	O
minimize	_	_	O
cost	_	_	B-OBJ_NAME
but	_	_	O
must	_	_	O
get	_	_	O
enough	_	_	O
protein	_	_	O
and	_	_	O
carbs	_	_	O
,	_	_	O
and	_	_	O
not	_	_	O
too	_	_	O
much	_	_	O
fat	_	_	O
.	_	_	O
Chocolate	_	_	B-VAR
protein	_	_	I-VAR
shakes	_	_	I-VAR
cost	_	_	B-OBJ_NAME
$	_	_	O
8	_	_	B-PARAM
per	_	_	O
serving	_	_	O
and	_	_	O
contain	_	_	O
35	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
carbs	_	_	O
,	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
Meal	_	_	B-VAR
replacement	_	_	I-VAR
smoothies	_	_	I-VAR
cost	_	_	B-OBJ_NAME
$	_	_	O
10	_	_	B-PARAM
per	_	_	O
serving	_	_	O
and	_	_	O
contain	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
25	_	_	B-PARAM
units	_	_	O
of	_	_	O
carbs	_	_	O
,	_	_	O
and	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
John	_	_	O
requires	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
150	_	_	B-LIMIT
units	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
130	_	_	B-LIMIT
units	_	_	O
of	_	_	O
carbs	_	_	O
but	_	_	O
must	_	_	O
not	_	_	B-CONST_DIR
eat	_	_	I-CONST_DIR
more	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
50	_	_	B-LIMIT
units	_	_	O
of	_	_	O
fat	_	_	O
each	_	_	O
day	_	_	O
.	_	_	O
Formulate	_	_	O
the	_	_	O
problem	_	_	O
as	_	_	O
an	_	_	O
LP	_	_	O
problem	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
.	_	_	O

One	_	_	O
batch	_	_	O
of	_	_	O
chocolate	_	_	B-VAR
chip	_	_	I-VAR
cookies	_	_	I-VAR
is	_	_	O
made	_	_	O
of	_	_	O
314	_	_	B-PARAM
g	_	_	O
of	_	_	O
flour	_	_	O
and	_	_	O
15	_	_	B-PARAM
g	_	_	O
of	_	_	O
butter	_	_	O
while	_	_	O
a	_	_	O
batch	_	_	O
of	_	_	O
oatmeal	_	_	B-VAR
cookies	_	_	I-VAR
requires	_	_	O
271	_	_	B-PARAM
g	_	_	O
of	_	_	O
flour	_	_	O
and	_	_	O
82	_	_	B-PARAM
g	_	_	O
of	_	_	O
butter	_	_	O
.	_	_	O
Find	_	_	O
the	_	_	O
maximum	_	_	B-OBJ_DIR
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
batches	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
cookies	_	_	I-OBJ_NAME
we	_	_	O
can	_	_	O
bake	_	_	O
using	_	_	B-CONST_DIR
3000	_	_	B-PARAM
g	_	_	O
of	_	_	O
flour	_	_	O
and	_	_	O
2000	_	_	B-PARAM
g	_	_	O
of	_	_	O
butter	_	_	O
assuming	_	_	O
that	_	_	O
there	_	_	O
is	_	_	O
no	_	_	O
shortage	_	_	O
of	_	_	O
the	_	_	O
other	_	_	O
ingredients	_	_	O
used	_	_	O
in	_	_	O
making	_	_	O
the	_	_	O
cookies	_	_	O
.	_	_	O

Bolts	_	_	O
and	_	_	O
Nuts	_	_	O
builds	_	_	O
scooters	_	_	B-VAR
and	_	_	O
bikes	_	_	B-VAR
.	_	_	O
One	_	_	O
scooter	_	_	B-VAR
requires	_	_	O
2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
tooling	_	_	O
on	_	_	O
the	_	_	O
grinder	_	_	O
and	_	_	O
then	_	_	O
3	_	_	B-PARAM
hours	_	_	O
of	_	_	O
tooling	_	_	O
on	_	_	O
the	_	_	O
polisher	_	_	O
.	_	_	O
One	_	_	O
bike	_	_	B-VAR
requires	_	_	O
4	_	_	B-PARAM
hours	_	_	O
of	_	_	O
tooling	_	_	O
on	_	_	O
the	_	_	O
grinder	_	_	O
and	_	_	O
then	_	_	O
3	_	_	B-PARAM
hours	_	_	O
of	_	_	O
tooling	_	_	O
on	_	_	O
polisher	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
makes	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
100	_	_	B-PARAM
per	_	_	O
scooter	_	_	B-VAR
and	_	_	O
$	_	_	O
50	_	_	B-PARAM
per	_	_	O
bike	_	_	B-VAR
.	_	_	O
Each	_	_	O
machine	_	_	O
,	_	_	O
the	_	_	O
grinder	_	_	O
and	_	_	O
polisher	_	_	O
,	_	_	O
can	_	_	O
only	_	_	O
be	_	_	O
used	_	_	O
for	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
10	_	_	B-LIMIT
hours	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
units	_	_	O
of	_	_	O
each	_	_	O
,	_	_	O
scooters	_	_	B-VAR
and	_	_	O
bikes	_	_	B-VAR
,	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
produce	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
paper	_	_	O
company	_	_	O
makes	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
paper	_	_	O
:	_	_	O
lined	_	_	B-VAR
and	_	_	O
unlined	_	_	B-VAR
paper	_	_	I-VAR
.	_	_	O
Each	_	_	O
type	_	_	O
of	_	_	O
paper	_	_	O
requires	_	_	O
use	_	_	O
of	_	_	O
two	_	_	O
machines	_	_	O
,	_	_	O
a	_	_	O
printing	_	_	O
machine	_	_	O
and	_	_	O
a	_	_	O
scanning	_	_	O
machine	_	_	O
.	_	_	O
It	_	_	O
takes	_	_	O
2	_	_	B-PARAM
minute	_	_	O
on	_	_	O
the	_	_	O
printing	_	_	O
machine	_	_	O
and	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
scanning	_	_	O
machine	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
ream	_	_	O
of	_	_	O
lined	_	_	B-VAR
paper	_	_	I-VAR
.	_	_	O
On	_	_	O
the	_	_	O
other	_	_	O
hand	_	_	O
,	_	_	O
it	_	_	O
takes	_	_	O
1	_	_	B-PARAM
minute	_	_	O
on	_	_	O
the	_	_	O
printing	_	_	O
machine	_	_	O
and	_	_	O
2	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
scanning	_	_	O
machine	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
ream	_	_	O
of	_	_	O
unlined	_	_	B-VAR
paper	_	_	I-VAR
.	_	_	O
Each	_	_	O
machine	_	_	O
is	_	_	O
available	_	_	O
for	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
400	_	_	B-LIMIT
minutes	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
sells	_	_	O
a	_	_	O
package	_	_	O
of	_	_	O
lined	_	_	B-VAR
paper	_	_	I-VAR
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
a	_	_	O
package	_	_	O
of	_	_	O
unlined	_	_	B-VAR
paper	_	_	I-VAR
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
3	_	_	B-PARAM
.	_	_	O
The	_	_	O
company	_	_	O
can	_	_	O
sell	_	_	O
all	_	_	O
the	_	_	O
paper	_	_	O
it	_	_	O
makes	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
reams	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
produce	_	_	O
in	_	_	O
a	_	_	O
day	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O
What	_	_	O
is	_	_	O
that	_	_	O
profit	_	_	O
?	_	_	O

A	_	_	O
woodshop	_	_	O
makes	_	_	O
tables	_	_	B-VAR
and	_	_	O
chairs	_	_	B-VAR
,	_	_	O
using	_	_	O
two	_	_	O
processes	_	_	O
:	_	_	O
crafting	_	_	O
and	_	_	O
polishing	_	_	O
.	_	_	O
For	_	_	O
each	_	_	O
table	_	_	B-VAR
,	_	_	O
the	_	_	O
woodworkers	_	_	O
spend	_	_	O
5	_	_	B-PARAM
hours	_	_	O
crafting	_	_	O
and	_	_	O
2	_	_	B-PARAM
hours	_	_	O
polishing	_	_	O
.	_	_	O
For	_	_	O
each	_	_	O
chair	_	_	B-VAR
,	_	_	O
the	_	_	O
woodworkers	_	_	O
spend	_	_	O
2	_	_	B-PARAM
hours	_	_	O
crafting	_	_	O
and	_	_	O
1	_	_	B-PARAM
hour	_	_	O
polishing	_	_	O
.	_	_	O
On	_	_	O
any	_	_	O
day	_	_	O
,	_	_	O
there	_	_	O
is	_	_	O
a	_	_	O
maximum	_	_	O
of	_	_	O
25	_	_	B-LIMIT
crafting	_	_	O
hours	_	_	O
available	_	_	B-CONST_DIR
and	_	_	O
15	_	_	B-LIMIT
polishing	_	_	O
hours	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
from	_	_	O
the	_	_	O
sale	_	_	O
of	_	_	O
each	_	_	O
table	_	_	B-VAR
is	_	_	O
$	_	_	O
1000	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
from	_	_	O
the	_	_	O
sale	_	_	O
of	_	_	O
each	_	_	O
chair	_	_	B-VAR
is	_	_	O
$	_	_	O
300	_	_	B-PARAM
.	_	_	O
The	_	_	O
woodshop	_	_	O
can	_	_	O
sell	_	_	O
everything	_	_	O
they	_	_	O
make	_	_	O
.	_	_	O
How	_	_	O
should	_	_	O
they	_	_	O
schedule	_	_	O
daily	_	_	O
production	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
jewelry	_	_	O
shop	_	_	O
designs	_	_	O
and	_	_	O
crafts	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
necklaces	_	_	O
:	_	_	O
diamond	_	_	B-VAR
and	_	_	O
gold	_	_	B-VAR
necklaces	_	_	I-VAR
.	_	_	O
Each	_	_	O
diamond	_	_	B-VAR
necklaces	_	_	I-VAR
take	_	_	O
3	_	_	B-PARAM
hours	_	_	O
to	_	_	O
design	_	_	O
and	_	_	O
10	_	_	B-PARAM
hours	_	_	O
to	_	_	O
craft	_	_	O
.	_	_	O
Each	_	_	O
gold	_	_	B-VAR
necklaces	_	_	I-VAR
take	_	_	O
5	_	_	B-PARAM
hours	_	_	O
to	_	_	O
design	_	_	O
and	_	_	O
2	_	_	B-PARAM
hours	_	_	O
to	_	_	O
craft	_	_	O
.	_	_	O
The	_	_	O
designing	_	_	O
team	_	_	O
is	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
30	_	_	B-LIMIT
hours	_	_	O
and	_	_	O
the	_	_	O
crafting	_	_	O
team	_	_	O
is	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
45	_	_	B-LIMIT
hours	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
is	_	_	O
$	_	_	O
1500	_	_	B-PARAM
per	_	_	O
diamond	_	_	B-VAR
necklace	_	_	I-VAR
and	_	_	O
$	_	_	O
500	_	_	B-PARAM
per	_	_	O
gold	_	_	B-VAR
necklace	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
necklaces	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
the	_	_	O
shop	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
their	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

Banana	_	_	O
sells	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
subscription	_	_	O
software	_	_	O
packages	_	_	O
:	_	_	O
a	_	_	O
student	_	_	B-VAR
version	_	_	I-VAR
and	_	_	O
a	_	_	O
professional	_	_	B-VAR
version	_	_	I-VAR
which	_	_	O
will	_	_	O
cost	_	_	O
$	_	_	O
750	_	_	B-PARAM
and	_	_	O
$	_	_	O
3000	_	_	B-PARAM
to	_	_	O
produce	_	_	O
respectively	_	_	O
.	_	_	O
The	_	_	O
marketing	_	_	O
department	_	_	O
estimates	_	_	O
that	_	_	O
they	_	_	O
can	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
350	_	_	B-LIMIT
licenses	_	_	O
for	_	_	O
both	_	_	O
versions	_	_	O
combined	_	_	O
a	_	_	O
month	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
student	_	_	B-VAR
version	_	_	I-VAR
is	_	_	O
$	_	_	O
400	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
professional	_	_	B-VAR
version	_	_	I-VAR
is	_	_	O
$	_	_	O
1500	_	_	B-PARAM
.	_	_	O
If	_	_	O
Banana	_	_	O
does	_	_	O
not	_	_	O
want	_	_	O
to	_	_	O
spend	_	_	O
more	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
$	_	_	O
500000	_	_	B-LIMIT
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
software	_	_	O
package	_	_	O
should	_	_	O
they	_	_	O
produce	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
profits	_	_	B-OBJ_NAME
.	_	_	O

At	_	_	O
the	_	_	O
suggestion	_	_	O
of	_	_	O
a	_	_	O
dietitian	_	_	O
,	_	_	O
Jamie	_	_	O
wants	_	_	O
to	_	_	O
eat	_	_	O
a	_	_	O
diet	_	_	O
which	_	_	O
contains	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
100	_	_	B-LIMIT
units	_	_	O
of	_	_	O
proteins	_	_	O
and	_	_	O
60	_	_	B-LIMIT
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
She	_	_	O
can	_	_	O
eat	_	_	O
chicken	_	_	B-VAR
and	_	_	O
beef	_	_	B-VAR
to	_	_	O
supplement	_	_	O
her	_	_	O
current	_	_	O
vegetable	_	_	O
based	_	_	O
diet	_	_	O
.	_	_	O
Chicken	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
3.4	_	_	B-PARAM
per	_	_	O
unit	_	_	O
and	_	_	O
beef	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
7.5	_	_	B-PARAM
per	_	_	O
unit	_	_	O
.	_	_	O
One	_	_	O
unit	_	_	O
of	_	_	O
chicken	_	_	B-VAR
has	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
proteins	_	_	O
and	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
One	_	_	O
unit	_	_	O
of	_	_	O
beef	_	_	B-VAR
has	_	_	O
30	_	_	B-PARAM
units	_	_	O
of	_	_	O
proteins	_	_	O
and	_	_	O
40	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
Formulate	_	_	O
this	_	_	O
as	_	_	O
a	_	_	O
linear	_	_	O
programming	_	_	O
problem	_	_	O
.	_	_	O
Find	_	_	O
the	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
for	_	_	O
a	_	_	O
diet	_	_	O
that	_	_	O
consists	_	_	O
of	_	_	O
a	_	_	O
mixture	_	_	O
of	_	_	O
these	_	_	O
two	_	_	O
meats	_	_	O
and	_	_	O
also	_	_	O
meets	_	_	O
the	_	_	O
minimal	_	_	O
nutritional	_	_	O
requirements	_	_	O
.	_	_	O

The	_	_	O
TrainAcrossCanada	_	_	O
(	_	_	O
TAC	_	_	O
)	_	_	O
can	_	_	O
host	_	_	O
up	_	_	B-CONST_DIR
to	_	_	I-CONST_DIR
400	_	_	B-LIMIT
passengers	_	_	O
on	_	_	O
a	_	_	O
scenic	_	_	O
train	_	_	O
ride	_	_	O
.	_	_	O
Sleeper	_	_	B-VAR
class	_	_	I-VAR
seats	_	_	O
,	_	_	O
which	_	_	O
come	_	_	O
with	_	_	O
a	_	_	O
bed	_	_	O
,	_	_	O
are	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
$	_	_	O
500	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
each	_	_	O
while	_	_	O
regular	_	_	B-VAR
tickets	_	_	I-VAR
are	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
$	_	_	O
200	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
each	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
due	_	_	O
to	_	_	O
the	_	_	O
high	_	_	O
costs	_	_	O
,	_	_	O
more	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
5	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
many	_	_	O
passengers	_	_	O
prefer	_	_	O
to	_	_	O
travel	_	_	O
by	_	_	O
regular	_	_	B-VAR
seating	_	_	I-VAR
than	_	_	O
by	_	_	O
sleeper	_	_	B-VAR
class	_	_	I-VAR
and	_	_	O
will	_	_	O
sleep	_	_	O
sitting	_	_	O
up	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
there	_	_	O
are	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
seats	_	_	O
reserved	_	_	O
for	_	_	O
sleeper	_	_	B-VAR
class	_	_	I-VAR
passengers	_	_	O
.	_	_	O
Determine	_	_	O
how	_	_	O
many	_	_	O
tickets	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
must	_	_	O
be	_	_	O
sold	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
profit	_	_	B-OBJ_NAME
for	_	_	O
the	_	_	O
TAC	_	_	O
.	_	_	O
What	_	_	O
is	_	_	O
the	_	_	O
maximum	_	_	O
profit	_	_	O
?	_	_	O

A	_	_	O
bike	_	_	O
shop	_	_	O
sells	_	_	O
two	_	_	O
models	_	_	O
of	_	_	O
a	_	_	O
bike	_	_	O
:	_	_	O
a	_	_	O
mountain	_	_	B-VAR
bike	_	_	I-VAR
and	_	_	O
a	_	_	O
road	_	_	B-VAR
bike	_	_	I-VAR
.	_	_	O
The	_	_	O
mountain	_	_	B-VAR
bike	_	_	I-VAR
costs	_	_	O
$	_	_	O
750	_	_	B-PARAM
and	_	_	O
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
300	_	_	B-PARAM
.	_	_	O
The	_	_	O
road	_	_	B-VAR
bike	_	_	I-VAR
costs	_	_	O
$	_	_	O
1000	_	_	B-PARAM
and	_	_	O
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
500	_	_	B-PARAM
.	_	_	O
The	_	_	O
bike	_	_	O
shop	_	_	O
owner	_	_	O
knows	_	_	O
that	_	_	O
the	_	_	O
monthly	_	_	O
demand	_	_	O
will	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
150	_	_	B-LIMIT
bikes	_	_	O
.	_	_	O
He	_	_	O
also	_	_	O
wants	_	_	O
to	_	_	O
make	_	_	O
sure	_	_	O
that	_	_	O
there	_	_	O
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
40000	_	_	B-LIMIT
worth	_	_	O
of	_	_	O
bikes	_	_	O
in	_	_	O
stock	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
bikes	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
be	_	_	O
stocked	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Lily	_	_	O
's	_	_	O
dog	_	_	O
requires	_	_	O
his	_	_	O
food	_	_	O
to	_	_	O
be	_	_	O
mixed	_	_	O
.	_	_	O
In	_	_	O
order	_	_	O
to	_	_	O
keep	_	_	O
the	_	_	O
dog	_	_	O
healthy	_	_	O
but	_	_	O
also	_	_	O
keep	_	_	O
the	_	_	O
food	_	_	O
tasty	_	_	O
,	_	_	O
the	_	_	O
mix	_	_	O
needs	_	_	O
to	_	_	O
have	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
20	_	_	B-LIMIT
units	_	_	O
of	_	_	O
calcium	_	_	O
,	_	_	O
30	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamin	_	_	O
mix	_	_	O
,	_	_	O
and	_	_	O
50	_	_	B-LIMIT
units	_	_	O
of	_	_	O
meat	_	_	O
.	_	_	O
A	_	_	O
local	_	_	B-VAR
brand	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
30	_	_	B-PARAM
per	_	_	O
bag	_	_	O
and	_	_	O
contains	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
calcium	_	_	O
,	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
mix	_	_	O
,	_	_	O
and	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
meat	_	_	O
.	_	_	O
A	_	_	O
specialty	_	_	B-VAR
health	_	_	I-VAR
brand	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
50	_	_	B-PARAM
per	_	_	O
bag	_	_	O
and	_	_	O
contains	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
calcium	_	_	O
,	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
mix	_	_	O
,	_	_	O
and	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
meat	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
bags	_	_	O
of	_	_	O
each	_	_	O
brand	_	_	O
should	_	_	O
Lily	_	_	O
mix	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
while	_	_	O
also	_	_	O
meeting	_	_	O
the	_	_	O
taste	_	_	O
and	_	_	O
health	_	_	O
requirements	_	_	O
.	_	_	O

Two	_	_	O
paints	_	_	O
of	_	_	O
different	_	_	O
quality	_	_	O
,	_	_	O
cheap	_	_	B-VAR
and	_	_	O
expensive	_	_	B-VAR
,	_	_	O
have	_	_	O
quality	_	_	O
ratings	_	_	O
of	_	_	O
50	_	_	B-PARAM
and	_	_	O
90	_	_	B-PARAM
,	_	_	O
respectively	_	_	O
.	_	_	O
The	_	_	O
cheap	_	_	B-VAR
paint	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
0.30	_	_	B-PARAM
per	_	_	O
liter	_	_	O
while	_	_	O
the	_	_	O
expensive	_	_	B-VAR
paint	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
1.50	_	_	B-PARAM
per	_	_	O
liter	_	_	O
.	_	_	O
In	_	_	O
order	_	_	O
to	_	_	O
paint	_	_	O
his	_	_	O
fence	_	_	O
,	_	_	O
John	_	_	O
wants	_	_	O
to	_	_	O
use	_	_	O
a	_	_	O
mix	_	_	O
of	_	_	O
paint	_	_	O
with	_	_	O
a	_	_	O
quality	_	_	O
of	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
80	_	_	B-LIMIT
.	_	_	O
This	_	_	O
ensures	_	_	O
that	_	_	O
the	_	_	O
paint	_	_	O
on	_	_	O
the	_	_	O
fence	_	_	O
will	_	_	O
withstand	_	_	O
a	_	_	O
few	_	_	O
storms	_	_	O
.	_	_	O
What	_	_	O
blend	_	_	O
of	_	_	O
the	_	_	O
two	_	_	O
paints	_	_	O
should	_	_	O
he	_	_	O
mix	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
cost	_	_	B-OBJ_NAME
?	_	_	O
[	_	_	O
Hint	_	_	O
:	_	_	O
Let	_	_	O
x	_	_	O
be	_	_	O
the	_	_	O
fraction	_	_	O
of	_	_	O
each	_	_	O
liter	_	_	O
that	_	_	O
is	_	_	O
cheap	_	_	O
paint	_	_	O
and	_	_	O
y	_	_	O
be	_	_	O
the	_	_	O
fraction	_	_	O
that	_	_	O
is	_	_	O
expensive	_	_	O
paint	_	_	O
.	_	_	O
]	_	_	O

A	_	_	O
large	_	_	O
engineering	_	_	O
firm	_	_	O
employs	_	_	O
engineers	_	_	B-VAR
and	_	_	O
interns	_	_	B-VAR
.	_	_	O
Engineers	_	_	B-VAR
earn	_	_	B-OBJ_NAME
$	_	_	O
3000	_	_	B-PARAM
per	_	_	O
week	_	_	O
while	_	_	O
interns	_	_	B-VAR
earn	_	_	B-OBJ_NAME
$	_	_	O
750	_	_	B-PARAM
per	_	_	O
week	_	_	O
.	_	_	O
The	_	_	O
projects	_	_	O
requires	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
workers	_	_	O
,	_	_	O
of	_	_	O
whom	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
must	_	_	O
be	_	_	O
interns	_	_	B-VAR
.	_	_	O
To	_	_	O
maintain	_	_	O
relations	_	_	O
with	_	_	O
the	_	_	O
local	_	_	O
universities	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
interns	_	_	B-VAR
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
a	_	_	O
third	_	_	B-PARAM
the	_	_	O
number	_	_	O
of	_	_	O
engineers	_	_	B-VAR
.	_	_	O
The	_	_	O
company	_	_	O
wants	_	_	O
to	_	_	O
keep	_	_	O
the	_	_	O
weekly	_	_	O
payroll	_	_	O
to	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
200000	_	_	B-PARAM
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
wages	_	_	B-OBJ_NAME
.	_	_	O

Sam	_	_	O
owns	_	_	O
two	_	_	O
rice	_	_	O
mills	_	_	O
.	_	_	O
Mill	_	_	B-VAR
A	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
500	_	_	B-PARAM
to	_	_	O
operate	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
can	_	_	O
produce	_	_	O
and	_	_	O
deliver	_	_	O
5	_	_	B-PARAM
bags	_	_	O
of	_	_	O
basmati	_	_	O
rice	_	_	O
,	_	_	O
7	_	_	B-PARAM
bags	_	_	O
of	_	_	O
brown	_	_	O
rice	_	_	O
,	_	_	O
and	_	_	O
4	_	_	B-PARAM
bags	_	_	O
of	_	_	O
jasmine	_	_	O
rice	_	_	O
.	_	_	O
Mill	_	_	B-VAR
B	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
300	_	_	B-PARAM
to	_	_	O
operate	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
can	_	_	O
produce	_	_	O
and	_	_	O
deliver	_	_	O
7	_	_	B-PARAM
bags	_	_	O
of	_	_	O
basmati	_	_	O
rice	_	_	O
,	_	_	O
10	_	_	B-PARAM
bags	_	_	O
of	_	_	O
brown	_	_	O
rice	_	_	O
,	_	_	O
and	_	_	O
1	_	_	B-PARAM
bag	_	_	O
of	_	_	O
jasmine	_	_	O
rice	_	_	O
.	_	_	O
Sam	_	_	O
recently	_	_	O
obtained	_	_	O
a	_	_	O
contract	_	_	O
to	_	_	O
provide	_	_	B-CONST_DIR
a	_	_	O
restaurant	_	_	O
with	_	_	O
25	_	_	B-LIMIT
bags	_	_	O
of	_	_	O
basmati	_	_	O
rice	_	_	O
,	_	_	O
20	_	_	B-LIMIT
bags	_	_	O
of	_	_	O
brown	_	_	O
rice	_	_	O
,	_	_	O
and	_	_	O
20	_	_	B-LIMIT
bags	_	_	O
of	_	_	O
jasmine	_	_	O
rice	_	_	O
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
Sam	_	_	O
's	_	_	O
total	_	_	B-OBJ_NAME
costs	_	_	I-OBJ_NAME
.	_	_	O

A	_	_	O
logging	_	_	O
company	_	_	O
has	_	_	O
operations	_	_	O
in	_	_	O
opposite	_	_	O
ends	_	_	O
of	_	_	O
the	_	_	O
country	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
cuts	_	_	O
three	_	_	O
specific	_	_	O
trees	_	_	O
:	_	_	O
Elm	_	_	O
,	_	_	O
Oak	_	_	O
,	_	_	O
and	_	_	O
Aspen	_	_	O
.	_	_	O
The	_	_	O
west	_	_	B-VAR
side	_	_	I-VAR
operation	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
500	_	_	B-PARAM
to	_	_	O
operate	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
produces	_	_	O
10	_	_	B-PARAM
elm	_	_	O
trees	_	_	O
10	_	_	B-PARAM
oak	_	_	O
trees	_	_	O
,	_	_	O
and	_	_	O
3	_	_	B-PARAM
aspen	_	_	O
trees	_	_	O
daily	_	_	O
.	_	_	O
The	_	_	O
east	_	_	B-VAR
side	_	_	I-VAR
operation	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
400	_	_	B-PARAM
to	_	_	O
operate	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
produces	_	_	O
8	_	_	B-PARAM
elm	_	_	O
trees	_	_	O
,	_	_	O
3	_	_	B-PARAM
oak	_	_	O
trees	_	_	O
,	_	_	O
and	_	_	O
7	_	_	B-PARAM
aspen	_	_	O
trees	_	_	O
daily	_	_	O
.	_	_	O
The	_	_	O
logging	_	_	O
company	_	_	O
must	_	_	O
provide	_	_	B-CONST_DIR
a	_	_	O
paper	_	_	O
pulp	_	_	O
with	_	_	O
30	_	_	B-LIMIT
elm	_	_	O
trees	_	_	O
,	_	_	O
20	_	_	B-LIMIT
oak	_	_	O
trees	_	_	O
,	_	_	O
and	_	_	O
20	_	_	B-LIMIT
aspen	_	_	O
trees	_	_	O
per	_	_	O
week	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
days	_	_	O
a	_	_	O
week	_	_	O
should	_	_	O
each	_	_	O
operation	_	_	O
be	_	_	O
run	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
while	_	_	O
meeting	_	_	O
the	_	_	O
requirements	_	_	O
.	_	_	O

In	_	_	O
a	_	_	O
labor	_	_	O
camp	_	_	O
,	_	_	O
the	_	_	O
company	_	_	O
makes	_	_	O
soup	_	_	B-VAR
and	_	_	O
sandwiches	_	_	B-VAR
.	_	_	O
They	_	_	O
need	_	_	O
to	_	_	O
ensure	_	_	O
workers	_	_	O
get	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
2000	_	_	B-LIMIT
calories	_	_	O
,	_	_	O
100	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
and	_	_	O
100	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
carbs	_	_	O
.	_	_	O
A	_	_	O
can	_	_	O
of	_	_	O
soup	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
1	_	_	B-PARAM
and	_	_	O
contains	_	_	O
200	_	_	B-PARAM
calories	_	_	O
,	_	_	O
5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
and	_	_	O
4	_	_	B-PARAM
grams	_	_	O
of	_	_	O
carbs	_	_	O
.	_	_	O
One	_	_	O
sandwich	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
3	_	_	B-PARAM
and	_	_	O
contains	_	_	O
250	_	_	B-PARAM
calories	_	_	O
,	_	_	O
10	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
and	_	_	O
15	_	_	B-PARAM
grams	_	_	O
of	_	_	O
carbs	_	_	O
.	_	_	O
What	_	_	O
is	_	_	O
the	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
diet	_	_	O
that	_	_	O
the	_	_	O
company	_	_	O
can	_	_	O
provide	_	_	O
for	_	_	O
its	_	_	O
workers	_	_	O
?	_	_	O

A	_	_	O
popcorn	_	_	O
store	_	_	O
has	_	_	B-CONST_DIR
30	_	_	B-LIMIT
pounds	_	_	O
of	_	_	O
butter	_	_	O
popcorn	_	_	O
and	_	_	O
40	_	_	B-LIMIT
pounds	_	_	O
of	_	_	O
caramel	_	_	O
popcorn	_	_	O
.	_	_	O
They	_	_	O
sell	_	_	O
two	_	_	O
mixed	_	_	O
bags	_	_	O
:	_	_	O
a	_	_	O
sweet	_	_	B-VAR
mix	_	_	I-VAR
,	_	_	O
and	_	_	O
a	_	_	O
regular	_	_	B-VAR
mix	_	_	I-VAR
.	_	_	O
The	_	_	O
sweet	_	_	B-VAR
mix	_	_	I-VAR
sells	_	_	B-OBJ_NAME
for	_	_	O
$	_	_	O
3	_	_	B-PARAM
a	_	_	O
pound	_	_	O
while	_	_	O
the	_	_	O
regular	_	_	B-VAR
mix	_	_	I-VAR
sells	_	_	B-OBJ_NAME
for	_	_	O
$	_	_	O
2	_	_	B-PARAM
a	_	_	O
pound	_	_	O
.	_	_	O
The	_	_	O
sweet	_	_	B-VAR
mix	_	_	I-VAR
has	_	_	O
75	_	_	B-PARAM
%	_	_	I-PARAM
caramel	_	_	O
popcorn	_	_	O
and	_	_	O
25	_	_	B-PARAM
%	_	_	I-PARAM
butter	_	_	O
popcorn	_	_	O
.	_	_	O
The	_	_	O
regular	_	_	B-VAR
mix	_	_	I-VAR
has	_	_	O
50	_	_	B-PARAM
%	_	_	I-PARAM
caramel	_	_	O
popcorn	_	_	O
and	_	_	O
50	_	_	B-PARAM
%	_	_	I-PARAM
regular	_	_	O
popcorn	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
bags	_	_	O
of	_	_	O
each	_	_	O
mix	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Jane	_	_	O
goes	_	_	O
to	_	_	O
a	_	_	O
supplement	_	_	O
store	_	_	O
that	_	_	O
sells	_	_	O
two	_	_	O
powders	_	_	O
,	_	_	O
Alpha	_	_	B-VAR
and	_	_	O
Beta	_	_	B-VAR
,	_	_	O
for	_	_	O
iron	_	_	O
and	_	_	O
biotin	_	_	O
.	_	_	O
The	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
scoop	_	_	O
of	_	_	O
alpha	_	_	B-VAR
is	_	_	O
$	_	_	O
1	_	_	B-PARAM
while	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
scoop	_	_	O
of	_	_	O
Beta	_	_	B-VAR
is	_	_	O
$	_	_	O
2	_	_	B-PARAM
.	_	_	O
A	_	_	O
scoop	_	_	O
of	_	_	O
Alpha	_	_	B-VAR
contains	_	_	O
5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
iron	_	_	O
and	_	_	O
20	_	_	B-PARAM
grams	_	_	O
of	_	_	O
biotin	_	_	O
.	_	_	O
A	_	_	O
scoop	_	_	O
of	_	_	O
Beta	_	_	B-VAR
contains	_	_	O
10	_	_	B-PARAM
grams	_	_	O
if	_	_	O
iron	_	_	O
and	_	_	O
3	_	_	B-PARAM
grams	_	_	O
of	_	_	O
biotin	_	_	O
.	_	_	O
A	_	_	O
doctor	_	_	O
has	_	_	O
recommended	_	_	O
that	_	_	O
Jane	_	_	O
takes	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
iron	_	_	O
and	_	_	O
40	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
biotin	_	_	O
daily	_	_	O
.	_	_	O
Formulate	_	_	O
as	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
smoothie	_	_	O
shop	_	_	O
makes	_	_	O
peanut	_	_	B-VAR
butter	_	_	I-VAR
and	_	_	O
almond	_	_	B-VAR
butter	_	_	I-VAR
smoothies	_	_	I-VAR
.	_	_	O
Three	_	_	O
ingredients	_	_	O
are	_	_	O
needed	_	_	O
to	_	_	O
make	_	_	O
the	_	_	O
smoothies	_	_	O
:	_	_	O
peanut	_	_	O
butter	_	_	O
,	_	_	O
almond	_	_	O
butter	_	_	O
,	_	_	O
and	_	_	O
milk	_	_	O
.	_	_	O
One	_	_	O
peanut	_	_	B-VAR
butter	_	_	I-VAR
smoothie	_	_	I-VAR
requires	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
peanut	_	_	O
butter	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
milk	_	_	O
.	_	_	O
One	_	_	O
almond	_	_	B-VAR
butter	_	_	I-VAR
smoothie	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
almond	_	_	O
butter	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
milk	_	_	O
.	_	_	O
The	_	_	O
shop	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
80	_	_	B-LIMIT
units	_	_	O
of	_	_	O
peanut	_	_	O
butter	_	_	O
,	_	_	O
90	_	_	B-LIMIT
units	_	_	O
of	_	_	O
almond	_	_	O
butter	_	_	O
,	_	_	O
and	_	_	O
100	_	_	B-LIMIT
units	_	_	O
of	_	_	O
milk	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
peanut	_	_	B-VAR
butter	_	_	I-VAR
smoothie	_	_	I-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
almond	_	_	B-VAR
butter	_	_	I-VAR
smoothie	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
company	_	_	O
washes	_	_	O
cars	_	_	B-VAR
and	_	_	O
buses	_	_	B-VAR
.	_	_	O
Each	_	_	O
car	_	_	B-VAR
takes	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
watering	_	_	O
and	_	_	O
$	_	_	O
10	_	_	B-PARAM
worth	_	_	O
of	_	_	O
soap	_	_	O
.	_	_	O
Each	_	_	O
bus	_	_	B-VAR
takes	_	_	O
50	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
watering	_	_	O
and	_	_	O
$	_	_	O
20	_	_	B-PARAM
worth	_	_	O
of	_	_	O
soap	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
5000	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
watering	_	_	O
and	_	_	O
$	_	_	O
1500	_	_	B-LIMIT
worth	_	_	O
of	_	_	O
soap	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
company	_	_	O
earns	_	_	B-OBJ_NAME
$	_	_	O
50	_	_	B-PARAM
per	_	_	O
car	_	_	B-VAR
washed	_	_	O
and	_	_	O
$	_	_	O
75	_	_	B-PARAM
per	_	_	O
bus	_	_	B-VAR
washed	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
wash	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
their	_	_	O
earnings	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
leather	_	_	O
shop	_	_	O
makes	_	_	O
wallets	_	_	B-VAR
and	_	_	O
purses	_	_	B-VAR
.	_	_	O
Both	_	_	O
require	_	_	O
time	_	_	O
for	_	_	O
cutting	_	_	O
and	_	_	O
stitching	_	_	O
.	_	_	O
A	_	_	O
wallet	_	_	B-VAR
requires	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
cutting	_	_	O
and	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
stitching	_	_	O
.	_	_	O
A	_	_	O
purse	_	_	B-VAR
requires	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
cutting	_	_	O
and	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
stitching	_	_	O
.	_	_	O
The	_	_	O
shop	_	_	O
has	_	_	O
500	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
per	_	_	O
day	_	_	O
for	_	_	O
cutting	_	_	O
and	_	_	O
600	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
per	_	_	O
day	_	_	O
for	_	_	O
stitching	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
wallet	_	_	B-VAR
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
purse	_	_	B-VAR
is	_	_	O
$	_	_	O
100	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
item	_	_	O
should	_	_	O
the	_	_	O
shop	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
their	_	_	O
profits	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
car	_	_	O
company	_	_	O
makes	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
cars	_	_	O
,	_	_	O
a	_	_	O
race	_	_	B-VAR
car	_	_	I-VAR
and	_	_	O
a	_	_	O
regular	_	_	B-VAR
car	_	_	I-VAR
.	_	_	O
Two	_	_	O
different	_	_	O
teams	_	_	O
produce	_	_	O
each	_	_	O
of	_	_	O
these	_	_	O
cars	_	_	O
.	_	_	O
The	_	_	O
race	_	_	B-VAR
car	_	_	I-VAR
team	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
3	_	_	B-LIMIT
race	_	_	B-VAR
cars	_	_	I-VAR
per	_	_	O
day	_	_	O
while	_	_	O
the	_	_	O
regular	_	_	B-VAR
car	_	_	I-VAR
team	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
5	_	_	B-LIMIT
regular	_	_	B-VAR
cars	_	_	I-VAR
per	_	_	O
day	_	_	O
.	_	_	O
Both	_	_	O
cars	_	_	O
need	_	_	O
to	_	_	O
go	_	_	O
through	_	_	O
a	_	_	O
safety	_	_	O
check	_	_	O
,	_	_	O
and	_	_	O
in	_	_	O
a	_	_	O
day	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
6	_	_	B-LIMIT
cars	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
can	_	_	O
be	_	_	O
safety	_	_	O
checked	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
race	_	_	B-VAR
car	_	_	I-VAR
is	_	_	O
$	_	_	O
20000	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
regular	_	_	B-VAR
car	_	_	I-VAR
is	_	_	O
$	_	_	O
10000	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
their	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
bakery	_	_	O
makes	_	_	O
regular	_	_	B-VAR
donuts	_	_	I-VAR
and	_	_	O
jelly	_	_	B-VAR
filled	_	_	I-VAR
donuts	_	_	I-VAR
.	_	_	O
They	_	_	O
make	_	_	O
x1	_	_	O
regular	_	_	B-VAR
donuts	_	_	I-VAR
per	_	_	O
day	_	_	O
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
2	_	_	B-PARAM
per	_	_	O
donut	_	_	O
and	_	_	O
x2	_	_	O
jelly	_	_	B-VAR
filled	_	_	I-VAR
donuts	_	_	I-VAR
per	_	_	O
day	_	_	O
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
4	_	_	B-PARAM
per	_	_	O
donut	_	_	O
(	_	_	O
x1	_	_	O
and	_	_	O
x2	_	_	O
must	_	_	O
be	_	_	O
greater	_	_	O
than	_	_	O
or	_	_	O
equal	_	_	O
to	_	_	O
0).There	_	_	O
is	_	_	O
a	_	_	O
daily	_	_	O
demand	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
regular	_	_	B-VAR
donuts	_	_	I-VAR
and	_	_	O
75	_	_	B-LIMIT
jelly	_	_	B-VAR
filled	_	_	I-VAR
donuts	_	_	I-VAR
.	_	_	O
The	_	_	O
bakery	_	_	O
only	_	_	O
has	_	_	O
capacity	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
120	_	_	B-LIMIT
donuts	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
produce	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
dog	_	_	O
owner	_	_	O
mixes	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
dog	_	_	O
food	_	_	O
to	_	_	O
ensure	_	_	O
the	_	_	O
new	_	_	O
mixture	_	_	O
contains	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
12	_	_	B-LIMIT
units	_	_	O
of	_	_	O
meat	_	_	O
and	_	_	O
8	_	_	B-LIMIT
units	_	_	O
of	_	_	O
micronutrients	_	_	O
.	_	_	O
Type	_	_	B-VAR
A	_	_	I-VAR
food	_	_	I-VAR
contains	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
meat	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
micronutrients	_	_	O
per	_	_	O
kg	_	_	O
.	_	_	O
Type	_	_	B-VAR
B	_	_	I-VAR
food	_	_	I-VAR
contains	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
meat	_	_	O
and	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
micronutrients	_	_	O
per	_	_	O
kg	_	_	O
.	_	_	O
If	_	_	O
it	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
2	_	_	B-PARAM
per	_	_	O
kg	_	_	O
of	_	_	O
Type	_	_	B-VAR
A	_	_	I-VAR
food	_	_	I-VAR
and	_	_	O
$	_	_	O
5	_	_	B-PARAM
per	_	_	O
kg	_	_	O
of	_	_	O
Type	_	_	B-VAR
B	_	_	I-VAR
food	_	_	I-VAR
,	_	_	O
how	_	_	O
many	_	_	O
kg	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
owner	_	_	O
buy	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
her	_	_	O
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
farmer	_	_	O
has	_	_	B-CONST_DIR
80	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
on	_	_	O
which	_	_	O
he	_	_	O
grows	_	_	O
apple	_	_	B-VAR
trees	_	_	I-VAR
and	_	_	O
orange	_	_	B-VAR
trees	_	_	I-VAR
.	_	_	O
Per	_	_	O
acre	_	_	O
of	_	_	O
apple	_	_	B-VAR
trees	_	_	I-VAR
,	_	_	O
30	_	_	B-PARAM
kg	_	_	O
of	_	_	O
special	_	_	O
soil	_	_	O
is	_	_	O
required	_	_	O
.	_	_	O
Per	_	_	O
acre	_	_	O
of	_	_	O
orange	_	_	B-VAR
trees	_	_	I-VAR
,	_	_	O
25	_	_	B-PARAM
kg	_	_	O
of	_	_	O
special	_	_	O
soil	_	_	O
is	_	_	O
required	_	_	O
.	_	_	O
However	_	_	O
the	_	_	O
farmer	_	_	O
only	_	_	B-CONST_DIR
has	_	_	O
2200	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
special	_	_	O
soil	_	_	O
available	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
apple	_	_	B-VAR
trees	_	_	I-VAR
is	_	_	O
$	_	_	O
500	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
orange	_	_	B-VAR
trees	_	_	I-VAR
is	_	_	O
$	_	_	O
450	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
grown	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
toy	_	_	O
company	_	_	O
builds	_	_	O
and	_	_	O
paints	_	_	O
model	_	_	B-VAR
trains	_	_	I-VAR
and	_	_	O
planes	_	_	B-VAR
.	_	_	O
Each	_	_	O
model	_	_	B-VAR
train	_	_	I-VAR
takes	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
build	_	_	O
and	_	_	O
40	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
paint	_	_	O
.	_	_	O
Each	_	_	O
model	_	_	B-VAR
plane	_	_	I-VAR
takes	_	_	O
40	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
build	_	_	O
and	_	_	O
50	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
paint	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
at	_	_	O
most	_	_	O
5000	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
building	_	_	O
and	_	_	O
6000	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
painting	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
company	_	_	O
makes	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
7	_	_	B-PARAM
per	_	_	O
model	_	_	B-VAR
train	_	_	I-VAR
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
9	_	_	B-PARAM
per	_	_	O
model	_	_	B-VAR
plane	_	_	I-VAR
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
their	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
auto	_	_	O
manufacturing	_	_	O
plant	_	_	O
has	_	_	O
a	_	_	O
machine	_	_	O
that	_	_	O
makes	_	_	O
doors	_	_	B-VAR
and	_	_	O
bumpers	_	_	B-VAR
.	_	_	O
Each	_	_	O
door	_	_	B-VAR
takes	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
machine	_	_	O
time	_	_	O
and	_	_	O
each	_	_	O
bumper	_	_	B-VAR
takes	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
machine	_	_	O
time	_	_	O
.	_	_	O
In	_	_	O
a	_	_	O
week	_	_	O
the	_	_	O
machine	_	_	O
is	_	_	O
only	_	_	B-CONST_DIR
available	_	_	O
for	_	_	O
3000	_	_	B-LIMIT
minutes	_	_	O
.	_	_	O
The	_	_	O
plant	_	_	O
can	_	_	O
also	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
doors	_	_	B-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
200	_	_	B-LIMIT
bumpers	_	_	B-VAR
per	_	_	O
week	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
door	_	_	B-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
bumper	_	_	B-VAR
is	_	_	O
$	_	_	O
150	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
plant	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
doctor	_	_	O
prescribes	_	_	O
a	_	_	O
patient	_	_	O
two	_	_	O
options	_	_	O
for	_	_	O
his	_	_	O
blood	_	_	O
pressure	_	_	O
and	_	_	O
diabetes	_	_	O
requirements	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
two	_	_	O
pills	_	_	O
,	_	_	O
a	_	_	O
blue	_	_	B-VAR
pill	_	_	I-VAR
and	_	_	O
a	_	_	O
red	_	_	B-VAR
pill	_	_	I-VAR
.	_	_	O
The	_	_	O
blue	_	_	B-VAR
pill	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
1	_	_	B-PARAM
and	_	_	O
contains	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
blood	_	_	O
pressure	_	_	O
medication	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
diabetes	_	_	O
medication	_	_	O
.	_	_	O
The	_	_	O
red	_	_	B-VAR
pill	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
2	_	_	B-PARAM
and	_	_	O
contains	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
blood	_	_	O
pressure	_	_	O
medication	_	_	O
and	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
diabetes	_	_	O
medication	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
patient	_	_	O
requires	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
units	_	_	O
of	_	_	O
blood	_	_	O
pressure	_	_	O
medication	_	_	O
and	_	_	O
70	_	_	B-LIMIT
units	_	_	O
of	_	_	O
diabetes	_	_	O
medication	_	_	O
per	_	_	O
week	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
pill	_	_	O
should	_	_	O
he	_	_	O
purchase	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
cost	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
company	_	_	O
makes	_	_	O
regular	_	_	B-VAR
and	_	_	O
touchscreen	_	_	B-VAR
laptops	_	_	I-VAR
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
3000	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
manual	_	_	O
labor	_	_	O
and	_	_	O
2000	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
calibration	_	_	O
.	_	_	O
Each	_	_	O
regular	_	_	B-VAR
laptop	_	_	I-VAR
takes	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
manual	_	_	O
labor	_	_	O
and	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
calibration	_	_	O
.	_	_	O
Each	_	_	O
touchscreen	_	_	B-VAR
laptop	_	_	I-VAR
takes	_	_	O
25	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
manual	_	_	O
labor	_	_	O
and	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
calibration	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
regular	_	_	B-VAR
laptop	_	_	I-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
touchscreen	_	_	B-VAR
laptop	_	_	I-VAR
is	_	_	O
$	_	_	O
300	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Jason	_	_	O
has	_	_	O
$	_	_	O
1000000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
the	_	_	O
following	_	_	O
energy	_	_	O
sectors	_	_	O
:	_	_	O
solar	_	_	B-VAR
,	_	_	O
wind	_	_	B-VAR
,	_	_	O
nuclear	_	_	B-VAR
and	_	_	O
coal	_	_	B-VAR
.	_	_	O
The	_	_	O
annual	_	_	O
rate	_	_	O
of	_	_	O
return	_	_	B-OBJ_NAME
for	_	_	O
each	_	_	O
is	_	_	O
as	_	_	O
follows	_	_	O
:	_	_	O
solar	_	_	B-VAR
,	_	_	O
6	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
wind	_	_	B-VAR
,	_	_	O
9	_	_	B-PARAM
%	_	_	I-PARAM
,	_	_	O
nuclear	_	_	B-VAR
,	_	_	O
12	_	_	B-PARAM
%	_	_	I-PARAM
,	_	_	O
coal	_	_	B-VAR
,	_	_	O
3	_	_	B-PARAM
%	_	_	I-PARAM
.	_	_	O
Jason	_	_	O
has	_	_	O
the	_	_	O
following	_	_	O
conditions	_	_	O
.	_	_	O
The	_	_	O
amount	_	_	O
he	_	_	O
invests	_	_	O
in	_	_	O
coal	_	_	B-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
solar	_	_	B-VAR
.	_	_	O
Similarly	_	_	O
,	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
wind	_	_	B-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
nuclear	_	_	B-VAR
.	_	_	O
Lastly	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
10	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
investment	_	_	O
can	_	_	O
be	_	_	O
in	_	_	O
coal	_	_	B-VAR
.	_	_	O
How	_	_	O
much	_	_	O
money	_	_	O
should	_	_	O
Jason	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
sector	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
return	_	_	B-OBJ_NAME
?	_	_	O

Mark	_	_	O
has	_	_	O
to	_	_	O
take	_	_	O
supplements	_	_	O
to	_	_	O
meet	_	_	O
his	_	_	O
daily	_	_	O
requirements	_	_	B-CONST_DIR
of	_	_	O
30	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamin	_	_	O
A	_	_	O
,	_	_	O
20	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamin	_	_	O
C	_	_	O
,	_	_	O
40	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamin	_	_	O
D	_	_	O
,	_	_	O
and	_	_	O
30	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamin	_	_	O
E.	_	_	O
He	_	_	O
can	_	_	O
take	_	_	O
chewable	_	_	B-VAR
pills	_	_	I-VAR
that	_	_	O
each	_	_	O
contain	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
A	_	_	O
,	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
C	_	_	O
,	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
D	_	_	O
,	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
E	_	_	O
or	_	_	O
he	_	_	O
can	_	_	O
take	_	_	O
regular	_	_	B-VAR
pills	_	_	I-VAR
that	_	_	O
each	_	_	O
contain	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
A	_	_	O
,	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
C	_	_	O
,	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
D	_	_	O
,	_	_	O
and	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
E.	_	_	O
If	_	_	O
each	_	_	O
chewable	_	_	B-VAR
pill	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
0.50	_	_	B-PARAM
and	_	_	O
each	_	_	O
regular	_	_	B-VAR
pill	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
0.40	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
supplement	_	_	O
should	_	_	O
he	_	_	O
buy	_	_	O
to	_	_	O
meet	_	_	O
his	_	_	O
requirements	_	_	O
at	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
vine	_	_	O
farmer	_	_	O
has	_	_	B-CONST_DIR
100	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
to	_	_	O
grown	_	_	O
red	_	_	B-VAR
and	_	_	O
green	_	_	B-VAR
grapes	_	_	I-VAR
.	_	_	O
He	_	_	O
must	_	_	O
grow	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
red	_	_	B-VAR
grapes	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
25	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
green	_	_	B-VAR
grapes	_	_	I-VAR
.	_	_	O
The	_	_	O
farmer	_	_	O
prefers	_	_	O
to	_	_	O
grow	_	_	O
more	_	_	O
green	_	_	B-VAR
grapes	_	_	I-VAR
than	_	_	O
red	_	_	B-VAR
grapes	_	_	I-VAR
but	_	_	O
due	_	_	O
to	_	_	O
a	_	_	O
shortage	_	_	O
,	_	_	O
he	_	_	O
can	_	_	O
grow	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
twice	_	_	B-PARAM
the	_	_	O
amount	_	_	O
of	_	_	O
green	_	_	B-VAR
grapes	_	_	I-VAR
as	_	_	O
red	_	_	B-VAR
grapes	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
red	_	_	B-VAR
grapes	_	_	I-VAR
is	_	_	O
$	_	_	O
300	_	_	B-PARAM
,	_	_	O
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
green	_	_	B-VAR
grapes	_	_	I-VAR
is	_	_	O
$	_	_	O
250	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
grown	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
bodybuilder	_	_	O
only	_	_	O
eats	_	_	O
protein	_	_	O
bars	_	_	O
.	_	_	O
He	_	_	O
wants	_	_	O
to	_	_	O
make	_	_	O
sure	_	_	O
het	_	_	O
gets	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
80	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
50	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
fat	_	_	O
,	_	_	O
and	_	_	O
100	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
carbs	_	_	O
.	_	_	O
Protein	_	_	B-VAR
Bar	_	_	I-VAR
A	_	_	I-VAR
contains	_	_	O
10	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
3	_	_	B-PARAM
grams	_	_	O
of	_	_	O
fat	_	_	O
,	_	_	O
and	_	_	O
11	_	_	B-PARAM
grams	_	_	O
of	_	_	O
carbs	_	_	O
.	_	_	O
Protein	_	_	B-VAR
Bar	_	_	I-VAR
B	_	_	I-VAR
contains	_	_	O
15	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
fat	_	_	O
,	_	_	O
and	_	_	O
8	_	_	B-PARAM
grams	_	_	O
of	_	_	O
carbs	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
Protein	_	_	B-VAR
Bar	_	_	I-VAR
A	_	_	I-VAR
is	_	_	O
$	_	_	O
7	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
Protein	_	_	B-VAR
Bar	_	_	I-VAR
B	_	_	I-VAR
is	_	_	O
$	_	_	O
10	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
buy	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
printing	_	_	O
company	_	_	O
prints	_	_	O
books	_	_	B-VAR
and	_	_	O
magazines	_	_	B-VAR
for	_	_	O
sale	_	_	O
.	_	_	O
Each	_	_	O
book	_	_	B-VAR
takes	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
for	_	_	O
printing	_	_	O
and	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
for	_	_	O
binding	_	_	O
.	_	_	O
Each	_	_	O
magazine	_	_	B-VAR
takes	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
for	_	_	O
printing	_	_	O
and	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
for	_	_	O
binding	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
5000	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
printing	_	_	O
and	_	_	O
2000	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
binding	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
book	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
magazine	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
8	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
print	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profits	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
construction	_	_	O
company	_	_	O
makes	_	_	O
marble	_	_	B-VAR
and	_	_	O
granite	_	_	B-VAR
countertops	_	_	I-VAR
.	_	_	O
It	_	_	O
takes	_	_	O
1	_	_	B-PARAM
hour	_	_	O
of	_	_	O
cutting	_	_	O
and	_	_	O
2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
polishing	_	_	O
to	_	_	O
make	_	_	O
one	_	_	O
marble	_	_	B-VAR
countertop	_	_	I-VAR
.	_	_	O
It	_	_	O
takes	_	_	O
1.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
cutting	_	_	O
and	_	_	O
3	_	_	B-PARAM
hours	_	_	O
of	_	_	O
polishing	_	_	O
to	_	_	O
make	_	_	O
one	_	_	O
granite	_	_	B-VAR
countertop	_	_	I-VAR
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
300	_	_	B-LIMIT
hours	_	_	O
for	_	_	O
cutting	_	_	O
and	_	_	O
500	_	_	B-LIMIT
hours	_	_	O
for	_	_	O
polishing	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
marble	_	_	B-VAR
countertop	_	_	I-VAR
is	_	_	O
$	_	_	O
500	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
granite	_	_	B-VAR
countertop	_	_	I-VAR
is	_	_	O
$	_	_	O
750	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
furniture	_	_	O
company	_	_	O
sells	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
tables	_	_	O
–	_	_	O
a	_	_	O
dinning	_	_	B-VAR
table	_	_	I-VAR
and	_	_	O
a	_	_	O
coffee	_	_	B-VAR
table	_	_	I-VAR
.	_	_	O
They	_	_	O
cost	_	_	O
$	_	_	O
250	_	_	B-PARAM
and	_	_	O
$	_	_	O
150	_	_	B-PARAM
to	_	_	O
make	_	_	O
respectively	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
estimates	_	_	O
that	_	_	O
the	_	_	O
total	_	_	O
monthly	_	_	O
demand	_	_	O
of	_	_	O
these	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
tables	_	_	O
combined	_	_	O
will	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
200	_	_	B-LIMIT
units	_	_	O
.	_	_	O
The	_	_	O
monthly	_	_	O
manufacturing	_	_	O
budget	_	_	B-CONST_DIR
on	_	_	O
tables	_	_	O
is	_	_	O
$	_	_	O
20000	_	_	B-LIMIT
.	_	_	O
Determine	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
units	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
tables	_	_	O
the	_	_	O
company	_	_	O
should	_	_	O
make	_	_	O
to	_	_	O
get	_	_	O
maximum	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
if	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
on	_	_	O
each	_	_	O
dinning	_	_	B-VAR
table	_	_	I-VAR
and	_	_	O
coffee	_	_	B-VAR
table	_	_	I-VAR
are	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
$	_	_	O
100	_	_	B-PARAM
respectively	_	_	O
.	_	_	O

A	_	_	O
tech	_	_	O
company	_	_	O
makes	_	_	O
two	_	_	O
type	_	_	O
of	_	_	O
electronics	_	_	O
:	_	_	O
phones	_	_	B-VAR
and	_	_	O
laptops	_	_	B-VAR
.	_	_	O
Demand	_	_	O
is	_	_	O
high	_	_	O
but	_	_	O
production	_	_	O
is	_	_	O
limited	_	_	O
by	_	_	O
silicon	_	_	O
chip	_	_	O
availability	_	_	O
,	_	_	O
engineering	_	_	O
time	_	_	O
,	_	_	O
and	_	_	O
assembly	_	_	O
time	_	_	O
.	_	_	O
Each	_	_	O
phone	_	_	B-VAR
requires	_	_	O
2	_	_	B-PARAM
silicon	_	_	O
chips	_	_	O
,	_	_	O
5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
engineering	_	_	O
time	_	_	O
,	_	_	O
and	_	_	O
3	_	_	B-PARAM
hours	_	_	O
of	_	_	O
assembly	_	_	O
time	_	_	O
.	_	_	O
Each	_	_	O
laptop	_	_	B-VAR
requires	_	_	O
4	_	_	B-PARAM
silicon	_	_	O
chips	_	_	O
,	_	_	O
6	_	_	B-PARAM
hours	_	_	O
of	_	_	O
engineering	_	_	O
time	_	_	O
,	_	_	O
and	_	_	O
1	_	_	B-PARAM
hour	_	_	O
of	_	_	O
assembly	_	_	O
time	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
can	_	_	B-CONST_DIR
buy	_	_	I-CONST_DIR
200	_	_	B-LIMIT
silicon	_	_	O
chips	_	_	O
per	_	_	O
week	_	_	O
,	_	_	O
and	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
250	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
engineering	_	_	O
and	_	_	O
300	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
assembly	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
phone	_	_	B-VAR
is	_	_	O
$	_	_	O
300	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
laptop	_	_	B-VAR
is	_	_	O
$	_	_	O
500	_	_	B-PARAM
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
company	_	_	O
's	_	_	O
profit	_	_	B-OBJ_NAME
if	_	_	O
they	_	_	O
want	_	_	O
to	_	_	O
produce	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
units	_	_	O
of	_	_	O
phones	_	_	B-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
units	_	_	O
of	_	_	O
laptops	_	_	B-VAR
each	_	_	O
week	_	_	O
.	_	_	O

A	_	_	O
concert	_	_	O
has	_	_	B-CONST_DIR
300	_	_	B-LIMIT
seats	_	_	O
.	_	_	O
The	_	_	O
premium	_	_	B-VAR
seats	_	_	I-VAR
make	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
150	_	_	B-PARAM
each	_	_	O
and	_	_	O
the	_	_	O
regular	_	_	B-VAR
seats	_	_	I-VAR
make	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
50	_	_	B-PARAM
each	_	_	O
.	_	_	O
At	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
seats	_	_	O
will	_	_	O
be	_	_	O
assigned	_	_	O
as	_	_	O
premium	_	_	B-VAR
seats	_	_	I-VAR
.	_	_	O
On	_	_	O
the	_	_	O
other	_	_	O
hand	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
people	_	_	O
prefer	_	_	O
the	_	_	O
regular	_	_	B-VAR
seats	_	_	I-VAR
to	_	_	O
the	_	_	O
premium	_	_	B-VAR
seats	_	_	I-VAR
.	_	_	O
Find	_	_	O
the	_	_	O
maximum	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
.	_	_	O
Also	_	_	O
,	_	_	O
determine	_	_	O
how	_	_	O
many	_	_	O
seats	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
must	_	_	O
be	_	_	O
sold	_	_	O
to	_	_	O
reach	_	_	O
this	_	_	O
amount	_	_	O
.	_	_	O

Northwest	_	_	O
Golden	_	_	O
Bakery	_	_	O
wishes	_	_	O
to	_	_	O
make	_	_	O
some	_	_	O
cakes	_	_	O
that	_	_	O
have	_	_	O
some	_	_	O
chocolate	_	_	O
and	_	_	O
strawberry	_	_	B-VAR
toppings	_	_	I-VAR
.	_	_	O
Each	_	_	O
chocolate	_	_	B-VAR
topping	_	_	I-VAR
contains	_	_	O
1	_	_	B-PARAM
gram	_	_	O
of	_	_	O
sugar	_	_	O
and	_	_	O
2	_	_	B-PARAM
grams	_	_	O
of	_	_	O
butter	_	_	O
;	_	_	O
each	_	_	O
strawberry	_	_	B-VAR
topping	_	_	I-VAR
contains	_	_	O
0.5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
sugar	_	_	O
and	_	_	O
0.7	_	_	B-PARAM
grams	_	_	O
of	_	_	O
butter	_	_	O
.	_	_	O
For	_	_	O
health	_	_	O
reasons	_	_	O
,	_	_	O
the	_	_	O
cake	_	_	O
will	_	_	O
have	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
5	_	_	B-LIMIT
chocolate	_	_	B-VAR
toppings	_	_	I-VAR
.	_	_	O
To	_	_	O
make	_	_	O
a	_	_	O
tasty	_	_	O
cake	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
sugar	_	_	O
and	_	_	O
15	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
butter	_	_	O
must	_	_	O
be	_	_	O
used	_	_	O
in	_	_	O
the	_	_	O
toppings	_	_	O
of	_	_	O
the	_	_	O
cake	_	_	O
.	_	_	O
If	_	_	O
it	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
2	_	_	B-PARAM
to	_	_	O
make	_	_	O
one	_	_	O
chocolate	_	_	B-VAR
topping	_	_	I-VAR
and	_	_	O
$	_	_	O
3	_	_	B-PARAM
for	_	_	O
one	_	_	O
strawberry	_	_	B-VAR
topping	_	_	I-VAR
,	_	_	O
what	_	_	O
is	_	_	O
the	_	_	O
optimal	_	_	O
combination	_	_	O
of	_	_	O
chocolate	_	_	O
and	_	_	O
strawberry	_	_	B-VAR
toppings	_	_	I-VAR
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
cost	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
food	_	_	O
manufacturer	_	_	O
wishes	_	_	O
to	_	_	O
mix	_	_	O
pork	_	_	B-VAR
and	_	_	O
chicken	_	_	B-VAR
to	_	_	O
create	_	_	O
sausages	_	_	O
.	_	_	O
The	_	_	O
mixture	_	_	O
needs	_	_	O
to	_	_	O
contain	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
units	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
15	_	_	B-LIMIT
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
Pork	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
40	_	_	B-PARAM
per	_	_	O
kg	_	_	O
and	_	_	O
chicken	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
50	_	_	B-PARAM
per	_	_	O
kg	_	_	O
.	_	_	O
Per	_	_	O
kilogram	_	_	O
,	_	_	O
pork	_	_	B-VAR
contains	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
Per	_	_	O
kilogram	_	_	O
,	_	_	O
chicken	_	_	B-VAR
contains	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
Determine	_	_	O
the	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
of	_	_	O
the	_	_	O
mixture	_	_	O
.	_	_	O

A	_	_	O
company	_	_	O
manufactures	_	_	O
two	_	_	O
calculators	_	_	O
:	_	_	O
scientific	_	_	B-VAR
and	_	_	O
graphing	_	_	B-VAR
,	_	_	O
using	_	_	O
silicon	_	_	O
,	_	_	O
plastic	_	_	O
,	_	_	O
and	_	_	O
silver	_	_	O
.	_	_	O
To	_	_	O
make	_	_	O
a	_	_	O
scientific	_	_	B-VAR
calculator	_	_	I-VAR
,	_	_	O
2	_	_	B-PARAM
grams	_	_	O
of	_	_	O
silicon	_	_	O
,	_	_	O
4	_	_	B-PARAM
grams	_	_	O
of	_	_	O
plastic	_	_	O
,	_	_	O
and	_	_	O
1	_	_	B-PARAM
gram	_	_	O
of	_	_	O
silver	_	_	O
are	_	_	O
needed	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
scientific	_	_	B-VAR
calculator	_	_	I-VAR
is	_	_	O
$	_	_	O
6	_	_	B-PARAM
.	_	_	O
To	_	_	O
make	_	_	O
a	_	_	O
graphing	_	_	B-VAR
calculator	_	_	I-VAR
,	_	_	O
4	_	_	B-PARAM
grams	_	_	O
of	_	_	O
silicon	_	_	O
,	_	_	O
6	_	_	B-PARAM
grams	_	_	O
of	_	_	O
plastic	_	_	O
,	_	_	O
and	_	_	O
2	_	_	B-PARAM
grams	_	_	O
of	_	_	O
silver	_	_	O
are	_	_	O
needed	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
graphing	_	_	B-VAR
calculator	_	_	I-VAR
is	_	_	O
$	_	_	O
8	_	_	B-PARAM
.	_	_	O
Even	_	_	O
though	_	_	O
the	_	_	O
company	_	_	O
can	_	_	O
sell	_	_	O
as	_	_	O
many	_	_	O
calculators	_	_	O
as	_	_	O
it	_	_	O
produces	_	_	O
,	_	_	O
there	_	_	O
is	_	_	O
only	_	_	B-CONST_DIR
100	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
silicon	_	_	O
,	_	_	O
200	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
plastic	_	_	O
,	_	_	O
and	_	_	O
50	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
silver	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
wine	_	_	O
company	_	_	O
offers	_	_	O
two	_	_	O
promotion	_	_	O
packages	_	_	O
,	_	_	O
package	_	_	B-VAR
A	_	_	I-VAR
and	_	_	O
package	_	_	B-VAR
B.	_	_	I-VAR
Each	_	_	O
promotion	_	_	O
package	_	_	O
consists	_	_	O
of	_	_	O
some	_	_	O
combination	_	_	O
of	_	_	O
red	_	_	O
and	_	_	O
white	_	_	O
wines	_	_	O
.	_	_	O
Package	_	_	B-VAR
A	_	_	I-VAR
has	_	_	O
2	_	_	B-PARAM
bottles	_	_	O
of	_	_	O
red	_	_	O
wine	_	_	O
and	_	_	O
1	_	_	B-PARAM
bottle	_	_	O
of	_	_	O
white	_	_	O
wine	_	_	O
,	_	_	O
and	_	_	O
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
120	_	_	B-PARAM
.	_	_	O
In	_	_	O
comparison	_	_	O
,	_	_	O
package	_	_	B-VAR
B	_	_	I-VAR
has	_	_	O
2	_	_	B-PARAM
bottles	_	_	O
of	_	_	O
red	_	_	O
wine	_	_	O
and	_	_	O
3	_	_	B-PARAM
bottles	_	_	O
of	_	_	O
white	_	_	O
wine	_	_	O
,	_	_	O
and	_	_	O
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
200	_	_	B-PARAM
.	_	_	O
However	_	_	O
,	_	_	O
the	_	_	O
company	_	_	O
only	_	_	B-CONST_DIR
has	_	_	O
1000	_	_	B-LIMIT
bottles	_	_	O
of	_	_	O
red	_	_	O
wine	_	_	O
and	_	_	O
800	_	_	B-LIMIT
bottles	_	_	O
of	_	_	O
white	_	_	O
wine	_	_	O
.	_	_	O
Find	_	_	O
the	_	_	O
best	_	_	O
mix	_	_	O
of	_	_	O
packages	_	_	O
to	_	_	O
achieve	_	_	O
maximum	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
.	_	_	O

You	_	_	O
have	_	_	O
$	_	_	O
300000	_	_	B-LIMIT
available	_	_	B-CONST_DIR
to	_	_	O
invest	_	_	O
in	_	_	O
a	_	_	O
12	_	_	O
-	_	_	O
month	_	_	O
commitment	_	_	O
.	_	_	O
You	_	_	O
can	_	_	O
either	_	_	O
invest	_	_	O
in	_	_	O
real	_	_	B-VAR
estate	_	_	I-VAR
or	_	_	O
the	_	_	O
pharmaceuticals	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
The	_	_	O
money	_	_	O
placed	_	_	O
in	_	_	O
real	_	_	B-VAR
estate	_	_	I-VAR
yields	_	_	O
a	_	_	O
5	_	_	B-PARAM
%	_	_	I-PARAM
return	_	_	B-OBJ_NAME
,	_	_	O
while	_	_	O
the	_	_	O
money	_	_	O
placed	_	_	O
in	_	_	O
the	_	_	O
pharmaceuticals	_	_	B-VAR
industry	_	_	I-VAR
yields	_	_	O
a	_	_	O
10	_	_	B-PARAM
%	_	_	I-PARAM
return	_	_	B-OBJ_NAME
.	_	_	O
You	_	_	O
have	_	_	O
been	_	_	O
advised	_	_	O
to	_	_	O
place	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
investment	_	_	O
in	_	_	O
real	_	_	B-VAR
estate	_	_	I-VAR
.	_	_	O
Due	_	_	O
to	_	_	O
recent	_	_	O
issues	_	_	O
with	_	_	O
the	_	_	O
pharmaceutical	_	_	O
industry	_	_	O
,	_	_	O
you	_	_	O
have	_	_	O
decided	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
35	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
investment	_	_	O
be	_	_	O
placed	_	_	O
in	_	_	O
the	_	_	O
pharmaceuticals	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
How	_	_	O
much	_	_	O
should	_	_	O
you	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
area	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
your	_	_	O
return	_	_	B-OBJ_NAME
on	_	_	O
investment	_	_	O
?	_	_	O

A	_	_	O
film	_	_	O
agency	_	_	O
wants	_	_	O
to	_	_	O
promote	_	_	O
their	_	_	O
new	_	_	O
movie	_	_	O
.	_	_	O
They	_	_	O
want	_	_	O
to	_	_	O
maximize	_	_	O
the	_	_	O
exposure	_	_	B-OBJ_NAME
with	_	_	O
a	_	_	O
budget	_	_	O
of	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
500000	_	_	B-LIMIT
.	_	_	O
To	_	_	O
do	_	_	O
so	_	_	O
,	_	_	O
the	_	_	O
agency	_	_	O
needs	_	_	O
to	_	_	O
decide	_	_	O
how	_	_	O
much	_	_	O
of	_	_	O
the	_	_	O
budget	_	_	O
to	_	_	O
spend	_	_	O
on	_	_	O
each	_	_	O
of	_	_	O
its	_	_	O
two	_	_	O
most	_	_	O
effective	_	_	O
media	_	_	O
:	_	_	O
(	_	_	O
1	_	_	O
)	_	_	O
social	_	_	B-VAR
media	_	_	I-VAR
adverts	_	_	O
and	_	_	O
(	_	_	O
2	_	_	O
)	_	_	O
magazine	_	_	B-VAR
covers	_	_	I-VAR
.	_	_	O
Each	_	_	O
social	_	_	B-VAR
media	_	_	I-VAR
advert	_	_	O
costs	_	_	O
$	_	_	O
3000	_	_	B-PARAM
;	_	_	O
each	_	_	O
magazine	_	_	B-VAR
cover	_	_	I-VAR
costs	_	_	O
$	_	_	O
6000	_	_	B-PARAM
.	_	_	O
The	_	_	O
agency	_	_	O
director	_	_	O
knows	_	_	O
from	_	_	O
experience	_	_	O
that	_	_	O
it	_	_	O
is	_	_	O
important	_	_	O
to	_	_	O
use	_	_	O
both	_	_	O
media	_	_	O
.	_	_	O
The	_	_	O
movie	_	_	O
exposure	_	_	B-OBJ_NAME
is	_	_	O
100000	_	_	B-PARAM
viewers	_	_	O
for	_	_	O
each	_	_	O
social	_	_	B-VAR
media	_	_	I-VAR
posting	_	_	O
and	_	_	O
54000	_	_	B-PARAM
readers	_	_	O
for	_	_	O
each	_	_	O
magazine	_	_	B-VAR
cover	_	_	I-VAR
.	_	_	O
He	_	_	O
makes	_	_	O
a	_	_	O
decision	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
but	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
20	_	_	B-LIMIT
social	_	_	B-VAR
media	_	_	I-VAR
posts	_	_	O
be	_	_	O
ordered	_	_	O
,	_	_	O
and	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
24	_	_	B-LIMIT
magazine	_	_	B-VAR
covers	_	_	I-VAR
should	_	_	O
be	_	_	O
contracted	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
times	_	_	O
should	_	_	O
each	_	_	O
of	_	_	O
the	_	_	O
two	_	_	O
media	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
obtain	_	_	O
maximum	_	_	B-OBJ_DIR
exposure	_	_	B-OBJ_NAME
while	_	_	O
staying	_	_	O
within	_	_	O
the	_	_	O
budget	_	_	O
?	_	_	O

A	_	_	O
shoe	_	_	O
company	_	_	O
makes	_	_	O
black	_	_	B-VAR
and	_	_	O
blue	_	_	B-VAR
shoes	_	_	I-VAR
.	_	_	O
The	_	_	O
company	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
150	_	_	B-LIMIT
black	_	_	B-VAR
shoes	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
blue	_	_	B-VAR
shoes	_	_	I-VAR
everyday	_	_	O
.	_	_	O
Long	_	_	O
-	_	_	O
term	_	_	O
projections	_	_	O
indicate	_	_	O
an	_	_	O
expected	_	_	O
demand	_	_	O
of	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
75	_	_	B-LIMIT
black	_	_	B-VAR
shoes	_	_	I-VAR
and	_	_	O
60	_	_	B-LIMIT
blue	_	_	B-VAR
shoes	_	_	I-VAR
each	_	_	O
day	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
a	_	_	O
contract	_	_	O
with	_	_	O
a	_	_	O
store	_	_	O
,	_	_	O
and	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
125	_	_	B-LIMIT
shoes	_	_	O
must	_	_	O
be	_	_	O
shipped	_	_	O
each	_	_	O
day	_	_	O
.	_	_	O
If	_	_	O
each	_	_	O
black	_	_	B-VAR
shoe	_	_	I-VAR
sold	_	_	O
results	_	_	O
in	_	_	O
a	_	_	O
$	_	_	O
3	_	_	B-PARAM
loss	_	_	B-OBJ_NAME
,	_	_	O
but	_	_	O
each	_	_	O
blue	_	_	B-VAR
shoe	_	_	I-VAR
sold	_	_	O
results	_	_	O
in	_	_	O
a	_	_	O
$	_	_	O
6	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
shoe	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
daily	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
net	_	_	B-OBJ_NAME
profits	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
computer	_	_	O
network	_	_	O
company	_	_	O
designed	_	_	O
plans	_	_	O
to	_	_	O
bid	_	_	O
for	_	_	O
the	_	_	O
job	_	_	O
of	_	_	O
providing	_	_	O
a	_	_	O
computer	_	_	O
network	_	_	O
for	_	_	O
city	_	_	O
offices	_	_	O
.	_	_	O
He	_	_	O
will	_	_	O
use	_	_	O
workstations	_	_	O
,	_	_	O
servers	_	_	O
,	_	_	O
and	_	_	O
switches	_	_	O
in	_	_	O
three	_	_	O
types	_	_	O
of	_	_	O
layouts	_	_	O
.	_	_	O
He	_	_	O
has	_	_	B-CONST_DIR
3000	_	_	B-LIMIT
workstations	_	_	O
,	_	_	O
400	_	_	B-LIMIT
servers	_	_	O
,	_	_	O
and	_	_	O
200	_	_	B-LIMIT
switches	_	_	O
.	_	_	O
A	_	_	O
star	_	_	B-VAR
layout	_	_	I-VAR
uses	_	_	O
40	_	_	B-PARAM
workstations	_	_	O
,	_	_	O
10	_	_	B-PARAM
servers	_	_	O
,	_	_	O
and	_	_	O
2	_	_	B-PARAM
switches	_	_	O
;	_	_	O
a	_	_	O
circle	_	_	B-VAR
layout	_	_	I-VAR
uses	_	_	O
20	_	_	B-PARAM
workstations	_	_	O
,	_	_	O
12	_	_	B-PARAM
servers	_	_	O
,	_	_	O
and	_	_	O
5	_	_	B-PARAM
switches	_	_	O
;	_	_	O
and	_	_	O
a	_	_	O
snowflake	_	_	B-VAR
layout	_	_	I-VAR
uses	_	_	O
323	_	_	B-PARAM
workstations	_	_	O
,	_	_	O
122	_	_	B-PARAM
servers	_	_	O
,	_	_	O
and	_	_	O
41	_	_	B-PARAM
switches	_	_	O
.	_	_	O
The	_	_	O
net	_	_	O
profit	_	_	B-OBJ_NAME
is	_	_	O
$	_	_	O
2231	_	_	B-PARAM
for	_	_	O
each	_	_	O
star	_	_	B-VAR
layout	_	_	I-VAR
,	_	_	O
$	_	_	O
3434	_	_	B-PARAM
for	_	_	O
each	_	_	O
circle	_	_	B-VAR
layout	_	_	I-VAR
,	_	_	O
and	_	_	O
$	_	_	O
8621	_	_	B-PARAM
for	_	_	O
each	_	_	O
snowflake	_	_	B-VAR
layout	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
layouts	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
yield	_	_	O
maximum	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Avian	_	_	O
cosmetics	_	_	O
makes	_	_	O
luxury	_	_	O
beauty	_	_	O
products	_	_	O
whose	_	_	O
main	_	_	O
customers	_	_	O
are	_	_	O
wealthy	_	_	O
women	_	_	O
,	_	_	O
both	_	_	O
young	_	_	O
girls	_	_	O
and	_	_	O
middle	_	_	O
-	_	_	O
aged	_	_	O
women	_	_	O
.	_	_	O
In	_	_	O
order	_	_	O
to	_	_	O
promote	_	_	O
their	_	_	O
product	_	_	O
line	_	_	O
,	_	_	O
they	_	_	O
decided	_	_	O
to	_	_	O
invest	_	_	O
in	_	_	O
short	_	_	O
commercial	_	_	O
spots	_	_	O
on	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
programs	_	_	O
:	_	_	O
concerts	_	_	B-VAR
and	_	_	O
cinema	_	_	B-VAR
.	_	_	O
While	_	_	O
each	_	_	O
concert	_	_	B-VAR
commercial	_	_	I-VAR
is	_	_	O
seen	_	_	O
by	_	_	O
9	_	_	B-PARAM
million	_	_	O
young	_	_	O
girls	_	_	O
and	_	_	O
4	_	_	B-PARAM
million	_	_	O
middle	_	_	O
-	_	_	O
aged	_	_	O
women	_	_	O
,	_	_	O
each	_	_	O
cinema	_	_	B-VAR
commercial	_	_	I-VAR
is	_	_	O
seen	_	_	O
by	_	_	O
5	_	_	B-PARAM
million	_	_	O
young	_	_	O
girls	_	_	O
and	_	_	O
45	_	_	B-PARAM
million	_	_	O
middle	_	_	O
-	_	_	O
aged	_	_	O
women	_	_	O
.	_	_	O
A	_	_	O
1	_	_	O
-	_	_	O
minute	_	_	O
concert	_	_	B-VAR
ad	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
80,000	_	_	B-PARAM
,	_	_	O
and	_	_	O
a	_	_	O
1	_	_	O
-	_	_	O
minute	_	_	O
cinema	_	_	B-VAR
ad	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
30,000	_	_	B-PARAM
.	_	_	O
Avian	_	_	O
would	_	_	O
like	_	_	O
the	_	_	O
commercials	_	_	O
to	_	_	O
be	_	_	O
seen	_	_	O
by	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
86	_	_	B-LIMIT
million	_	_	O
young	_	_	O
girls	_	_	O
and	_	_	O
72	_	_	B-LIMIT
million	_	_	O
middle	_	_	O
-	_	_	O
aged	_	_	O
women	_	_	O
.	_	_	O
Use	_	_	O
linear	_	_	O
programming	_	_	O
to	_	_	O
determine	_	_	O
how	_	_	O
Avian	_	_	O
cosmetics	_	_	O
can	_	_	O
meet	_	_	O
its	_	_	O
advertising	_	_	O
requirements	_	_	O
at	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
.	_	_	O

An	_	_	O
ice	_	_	O
cream	_	_	O
bar	_	_	O
sells	_	_	O
vanilla	_	_	B-VAR
and	_	_	O
chocolate	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
cones	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
cone	_	_	O
of	_	_	O
vanilla	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
is	_	_	O
$	_	_	O
2	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
cone	_	_	O
of	_	_	O
chocolate	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
.	_	_	O
The	_	_	O
ice	_	_	O
cream	_	_	O
bar	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
lest	_	_	I-CONST_DIR
20	_	_	B-LIMIT
cones	_	_	O
of	_	_	O
vanilla	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
but	_	_	O
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
make	_	_	I-CONST_DIR
more	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
50	_	_	B-LIMIT
cones	_	_	O
.	_	_	O
It	_	_	O
must	_	_	O
also	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
25	_	_	B-LIMIT
cones	_	_	O
of	_	_	O
chocolate	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
but	_	_	O
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
make	_	_	I-CONST_DIR
more	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
60	_	_	B-LIMIT
cones	_	_	O
.	_	_	O
In	_	_	O
total	_	_	O
,	_	_	O
the	_	_	O
ice	_	_	O
cream	_	_	O
bar	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
80	_	_	B-LIMIT
cones	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
cones	_	_	O
of	_	_	O
each	_	_	O
flavor	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
store	_	_	O
sells	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
donuts	_	_	O
,	_	_	O
regular	_	_	B-VAR
and	_	_	O
jelly	_	_	B-VAR
-	_	_	I-VAR
filled	_	_	I-VAR
.	_	_	O
The	_	_	O
store	_	_	O
pays	_	_	O
a	_	_	O
baker	_	_	O
$	_	_	O
4	_	_	B-PARAM
and	_	_	O
$	_	_	O
6	_	_	B-PARAM
for	_	_	O
each	_	_	O
unit	_	_	O
of	_	_	O
a	_	_	O
regular	_	_	B-VAR
and	_	_	O
jelly	_	_	B-VAR
-	_	_	I-VAR
filled	_	_	I-VAR
donut	_	_	I-VAR
respectively	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
makes	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
2	_	_	B-PARAM
per	_	_	O
regular	_	_	B-VAR
donut	_	_	I-VAR
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
3	_	_	B-PARAM
per	_	_	O
jelly	_	_	B-VAR
-	_	_	I-VAR
filled	_	_	I-VAR
donut	_	_	I-VAR
.	_	_	O
In	_	_	O
a	_	_	O
month	_	_	O
,	_	_	O
the	_	_	O
store	_	_	O
owner	_	_	O
expects	_	_	O
to	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
1000	_	_	B-LIMIT
donuts	_	_	O
and	_	_	O
wants	_	_	O
to	_	_	O
spend	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
5000	_	_	B-LIMIT
in	_	_	O
buying	_	_	O
donuts	_	_	O
from	_	_	O
the	_	_	O
bakery	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
donut	_	_	O
should	_	_	O
be	_	_	O
bought	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
monthly	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

There	_	_	O
is	_	_	O
only	_	_	B-CONST_DIR
5000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
a	_	_	O
rare	_	_	O
flower	_	_	O
extract	_	_	O
needed	_	_	O
to	_	_	O
make	_	_	O
both	_	_	O
youth	_	_	B-VAR
and	_	_	O
adult	_	_	B-VAR
doses	_	_	I-VAR
.	_	_	O
Youth	_	_	B-VAR
doses	_	_	I-VAR
contain	_	_	O
20	_	_	B-PARAM
grams	_	_	O
of	_	_	O
extract	_	_	O
and	_	_	O
adult	_	_	B-VAR
doses	_	_	I-VAR
contain	_	_	O
35	_	_	B-PARAM
grams	_	_	O
.	_	_	O
Demand	_	_	O
is	_	_	O
such	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
three	_	_	B-LIMIT
times	_	_	O
as	_	_	O
many	_	_	O
youth	_	_	B-VAR
doses	_	_	I-VAR
are	_	_	O
needed	_	_	O
than	_	_	O
the	_	_	O
adult	_	_	B-VAR
doses	_	_	I-VAR
.	_	_	O
A	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
10	_	_	B-LIMIT
adult	_	_	B-VAR
doses	_	_	I-VAR
need	_	_	O
to	_	_	O
be	_	_	O
made	_	_	O
.	_	_	O
Youth	_	_	B-VAR
doses	_	_	I-VAR
are	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
5	_	_	B-PARAM
while	_	_	O
adult	_	_	B-VAR
doses	_	_	I-VAR
are	_	_	O
sold	_	_	O
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
3	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
dose	_	_	O
should	_	_	O
be	_	_	O
prepared	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
clothing	_	_	O
designer	_	_	O
manufactures	_	_	O
three	_	_	O
dresses	_	_	O
:	_	_	O
long	_	_	O
,	_	_	O
short	_	_	O
,	_	_	O
and	_	_	O
mini	_	_	O
.	_	_	O
These	_	_	O
dresses	_	_	O
are	_	_	O
produced	_	_	O
in	_	_	O
two	_	_	O
different	_	_	O
factories	_	_	O
:	_	_	O
a	_	_	O
local	_	_	O
one	_	_	O
,	_	_	O
and	_	_	O
a	_	_	O
foreign	_	_	O
one	_	_	O
.	_	_	O
Running	_	_	O
the	_	_	O
local	_	_	B-VAR
factory	_	_	I-VAR
for	_	_	O
an	_	_	O
hour	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
600	_	_	B-PARAM
and	_	_	O
produces	_	_	O
23	_	_	B-PARAM
long	_	_	O
dresses	_	_	O
,	_	_	O
11	_	_	B-PARAM
short	_	_	O
dresses	_	_	O
,	_	_	O
and	_	_	O
13	_	_	B-PARAM
mini	_	_	B-VAR
dresses	_	_	I-VAR
.	_	_	O
Running	_	_	O
the	_	_	O
foreign	_	_	B-VAR
factory	_	_	I-VAR
for	_	_	O
an	_	_	O
hour	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
300	_	_	B-PARAM
and	_	_	O
yields	_	_	O
15	_	_	B-PARAM
long	_	_	O
dresses	_	_	O
,	_	_	O
30	_	_	B-PARAM
short	_	_	O
dresses	_	_	O
,	_	_	O
and	_	_	O
15	_	_	B-PARAM
mini	_	_	B-VAR
dresses	_	_	I-VAR
.	_	_	O
To	_	_	O
meet	_	_	O
customer	_	_	O
demands	_	_	O
,	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
74	_	_	B-LIMIT
long	_	_	O
dresses	_	_	O
,	_	_	O
34	_	_	B-LIMIT
short	_	_	O
dresses	_	_	O
,	_	_	O
and	_	_	O
26	_	_	B-LIMIT
mini	_	_	O
dresses	_	_	O
must	_	_	O
be	_	_	O
produced	_	_	O
daily	_	_	O
.	_	_	O
Graphically	_	_	O
determine	_	_	O
a	_	_	O
daily	_	_	O
production	_	_	O
plan	_	_	O
that	_	_	O
minimizes	_	_	B-OBJ_DIR
the	_	_	O
cost	_	_	B-OBJ_NAME
of	_	_	O
meeting	_	_	O
the	_	_	O
clothing	_	_	O
designer	_	_	O
’s	_	_	O
daily	_	_	O
demands	_	_	O
.	_	_	O

A	_	_	O
store	_	_	O
manufactures	_	_	O
2	_	_	O
types	_	_	O
of	_	_	O
tools	_	_	O
,	_	_	O
hammers	_	_	B-VAR
and	_	_	O
screwdrivers	_	_	B-VAR
,	_	_	O
which	_	_	O
require	_	_	O
the	_	_	O
use	_	_	O
of	_	_	O
two	_	_	O
machines	_	_	O
,	_	_	O
a	_	_	O
lathe	_	_	O
and	_	_	O
a	_	_	O
CNG	_	_	O
.	_	_	O
It	_	_	O
takes	_	_	O
28	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
lathe	_	_	O
and	_	_	O
82	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
CNG	_	_	O
machine	_	_	O
to	_	_	O
manufacture	_	_	O
a	_	_	O
package	_	_	O
of	_	_	O
hammers	_	_	B-VAR
,	_	_	O
while	_	_	O
it	_	_	O
takes	_	_	O
23	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
lathe	_	_	O
and	_	_	O
76	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
CNG	_	_	O
machine	_	_	O
to	_	_	O
manufacture	_	_	O
a	_	_	O
package	_	_	O
of	_	_	O
screwdrivers	_	_	B-VAR
.	_	_	O
Each	_	_	O
machine	_	_	O
is	_	_	O
available	_	_	O
for	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
720	_	_	B-LIMIT
minutes	_	_	O
on	_	_	O
any	_	_	O
day	_	_	O
.	_	_	O
The	_	_	O
manufacturer	_	_	O
can	_	_	O
sell	_	_	O
a	_	_	O
package	_	_	O
of	_	_	O
hammers	_	_	B-VAR
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
72	_	_	B-PARAM
and	_	_	O
a	_	_	O
package	_	_	O
of	_	_	O
screwdrivers	_	_	B-VAR
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
70	_	_	B-PARAM
.	_	_	O
Assuming	_	_	O
that	_	_	O
he	_	_	O
can	_	_	O
sell	_	_	O
all	_	_	O
the	_	_	O
tools	_	_	O
he	_	_	O
manufactures	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
packages	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
the	_	_	O
store	_	_	O
owner	_	_	O
produce	_	_	O
in	_	_	O
a	_	_	O
day	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O
Determine	_	_	O
the	_	_	O
maximum	_	_	O
profit	_	_	O
.	_	_	O

A	_	_	O
gardener	_	_	O
has	_	_	B-CONST_DIR
a	_	_	O
field	_	_	O
of	_	_	O
100	_	_	B-LIMIT
square	_	_	O
feet	_	_	O
in	_	_	O
which	_	_	O
he	_	_	O
plants	_	_	O
sunflowers	_	_	B-VAR
and	_	_	O
roses	_	_	B-VAR
.	_	_	O
The	_	_	O
seed	_	_	O
for	_	_	O
sunflowers	_	_	B-VAR
costs	_	_	O
$	_	_	O
67	_	_	B-PARAM
per	_	_	O
square	_	_	O
foot	_	_	O
.	_	_	O
The	_	_	O
seed	_	_	O
for	_	_	O
roses	_	_	B-VAR
costs	_	_	O
$	_	_	O
52	_	_	B-PARAM
per	_	_	O
square	_	_	O
foot	_	_	O
.	_	_	O
The	_	_	O
gardener	_	_	O
has	_	_	O
available	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
6500	_	_	B-LIMIT
to	_	_	O
spend	_	_	O
on	_	_	O
seeds	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
square	_	_	O
foot	_	_	O
of	_	_	O
sunflowers	_	_	B-VAR
is	_	_	O
$	_	_	O
450	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
square	_	_	O
foot	_	_	O
of	_	_	O
roses	_	_	B-VAR
is	_	_	O
$	_	_	O
100	_	_	B-PARAM
.	_	_	O
Find	_	_	O
the	_	_	O
optimal	_	_	O
solution	_	_	O
for	_	_	O
the	_	_	O
gardener	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
fashion	_	_	O
company	_	_	O
makes	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
bags	_	_	O
:	_	_	O
hand	_	_	B-VAR
-	_	_	I-VAR
bags	_	_	I-VAR
and	_	_	O
backpacks	_	_	B-VAR
.	_	_	O
Each	_	_	O
hand	_	_	B-VAR
-	_	_	I-VAR
bag	_	_	I-VAR
requires	_	_	O
6	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
sewing	_	_	O
while	_	_	O
each	_	_	O
backpack	_	_	B-VAR
requires	_	_	O
7	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
sewing	_	_	O
.	_	_	O
Each	_	_	O
hand	_	_	B-VAR
-	_	_	I-VAR
bag	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
painting	_	_	O
while	_	_	O
each	_	_	O
backpack	_	_	B-VAR
requires	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
painting	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
400	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
sewing	_	_	O
and	_	_	O
600	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
painting	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
hand	_	_	B-VAR
-	_	_	I-VAR
bag	_	_	I-VAR
is	_	_	O
$	_	_	O
75	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
backpack	_	_	B-VAR
is	_	_	O
$	_	_	O
60	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
bag	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
make	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
young	_	_	O
boy	_	_	O
is	_	_	O
trying	_	_	O
to	_	_	O
gain	_	_	O
weight	_	_	O
and	_	_	O
put	_	_	O
muscle	_	_	O
.	_	_	O
He	_	_	O
can	_	_	O
eat	_	_	O
both	_	_	O
tuna	_	_	B-VAR
salad	_	_	I-VAR
sandwiches	_	_	I-VAR
and	_	_	O
chicken	_	_	B-VAR
salad	_	_	I-VAR
sandwiches	_	_	I-VAR
.	_	_	O
He	_	_	O
wants	_	_	O
to	_	_	O
get	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
100	_	_	B-LIMIT
units	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
150	_	_	B-LIMIT
units	_	_	O
of	_	_	O
fat	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
A	_	_	O
tuna	_	_	B-VAR
salad	_	_	I-VAR
sandwich	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
contains	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
25	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
A	_	_	O
chicken	_	_	B-VAR
salad	_	_	I-VAR
sandwich	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
7	_	_	B-PARAM
and	_	_	O
contains	_	_	O
25	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
eat	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
cost	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
tropical	_	_	O
farmer	_	_	O
has	_	_	B-CONST_DIR
200	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
to	_	_	O
grow	_	_	O
mangoes	_	_	B-VAR
and	_	_	O
pineapples	_	_	B-VAR
.	_	_	O
Each	_	_	O
acre	_	_	O
of	_	_	O
mangoes	_	_	B-VAR
costs	_	_	O
$	_	_	O
80	_	_	B-PARAM
for	_	_	O
nutrients	_	_	O
and	_	_	O
takes	_	_	O
2	_	_	B-PARAM
hours	_	_	O
for	_	_	O
picking	_	_	O
.	_	_	O
Each	_	_	O
acre	_	_	O
of	_	_	O
pineapples	_	_	B-VAR
costs	_	_	O
$	_	_	O
100	_	_	B-PARAM
for	_	_	O
nutrients	_	_	O
and	_	_	O
takes	_	_	O
1.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
picking	_	_	O
.	_	_	O
The	_	_	O
farmer	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
$	_	_	O
18000	_	_	B-LIMIT
to	_	_	O
spend	_	_	O
on	_	_	O
nutrients	_	_	O
and	_	_	O
350	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
picking	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
mangos	_	_	B-VAR
is	_	_	O
$	_	_	O
400	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
pineapples	_	_	B-VAR
is	_	_	O
$	_	_	O
450	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
grown	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
meat	_	_	O
factory	_	_	O
makes	_	_	O
burgers	_	_	B-VAR
and	_	_	O
hot	_	_	B-VAR
-	_	_	I-VAR
dogs	_	_	I-VAR
.	_	_	O
Each	_	_	O
burger	_	_	B-VAR
requires	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
meat	_	_	O
and	_	_	O
2	_	_	B-PARAM
unit	_	_	O
of	_	_	O
binding	_	_	O
agent	_	_	O
.	_	_	O
Each	_	_	O
hot	_	_	B-VAR
-	_	_	I-VAR
dog	_	_	I-VAR
requires	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
meat	_	_	O
and	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
binding	_	_	O
agent	_	_	O
.	_	_	O
The	_	_	O
factory	_	_	O
has	_	_	O
2000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
meat	_	_	O
and	_	_	O
1800	_	_	B-LIMIT
units	_	_	O
of	_	_	O
binding	_	_	O
agent	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
If	_	_	O
the	_	_	O
revenue	_	_	B-OBJ_NAME
per	_	_	O
burger	_	_	B-VAR
made	_	_	O
is	_	_	O
$	_	_	O
0.30	_	_	B-PARAM
and	_	_	O
the	_	_	O
revenue	_	_	B-OBJ_NAME
per	_	_	O
hot	_	_	B-VAR
-	_	_	I-VAR
dog	_	_	I-VAR
made	_	_	O
is	_	_	O
$	_	_	O
0.20	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
revenue	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
mattress	_	_	O
company	_	_	O
makes	_	_	O
queen	_	_	B-VAR
and	_	_	O
king	_	_	B-VAR
sized	_	_	O
mattresses	_	_	O
.	_	_	O
Queen	_	_	B-VAR
size	_	_	I-VAR
mattresses	_	_	I-VAR
require	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
foam	_	_	O
while	_	_	O
king	_	_	B-VAR
size	_	_	I-VAR
mattresses	_	_	I-VAR
require	_	_	O
30	_	_	B-PARAM
units	_	_	O
of	_	_	O
foam	_	_	O
.	_	_	O
Queen	_	_	B-VAR
size	_	_	I-VAR
mattresses	_	_	I-VAR
take	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
package	_	_	O
while	_	_	O
king	_	_	B-VAR
size	_	_	I-VAR
mattresses	_	_	I-VAR
take	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
package	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
5000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
foam	_	_	O
available	_	_	B-CONST_DIR
and	_	_	O
2500	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
packaging	_	_	O
time	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
queen	_	_	B-VAR
mattress	_	_	I-VAR
is	_	_	O
$	_	_	O
300	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
king	_	_	B-VAR
mattress	_	_	I-VAR
is	_	_	O
$	_	_	O
500	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
pottery	_	_	O
artist	_	_	O
makes	_	_	O
mugs	_	_	B-VAR
and	_	_	O
bowls	_	_	B-VAR
from	_	_	O
clay	_	_	O
.	_	_	O
Each	_	_	O
mug	_	_	B-VAR
takes	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
make	_	_	O
while	_	_	O
each	_	_	O
bowl	_	_	B-VAR
takes	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
make	_	_	O
.	_	_	O
In	_	_	O
a	_	_	O
week	_	_	O
,	_	_	O
the	_	_	O
artist	_	_	O
only	_	_	O
has	_	_	O
1200	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
to	_	_	O
do	_	_	O
pottery	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
he	_	_	O
only	_	_	O
has	_	_	O
enough	_	_	O
clay	_	_	O
to	_	_	O
make	_	_	O
50	_	_	B-LIMIT
items	_	_	O
total	_	_	B-CONST_DIR
.	_	_	O
If	_	_	O
he	_	_	O
makes	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
10	_	_	B-PARAM
per	_	_	O
mug	_	_	B-VAR
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
15	_	_	B-PARAM
per	_	_	O
bowl	_	_	B-VAR
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
game	_	_	O
involves	_	_	O
throwing	_	_	O
red	_	_	B-VAR
bean	_	_	I-VAR
bags	_	_	I-VAR
and	_	_	O
blue	_	_	B-VAR
bean	_	_	I-VAR
bags	_	_	I-VAR
at	_	_	O
a	_	_	O
target	_	_	O
.	_	_	O
Each	_	_	O
red	_	_	B-VAR
bean	_	_	I-VAR
bag	_	_	I-VAR
that	_	_	O
hits	_	_	O
the	_	_	O
target	_	_	O
is	_	_	O
worth	_	_	O
5	_	_	B-PARAM
points	_	_	B-OBJ_NAME
and	_	_	O
each	_	_	O
blue	_	_	B-VAR
bean	_	_	I-VAR
bag	_	_	I-VAR
that	_	_	O
hits	_	_	O
the	_	_	O
target	_	_	O
is	_	_	O
worth	_	_	O
8	_	_	B-PARAM
points	_	_	B-OBJ_NAME
.	_	_	O
You	_	_	O
must	_	_	O
throw	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-LIMIT
red	_	_	B-VAR
bean	_	_	I-VAR
bags	_	_	I-VAR
and	_	_	O
2	_	_	B-LIMIT
blue	_	_	B-VAR
bean	_	_	I-VAR
bags	_	_	I-VAR
,	_	_	O
but	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
8	_	_	B-LIMIT
of	_	_	O
either	_	_	O
type	_	_	O
.	_	_	O
In	_	_	O
total	_	_	B-CONST_DIR
,	_	_	O
you	_	_	O
must	_	_	O
throw	_	_	O
12	_	_	B-LIMIT
bean	_	_	O
bags	_	_	O
.	_	_	O
Assuming	_	_	O
you	_	_	O
always	_	_	O
hit	_	_	O
the	_	_	O
target	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
color	_	_	O
bean	_	_	O
bag	_	_	O
should	_	_	O
you	_	_	O
throw	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
your	_	_	O
points	_	_	B-OBJ_NAME
?	_	_	O

In	_	_	O
a	_	_	O
video	_	_	O
game	_	_	O
,	_	_	O
George	_	_	O
has	_	_	B-CONST_DIR
to	_	_	I-CONST_DIR
collect	_	_	I-CONST_DIR
50	_	_	B-LIMIT
units	_	_	O
of	_	_	O
wood	_	_	O
and	_	_	O
60	_	_	B-LIMIT
units	_	_	O
of	_	_	O
metal	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
two	_	_	O
areas	_	_	O
.	_	_	O
area	_	_	B-VAR
one	_	_	I-VAR
and	_	_	O
area	_	_	B-VAR
two	_	_	I-VAR
,	_	_	O
where	_	_	O
he	_	_	O
can	_	_	O
find	_	_	O
these	_	_	O
resources	_	_	O
.	_	_	O
For	_	_	O
each	_	_	O
hour	_	_	O
in	_	_	O
area	_	_	B-VAR
one	_	_	I-VAR
that	_	_	O
he	_	_	O
spends	_	_	O
,	_	_	O
he	_	_	O
gets	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
wood	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
metal	_	_	O
.	_	_	O
For	_	_	O
each	_	_	O
hour	_	_	O
in	_	_	O
area	_	_	B-VAR
two	_	_	I-VAR
that	_	_	O
he	_	_	O
spends	_	_	O
,	_	_	O
he	_	_	O
gets	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
wood	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
metal	_	_	O
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
time	_	_	I-OBJ_NAME
spent	_	_	O
in	_	_	O
both	_	_	O
areas	_	_	O
.	_	_	O

A	_	_	O
furniture	_	_	O
store	_	_	O
stocks	_	_	O
couches	_	_	B-VAR
and	_	_	O
beds	_	_	B-VAR
.	_	_	O
Each	_	_	O
couch	_	_	B-VAR
takes	_	_	O
15	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
of	_	_	O
space	_	_	O
while	_	_	O
each	_	_	O
bed	_	_	B-VAR
takes	_	_	O
20	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
of	_	_	O
space	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
a	_	_	O
total	_	_	O
of	_	_	O
300	_	_	B-LIMIT
sq	_	_	O
ft	_	_	O
of	_	_	O
space	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
Based	_	_	O
on	_	_	O
past	_	_	O
seasons	_	_	O
,	_	_	O
the	_	_	O
store	_	_	O
makes	_	_	O
sure	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
50	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
all	_	_	O
items	_	_	O
in	_	_	O
stock	_	_	O
are	_	_	O
beds	_	_	B-VAR
.	_	_	O
In	_	_	O
terms	_	_	O
of	_	_	O
capital	_	_	O
,	_	_	O
the	_	_	O
store	_	_	O
wants	_	_	O
to	_	_	O
spend	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
8000	_	_	B-LIMIT
.	_	_	O
Each	_	_	O
couch	_	_	B-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
300	_	_	B-PARAM
and	_	_	O
each	_	_	O
bed	_	_	B-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
600	_	_	B-PARAM
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
couch	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
bed	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
400	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
stocked	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
small	_	_	O
family	_	_	O
business	_	_	O
makes	_	_	O
homemade	_	_	O
strawberry	_	_	B-VAR
jam	_	_	I-VAR
and	_	_	O
peach	_	_	B-VAR
jam	_	_	I-VAR
.	_	_	O
It	_	_	O
takes	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
make	_	_	O
one	_	_	O
bottle	_	_	O
of	_	_	O
strawberry	_	_	B-VAR
jam	_	_	I-VAR
and	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
make	_	_	O
one	_	_	O
bottle	_	_	O
of	_	_	O
peach	_	_	B-VAR
jam	_	_	I-VAR
.	_	_	O
The	_	_	O
family	_	_	O
business	_	_	O
only	_	_	B-CONST_DIR
operates	_	_	O
for	_	_	O
3500	_	_	B-LIMIT
minutes	_	_	O
per	_	_	O
week	_	_	O
.	_	_	O
Due	_	_	O
to	_	_	O
fruit	_	_	O
availability	_	_	O
,	_	_	O
they	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
bottles	_	_	O
of	_	_	O
strawberry	_	_	B-VAR
jam	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
80	_	_	B-LIMIT
bottles	_	_	O
of	_	_	O
peach	_	_	B-VAR
jam	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
bottle	_	_	O
of	_	_	O
strawberry	_	_	B-VAR
jam	_	_	I-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
bottle	_	_	O
of	_	_	O
peach	_	_	B-VAR
jam	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
bottles	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
their	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
lighting	_	_	O
company	_	_	O
makes	_	_	O
glass	_	_	B-VAR
and	_	_	O
brass	_	_	B-VAR
chandeliers	_	_	O
.	_	_	O
Each	_	_	O
glass	_	_	B-VAR
chandelier	_	_	I-VAR
takes	_	_	O
2	_	_	B-PARAM
hours	_	_	O
for	_	_	O
crafting	_	_	O
and	_	_	O
1	_	_	B-PARAM
hour	_	_	O
for	_	_	O
installation	_	_	O
.	_	_	O
Each	_	_	O
brass	_	_	B-VAR
chandelier	_	_	I-VAR
takes	_	_	O
1.5	_	_	B-PARAM
hours	_	_	O
for	_	_	O
crafting	_	_	O
and	_	_	O
0.75	_	_	B-PARAM
hours	_	_	O
for	_	_	O
installation	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
750	_	_	B-LIMIT
hours	_	_	O
for	_	_	O
crafting	_	_	O
and	_	_	O
500	_	_	B-LIMIT
hours	_	_	O
for	_	_	O
installation	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
glass	_	_	B-VAR
chandelier	_	_	I-VAR
is	_	_	O
$	_	_	O
400	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
brass	_	_	B-VAR
chandelier	_	_	I-VAR
is	_	_	O
$	_	_	O
300	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
craft	_	_	O
and	_	_	O
install	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
stationary	_	_	O
store	_	_	O
sells	_	_	O
pens	_	_	B-VAR
and	_	_	O
pencils	_	_	B-VAR
.	_	_	O
Each	_	_	O
pen	_	_	B-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
2	_	_	B-PARAM
and	_	_	O
each	_	_	O
pencil	_	_	B-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
1	_	_	B-PARAM
.	_	_	O
The	_	_	O
store	_	_	O
owner	_	_	O
can	_	_	O
spend	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
500	_	_	B-LIMIT
on	_	_	O
inventory	_	_	O
.	_	_	O
Each	_	_	O
pen	_	_	B-VAR
is	_	_	O
then	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
3	_	_	B-PARAM
while	_	_	O
each	_	_	O
pencil	_	_	B-VAR
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
1	_	_	B-PARAM
.	_	_	O
The	_	_	O
owner	_	_	O
estimates	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
pens	_	_	B-VAR
but	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
150	_	_	B-LIMIT
pens	_	_	B-VAR
are	_	_	O
sold	_	_	O
each	_	_	O
month	_	_	O
.	_	_	O
He	_	_	O
also	_	_	O
estimate	_	_	O
that	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
pencils	_	_	B-VAR
sold	_	_	O
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
twice	_	_	B-PARAM
the	_	_	O
amount	_	_	O
of	_	_	O
pens	_	_	B-VAR
sold	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
bought	_	_	O
and	_	_	O
sold	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
man	_	_	O
drinks	_	_	O
two	_	_	O
energy	_	_	O
drinks	_	_	O
to	_	_	O
get	_	_	O
his	_	_	O
daily	_	_	O
caffeine	_	_	O
and	_	_	O
water	_	_	O
requirements	_	_	O
.	_	_	O
A	_	_	O
can	_	_	O
of	_	_	O
energy	_	_	B-VAR
drink	_	_	I-VAR
R	_	_	I-VAR
contains	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
caffeine	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	O
.	_	_	O
A	_	_	O
can	_	_	O
of	_	_	O
energy	_	_	B-VAR
drink	_	_	I-VAR
M	_	_	I-VAR
contains	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
caffeine	_	_	O
and	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	O
.	_	_	O
The	_	_	O
man	_	_	O
needs	_	_	O
to	_	_	O
get	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
30	_	_	B-LIMIT
units	_	_	O
of	_	_	O
caffeine	_	_	O
and	_	_	O
50	_	_	B-LIMIT
units	_	_	O
of	_	_	O
water	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
can	_	_	O
of	_	_	O
energy	_	_	B-VAR
drink	_	_	I-VAR
R	_	_	I-VAR
is	_	_	O
$	_	_	O
4	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
can	_	_	O
of	_	_	O
energy	_	_	B-VAR
drink	_	_	I-VAR
M	_	_	I-VAR
is	_	_	O
$	_	_	O
7	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
cans	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
buy	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
fitness	_	_	O
company	_	_	O
sells	_	_	O
and	_	_	O
installs	_	_	O
treadmills	_	_	B-VAR
and	_	_	O
stationary	_	_	B-VAR
bikes	_	_	I-VAR
.	_	_	O
Each	_	_	O
treadmill	_	_	B-VAR
takes	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
mover	_	_	O
time	_	_	O
and	_	_	O
50	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
setup	_	_	O
time	_	_	O
.	_	_	O
Each	_	_	O
stationary	_	_	B-VAR
bike	_	_	I-VAR
takes	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
mover	_	_	O
time	_	_	O
and	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
setup	_	_	O
time	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
10000	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
mover	_	_	O
time	_	_	O
and	_	_	O
15000	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
setup	_	_	O
time	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
treadmill	_	_	B-VAR
is	_	_	O
$	_	_	O
300	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
stationary	_	_	B-VAR
bike	_	_	I-VAR
is	_	_	O
$	_	_	O
120	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
sell	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
bagel	_	_	O
company	_	_	O
has	_	_	O
two	_	_	O
bakeries	_	_	O
,	_	_	O
an	_	_	O
Eastside	_	_	B-VAR
bakery	_	_	I-VAR
and	_	_	O
a	_	_	O
Westside	_	_	B-VAR
bakery	_	_	I-VAR
.	_	_	O
The	_	_	O
Eastside	_	_	B-VAR
bakery	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
300	_	_	B-PARAM
to	_	_	O
run	_	_	O
for	_	_	O
1	_	_	O
hour	_	_	O
while	_	_	O
the	_	_	O
Westside	_	_	B-VAR
bakery	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
500	_	_	B-PARAM
to	_	_	O
run	_	_	O
for	_	_	O
1	_	_	O
hour	_	_	O
.	_	_	O
In	_	_	O
an	_	_	O
hour	_	_	O
,	_	_	O
the	_	_	O
Eastside	_	_	B-VAR
bakery	_	_	I-VAR
yields	_	_	O
100	_	_	B-PARAM
everything	_	_	O
bagels	_	_	O
,	_	_	O
80	_	_	B-PARAM
blueberry	_	_	O
bagels	_	_	O
,	_	_	O
and	_	_	O
30	_	_	B-PARAM
regular	_	_	O
bagels	_	_	O
.	_	_	O
In	_	_	O
an	_	_	O
hour	_	_	O
,	_	_	O
the	_	_	O
Westside	_	_	B-VAR
bakery	_	_	I-VAR
yields	_	_	O
50	_	_	B-PARAM
everything	_	_	O
bagels	_	_	O
,	_	_	O
60	_	_	B-PARAM
blueberry	_	_	O
bagels	_	_	O
,	_	_	O
and	_	_	O
100	_	_	B-PARAM
regular	_	_	O
bagels	_	_	O
.	_	_	O
The	_	_	O
bagel	_	_	O
company	_	_	O
must	_	_	O
produce	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
800	_	_	B-LIMIT
everything	_	_	O
bagels	_	_	O
,	_	_	O
600	_	_	B-LIMIT
blueberry	_	_	O
bagels	_	_	O
,	_	_	O
and	_	_	O
1000	_	_	B-LIMIT
regular	_	_	O
bagels	_	_	O
in	_	_	O
total	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
hours	_	_	O
should	_	_	O
each	_	_	O
bakery	_	_	O
be	_	_	O
run	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
cosmetics	_	_	O
company	_	_	O
makes	_	_	O
low	_	_	B-VAR
,	_	_	O
medium	_	_	B-VAR
,	_	_	O
and	_	_	O
high	_	_	B-VAR
quality	_	_	I-VAR
face	_	_	O
wash	_	_	O
.	_	_	O
A	_	_	O
low	_	_	B-VAR
quality	_	_	I-VAR
face	_	_	O
wash	_	_	O
contains	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
rare	_	_	O
ingredients	_	_	O
and	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	O
.	_	_	O
A	_	_	O
medium	_	_	B-VAR
quality	_	_	I-VAR
face	_	_	O
wash	_	_	O
contains	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
rare	_	_	O
ingredients	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	O
.	_	_	O
A	_	_	O
high	_	_	B-VAR
quality	_	_	I-VAR
face	_	_	O
wash	_	_	O
contains	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
rare	_	_	O
ingredients	_	_	O
and	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
water	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
100	_	_	B-LIMIT
units	_	_	O
of	_	_	O
rare	_	_	O
ingredients	_	_	O
and	_	_	O
200	_	_	B-LIMIT
units	_	_	O
of	_	_	O
water	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
low	_	_	B-VAR
quality	_	_	I-VAR
face	_	_	O
wash	_	_	O
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
,	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
medium	_	_	B-VAR
quality	_	_	I-VAR
face	_	_	O
wash	_	_	O
is	_	_	O
$	_	_	O
7	_	_	B-PARAM
,	_	_	O
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
high	_	_	B-VAR
quality	_	_	I-VAR
face	_	_	O
wash	_	_	O
is	_	_	O
$	_	_	O
9	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profits	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
dietician	_	_	O
recommends	_	_	O
that	_	_	O
his	_	_	O
patient	_	_	O
eat	_	_	O
jelly	_	_	O
supplements	_	_	O
to	_	_	O
get	_	_	O
his	_	_	O
mineral	_	_	O
requirements	_	_	O
.	_	_	O
Each	_	_	O
blue	_	_	B-VAR
jelly	_	_	I-VAR
pouch	_	_	I-VAR
contains	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
calcium	_	_	O
,	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
potassium	_	_	O
,	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
sodium	_	_	O
.	_	_	O
Each	_	_	O
red	_	_	B-VAR
jelly	_	_	I-VAR
pouch	_	_	I-VAR
contains	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
calcium	_	_	O
,	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
potassium	_	_	O
,	_	_	O
and	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
sodium	_	_	O
.	_	_	O
The	_	_	O
patient	_	_	O
must	_	_	O
get	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
units	_	_	O
of	_	_	O
calcium	_	_	O
,	_	_	O
25	_	_	B-LIMIT
units	_	_	O
of	_	_	O
potassium	_	_	O
,	_	_	O
and	_	_	O
30	_	_	B-LIMIT
units	_	_	O
of	_	_	O
sodium	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
blue	_	_	B-VAR
jelly	_	_	I-VAR
pouch	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
red	_	_	B-VAR
jelly	_	_	I-VAR
pouch	_	_	I-VAR
is	_	_	O
$	_	_	O
7	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
patient	_	_	O
purchase	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
puzzle	_	_	O
company	_	_	O
makes	_	_	O
small	_	_	B-VAR
and	_	_	O
large	_	_	B-VAR
puzzles	_	_	O
.	_	_	O
Each	_	_	O
small	_	_	B-VAR
puzzle	_	_	I-VAR
takes	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
cutting	_	_	O
and	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
quality	_	_	O
checking	_	_	O
.	_	_	O
Each	_	_	O
large	_	_	B-VAR
puzzle	_	_	I-VAR
takes	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
cutting	_	_	O
and	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
quality	_	_	O
checking	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
600	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
cutting	_	_	O
and	_	_	O
1000	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
quality	_	_	O
checking	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
small	_	_	B-VAR
puzzle	_	_	I-VAR
is	_	_	O
$	_	_	O
8	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
large	_	_	B-VAR
puzzle	_	_	I-VAR
is	_	_	O
$	_	_	O
12	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

George	_	_	O
has	_	_	O
acquired	_	_	B-CONST_DIR
200	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
in	_	_	O
the	_	_	O
tropics	_	_	O
.	_	_	O
He	_	_	O
wants	_	_	O
to	_	_	O
plant	_	_	O
coconut	_	_	B-VAR
trees	_	_	I-VAR
and	_	_	O
banana	_	_	B-VAR
trees	_	_	I-VAR
,	_	_	O
as	_	_	O
he	_	_	O
knows	_	_	O
he	_	_	O
can	_	_	O
sell	_	_	O
all	_	_	O
the	_	_	O
bananas	_	_	B-VAR
and	_	_	O
coconuts	_	_	B-VAR
harvested	_	_	O
.	_	_	O
Coconut	_	_	B-VAR
trees	_	_	I-VAR
cost	_	_	O
$	_	_	O
200	_	_	B-PARAM
per	_	_	O
acre	_	_	O
to	_	_	O
maintain	_	_	O
,	_	_	O
yield	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
400	_	_	B-PARAM
per	_	_	O
acre	_	_	O
,	_	_	O
and	_	_	O
require	_	_	O
5	_	_	B-PARAM
days	_	_	O
worth	_	_	O
of	_	_	O
labor	_	_	O
per	_	_	O
acre	_	_	O
.	_	_	O
Banana	_	_	B-VAR
trees	_	_	I-VAR
cost	_	_	O
$	_	_	O
150	_	_	B-PARAM
per	_	_	O
acre	_	_	O
to	_	_	O
maintain	_	_	O
,	_	_	O
yield	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
350	_	_	B-PARAM
per	_	_	O
acre	_	_	O
,	_	_	O
and	_	_	O
require	_	_	O
4	_	_	B-PARAM
days	_	_	O
worth	_	_	O
of	_	_	O
labor	_	_	O
per	_	_	O
acre	_	_	O
.	_	_	O
George	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
15000	_	_	B-LIMIT
and	_	_	O
750	_	_	B-LIMIT
days	_	_	O
worth	_	_	O
of	_	_	O
labor	_	_	O
available	_	_	B-CONST_DIR
(	_	_	O
among	_	_	O
all	_	_	O
his	_	_	O
workers	_	_	O
)	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
tree	_	_	O
should	_	_	O
George	_	_	O
plant	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
keyboard	_	_	O
company	_	_	O
produces	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
analog	_	_	O
synthesizer	_	_	O
keyboards	_	_	O
,	_	_	O
one	_	_	O
with	_	_	O
61	_	_	B-VAR
keys	_	_	I-VAR
and	_	_	O
another	_	_	O
with	_	_	O
81	_	_	B-VAR
keys	_	_	I-VAR
.	_	_	O
Both	_	_	O
keyboards	_	_	O
are	_	_	O
sold	_	_	B-OBJ_NAME
for	_	_	O
$	_	_	O
1500	_	_	B-PARAM
and	_	_	O
$	_	_	O
2500	_	_	B-PARAM
respectively	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
about	_	_	O
3000	_	_	B-LIMIT
oscillator	_	_	O
chips	_	_	O
available	_	_	B-CONST_DIR
every	_	_	O
day	_	_	O
from	_	_	O
which	_	_	O
the	_	_	O
61	_	_	B-VAR
key	_	_	I-VAR
version	_	_	I-VAR
requires	_	_	O
8	_	_	B-PARAM
chips	_	_	O
while	_	_	O
the	_	_	O
81	_	_	B-VAR
key	_	_	I-VAR
version	_	_	I-VAR
requires	_	_	O
16	_	_	B-PARAM
chips	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
a	_	_	O
total	_	_	B-CONST_DIR
8	_	_	B-LIMIT
working	_	_	O
hours	_	_	O
a	_	_	O
day	_	_	O
.	_	_	O
Both	_	_	O
of	_	_	O
these	_	_	O
synthesizers	_	_	O
require	_	_	O
a	_	_	O
production	_	_	O
time	_	_	O
of	_	_	O
1.5	_	_	B-PARAM
hours	_	_	O
.	_	_	O
What	_	_	O
should	_	_	O
be	_	_	O
the	_	_	O
manufacturing	_	_	O
quantity	_	_	O
for	_	_	O
each	_	_	O
of	_	_	O
the	_	_	O
keyboards	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
revenue	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
clothing	_	_	O
company	_	_	O
would	_	_	O
like	_	_	O
to	_	_	O
ship	_	_	O
pants	_	_	O
from	_	_	O
China	_	_	O
,	_	_	O
grey	_	_	B-VAR
and	_	_	O
black	_	_	B-VAR
pants	_	_	I-VAR
.	_	_	O
Both	_	_	O
require	_	_	O
processing	_	_	O
at	_	_	O
two	_	_	O
factories	_	_	O
named	_	_	O
Wimo	_	_	O
and	_	_	O
Webo	_	_	O
.	_	_	O
The	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
pair	_	_	O
of	_	_	O
grey	_	_	B-VAR
pants	_	_	I-VAR
is	_	_	O
$	_	_	O
25	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	O
per	_	_	O
pair	_	_	O
of	_	_	O
black	_	_	B-VAR
pants	_	_	I-VAR
is	_	_	O
$	_	_	O
15	_	_	B-PARAM
.	_	_	O
Each	_	_	O
pair	_	_	O
of	_	_	O
grey	_	_	B-VAR
pants	_	_	I-VAR
requires	_	_	O
40	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
processing	_	_	O
time	_	_	O
at	_	_	O
Wimo	_	_	O
and	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
processing	_	_	O
time	_	_	O
at	_	_	O
Webo	_	_	O
.	_	_	O
Each	_	_	O
pair	_	_	O
of	_	_	O
black	_	_	B-VAR
pants	_	_	I-VAR
requires	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
processing	_	_	O
time	_	_	O
at	_	_	O
Wimo	_	_	O
and	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
processing	_	_	O
time	_	_	O
at	_	_	O
Webo	_	_	O
.	_	_	O
Wimo	_	_	O
is	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
2100	_	_	B-LIMIT
minutes	_	_	O
and	_	_	O
Webo	_	_	O
is	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
3000	_	_	B-LIMIT
minutes	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
pant	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
small	_	_	O
business	_	_	O
makes	_	_	O
soccer	_	_	B-VAR
balls	_	_	I-VAR
and	_	_	O
basket	_	_	B-VAR
balls	_	_	I-VAR
by	_	_	O
hand	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
soccer	_	_	B-VAR
ball	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
,	_	_	O
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
basket	_	_	B-VAR
ball	_	_	I-VAR
is	_	_	O
$	_	_	O
8	_	_	B-PARAM
.	_	_	O
To	_	_	O
make	_	_	O
one	_	_	O
soccer	_	_	B-VAR
ball	_	_	I-VAR
,	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
sewing	_	_	O
and	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
quality	_	_	O
checking	_	_	O
is	_	_	O
required	_	_	O
.	_	_	O
To	_	_	O
make	_	_	O
a	_	_	O
basket	_	_	B-VAR
ball	_	_	I-VAR
15	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
sewing	_	_	O
and	_	_	O
12	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
quality	_	_	O
checking	_	_	O
is	_	_	O
required	_	_	O
.	_	_	O
In	_	_	O
a	_	_	O
month	_	_	O
,	_	_	O
5000	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
sewing	_	_	O
time	_	_	O
and	_	_	O
4500	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
quality	_	_	O
checking	_	_	O
time	_	_	O
is	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
ball	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
gardener	_	_	O
has	_	_	O
a	_	_	O
garden	_	_	O
full	_	_	O
of	_	_	O
daisies	_	_	B-VAR
and	_	_	O
lilies	_	_	B-VAR
,	_	_	O
and	_	_	O
picks	_	_	O
them	_	_	O
everyday	_	_	O
for	_	_	O
sale	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
bouquet	_	_	O
of	_	_	O
daisies	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
bouquet	_	_	O
of	_	_	O
lilies	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
4	_	_	B-PARAM
.	_	_	O
Each	_	_	O
bouquet	_	_	O
of	_	_	O
daisies	_	_	B-VAR
needs	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
clipping	_	_	O
and	_	_	O
2	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
packaging	_	_	O
.	_	_	O
Each	_	_	O
bouquet	_	_	O
of	_	_	O
lilies	_	_	B-VAR
requires	_	_	O
1	_	_	B-PARAM
minute	_	_	O
of	_	_	O
clipping	_	_	O
and	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
packaging	_	_	O
.	_	_	O
In	_	_	O
total	_	_	O
,	_	_	O
there	_	_	O
are	_	_	O
1000	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
clipping	_	_	O
and	_	_	O
650	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
packaging	_	_	O
.	_	_	O
Having	_	_	O
signed	_	_	O
a	_	_	O
contract	_	_	O
with	_	_	O
a	_	_	O
local	_	_	O
restaurant	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
25	_	_	B-LIMIT
bouquets	_	_	O
of	_	_	O
daisies	_	_	B-VAR
must	_	_	O
be	_	_	O
picked	_	_	O
.	_	_	O
There	_	_	O
is	_	_	O
no	_	_	O
such	_	_	O
limit	_	_	O
on	_	_	O
bouquets	_	_	O
of	_	_	O
lilies	_	_	B-VAR
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
.	_	_	O

Fiber	_	_	O
and	_	_	O
iron	_	_	O
can	_	_	O
be	_	_	O
obtained	_	_	O
in	_	_	O
two	_	_	O
supplement	_	_	O
drinks	_	_	O
.	_	_	O
One	_	_	O
is	_	_	O
orange	_	_	B-VAR
flavored	_	_	I-VAR
and	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
8	_	_	B-PARAM
per	_	_	O
serving	_	_	O
.	_	_	O
The	_	_	O
other	_	_	O
is	_	_	O
apple	_	_	B-VAR
flavored	_	_	I-VAR
and	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
5	_	_	B-PARAM
per	_	_	O
serving	_	_	O
.	_	_	O
One	_	_	O
serving	_	_	O
of	_	_	O
the	_	_	O
orange	_	_	B-VAR
flavored	_	_	I-VAR
drink	_	_	I-VAR
contains	_	_	O
4	_	_	B-PARAM
grams	_	_	O
of	_	_	O
fiber	_	_	O
and	_	_	O
5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
iron	_	_	O
.	_	_	O
One	_	_	O
serving	_	_	O
of	_	_	O
the	_	_	O
apple	_	_	B-VAR
flavored	_	_	I-VAR
drink	_	_	I-VAR
contains	_	_	O
6	_	_	B-PARAM
grams	_	_	O
of	_	_	O
fiber	_	_	O
and	_	_	O
3	_	_	B-PARAM
grams	_	_	O
of	_	_	O
iron	_	_	O
.	_	_	O
In	_	_	O
a	_	_	O
day	_	_	O
,	_	_	O
it	_	_	O
is	_	_	O
recommended	_	_	O
to	_	_	O
get	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
13	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
fiber	_	_	O
and	_	_	O
iron	_	_	O
each	_	_	O
.	_	_	O
Find	_	_	O
the	_	_	O
mix	_	_	O
and	_	_	O
formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
large	_	_	O
factory	_	_	O
in	_	_	O
Brazil	_	_	O
makes	_	_	O
cocoa	_	_	B-VAR
beans	_	_	I-VAR
and	_	_	O
coffee	_	_	B-VAR
beans	_	_	I-VAR
and	_	_	O
has	_	_	O
a	_	_	O
production	_	_	B-CONST_DIR
capacity	_	_	I-CONST_DIR
of	_	_	O
15	_	_	B-LIMIT
tons	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
Coffee	_	_	B-VAR
beans	_	_	I-VAR
and	_	_	O
cocoa	_	_	B-VAR
beans	_	_	I-VAR
require	_	_	O
the	_	_	O
same	_	_	O
production	_	_	O
capacity	_	_	O
.	_	_	O
Each	_	_	O
ton	_	_	O
of	_	_	O
coffee	_	_	B-VAR
beans	_	_	I-VAR
and	_	_	O
cocoa	_	_	B-VAR
beans	_	_	I-VAR
requires	_	_	O
15	_	_	B-PARAM
hours	_	_	O
of	_	_	O
roasting	_	_	O
each	_	_	O
.	_	_	O
The	_	_	O
roasting	_	_	O
machine	_	_	O
is	_	_	O
available	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
1000	_	_	B-LIMIT
hours	_	_	O
.	_	_	O
The	_	_	O
factory	_	_	O
must	_	_	O
make	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
3	_	_	B-LIMIT
tons	_	_	O
of	_	_	O
cocoa	_	_	B-VAR
beans	_	_	I-VAR
and	_	_	O
5	_	_	B-LIMIT
tons	_	_	O
of	_	_	O
coffee	_	_	B-VAR
beans	_	_	I-VAR
per	_	_	O
day	_	_	O
.	_	_	O
Profit	_	_	B-OBJ_NAME
per	_	_	O
ton	_	_	O
of	_	_	O
cocoa	_	_	B-VAR
beans	_	_	I-VAR
is	_	_	O
$	_	_	O
500	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
ton	_	_	O
of	_	_	O
coffee	_	_	B-VAR
beans	_	_	I-VAR
is	_	_	O
$	_	_	O
750	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
ton	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
bean	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
farming	_	_	O
group	_	_	O
has	_	_	B-CONST_DIR
1000	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
on	_	_	O
which	_	_	O
they	_	_	O
plan	_	_	O
to	_	_	O
grow	_	_	O
potatoes	_	_	B-VAR
and	_	_	O
squash	_	_	B-VAR
.	_	_	O
They	_	_	O
have	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
1200	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
tractor	_	_	O
time	_	_	O
available	_	_	O
and	_	_	O
$	_	_	O
26400	_	_	B-LIMIT
of	_	_	O
capital	_	_	O
available	_	_	O
.	_	_	O
Each	_	_	O
acre	_	_	O
of	_	_	O
potatoes	_	_	B-VAR
requires	_	_	O
20	_	_	B-PARAM
hours	_	_	O
of	_	_	O
tractor	_	_	O
work	_	_	O
and	_	_	O
$	_	_	O
10	_	_	B-PARAM
of	_	_	O
capital	_	_	O
,	_	_	O
and	_	_	O
each	_	_	O
acre	_	_	O
of	_	_	O
squash	_	_	B-VAR
requires	_	_	O
23	_	_	B-PARAM
hours	_	_	O
of	_	_	O
tractor	_	_	O
work	_	_	O
and	_	_	O
$	_	_	O
110	_	_	B-PARAM
of	_	_	O
capital	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
from	_	_	O
an	_	_	O
acre	_	_	O
of	_	_	O
potatoes	_	_	B-VAR
is	_	_	O
$	_	_	O
700	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
from	_	_	O
an	_	_	O
acre	_	_	O
of	_	_	O
squash	_	_	B-VAR
is	_	_	O
$	_	_	O
144	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
crop	_	_	O
should	_	_	O
they	_	_	O
plant	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
their	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
tailor	_	_	O
shop	_	_	O
makes	_	_	O
pants	_	_	B-VAR
and	_	_	O
short	_	_	B-VAR
each	_	_	O
requiring	_	_	O
the	_	_	O
use	_	_	O
of	_	_	O
three	_	_	O
operations	_	_	O
done	_	_	O
by	_	_	O
three	_	_	O
teams	_	_	O
:	_	_	O
measuring	_	_	O
,	_	_	O
cutting	_	_	O
,	_	_	O
and	_	_	O
sewing	_	_	O
.	_	_	O
The	_	_	O
measuring	_	_	O
team	_	_	O
is	_	_	O
available	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
60	_	_	B-LIMIT
hours	_	_	O
,	_	_	O
the	_	_	O
cutting	_	_	O
team	_	_	O
is	_	_	O
available	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
80	_	_	B-LIMIT
hours	_	_	O
,	_	_	O
and	_	_	O
the	_	_	O
sewing	_	_	O
team	_	_	O
is	_	_	O
available	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
75	_	_	B-LIMIT
hours	_	_	O
.	_	_	O
A	_	_	O
pant	_	_	B-VAR
requires	_	_	O
0.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
measuring	_	_	O
,	_	_	O
0.2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
cutting	_	_	O
,	_	_	O
and	_	_	O
0.7	_	_	B-PARAM
hours	_	_	O
of	_	_	O
sewing	_	_	O
.	_	_	O
A	_	_	O
short	_	_	B-VAR
requires	_	_	O
0.1	_	_	B-PARAM
hours	_	_	O
of	_	_	O
measuring	_	_	O
,	_	_	O
0.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
cutting	_	_	O
,	_	_	O
and	_	_	O
0.6	_	_	B-PARAM
hours	_	_	O
of	_	_	O
sewing	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
pant	_	_	B-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
short	_	_	B-VAR
is	_	_	O
$	_	_	O
7	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

In	_	_	O
a	_	_	O
company	_	_	O
,	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
teams	_	_	O
can	_	_	O
be	_	_	O
formed	_	_	O
:	_	_	O
a	_	_	O
small	_	_	B-VAR
team	_	_	I-VAR
and	_	_	O
a	_	_	O
large	_	_	B-VAR
team	_	_	I-VAR
.	_	_	O
A	_	_	O
small	_	_	B-VAR
team	_	_	I-VAR
can	_	_	O
preform	_	_	O
8	_	_	B-PARAM
tasks	_	_	O
per	_	_	O
hour	_	_	O
,	_	_	O
requires	_	_	O
1	_	_	B-PARAM
supervisor	_	_	O
,	_	_	O
and	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
5000	_	_	B-PARAM
.	_	_	O
A	_	_	O
large	_	_	B-VAR
team	_	_	I-VAR
can	_	_	O
preform	_	_	O
20	_	_	B-PARAM
tasks	_	_	O
per	_	_	O
hour	_	_	O
,	_	_	O
requires	_	_	O
3	_	_	B-PARAM
supervisors	_	_	O
,	_	_	O
and	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
15000	_	_	B-PARAM
.	_	_	O
The	_	_	O
company	_	_	O
wants	_	_	O
to	_	_	O
competes	_	_	B-CONST_DIR
100	_	_	B-LIMIT
tasks	_	_	O
per	_	_	O
hour	_	_	O
with	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
10	_	_	B-LIMIT
supervisors	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
team	_	_	O
,	_	_	O
small	_	_	B-VAR
and	_	_	O
large	_	_	B-VAR
,	_	_	O
need	_	_	O
to	_	_	O
be	_	_	O
formed	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
and	_	_	O
meet	_	_	O
the	_	_	O
requirements	_	_	O
?	_	_	O

A	_	_	O
salesman	_	_	O
wants	_	_	O
to	_	_	O
sell	_	_	O
his	_	_	O
inventory	_	_	B-CONST_DIR
composed	_	_	O
of	_	_	O
seven	_	_	B-LIMIT
wireless	_	_	O
earbuds	_	_	O
,	_	_	O
ten	_	_	B-LIMIT
wired	_	_	O
earbuds	_	_	O
,	_	_	O
and	_	_	O
twenty	_	_	B-LIMIT
USB	_	_	O
dongles	_	_	O
.	_	_	O
He	_	_	O
decides	_	_	O
to	_	_	O
offer	_	_	O
two	_	_	O
bundles	_	_	O
:	_	_	O
Bundle	_	_	B-VAR
A	_	_	I-VAR
and	_	_	O
Bundle	_	_	B-VAR
B.	_	_	I-VAR
Bundle	_	_	B-VAR
A	_	_	I-VAR
brings	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
10	_	_	B-PARAM
and	_	_	O
contains	_	_	O
1	_	_	B-PARAM
wireless	_	_	O
earbud	_	_	O
and	_	_	O
3	_	_	B-PARAM
USB	_	_	O
dongles	_	_	O
.	_	_	O
Bundle	_	_	B-VAR
B	_	_	I-VAR
brings	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
12	_	_	B-PARAM
and	_	_	O
contains	_	_	O
1	_	_	B-PARAM
wireless	_	_	O
earbud	_	_	O
,	_	_	O
2	_	_	B-PARAM
wired	_	_	O
earbuds	_	_	O
,	_	_	O
and	_	_	O
2	_	_	B-PARAM
USB	_	_	O
dongles	_	_	O
.	_	_	O
Assuming	_	_	O
he	_	_	O
can	_	_	O
sell	_	_	O
all	_	_	O
bundles	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
prepare	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

My	_	_	O
cousin	_	_	O
sells	_	_	O
two	_	_	O
different	_	_	O
coffee	_	_	O
blends	_	_	O
:	_	_	O
the	_	_	O
Drummondville	_	_	B-VAR
blend	_	_	I-VAR
and	_	_	O
the	_	_	O
Victoriaville	_	_	B-VAR
blend	_	_	I-VAR
.	_	_	O
Each	_	_	O
blend	_	_	O
contains	_	_	O
both	_	_	O
arabica	_	_	O
and	_	_	O
robusta	_	_	O
coffee	_	_	O
beans	_	_	O
.	_	_	O
A	_	_	O
bag	_	_	O
of	_	_	O
the	_	_	O
Drummondville	_	_	B-VAR
blend	_	_	I-VAR
contains	_	_	O
600	_	_	B-PARAM
grams	_	_	O
of	_	_	O
arabica	_	_	O
beans	_	_	O
and	_	_	O
400	_	_	B-PARAM
grams	_	_	O
of	_	_	O
robusta	_	_	O
beans	_	_	O
,	_	_	O
whereas	_	_	O
a	_	_	O
bag	_	_	O
of	_	_	O
the	_	_	O
Victoriaville	_	_	B-VAR
blend	_	_	I-VAR
contains	_	_	O
375	_	_	B-PARAM
grams	_	_	O
of	_	_	O
arabica	_	_	O
beans	_	_	O
and	_	_	O
625	_	_	B-PARAM
grams	_	_	O
of	_	_	O
robusta	_	_	O
beans	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
from	_	_	O
each	_	_	O
bag	_	_	O
of	_	_	O
Drummondville	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
from	_	_	O
each	_	_	O
bag	_	_	O
of	_	_	O
Victoriaville	_	_	B-VAR
blend	_	_	I-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
7	_	_	B-PARAM
.	_	_	O
If	_	_	O
his	_	_	O
total	_	_	O
production	_	_	O
must	_	_	O
not	_	_	O
exceed	_	_	O
his	_	_	O
available	_	_	B-CONST_DIR
stock	_	_	I-CONST_DIR
of	_	_	O
24000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
arabica	_	_	O
beans	_	_	O
and	_	_	O
17000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
robusta	_	_	O
beans	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
bags	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
blend	_	_	O
should	_	_	O
be	_	_	O
blended	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profits	_	_	B-OBJ_NAME
?	_	_	O
Formulate	_	_	O
and	_	_	O
solve	_	_	O
.	_	_	O

A	_	_	O
farmer	_	_	O
has	_	_	O
30	_	_	O
cows	_	_	O
and	_	_	O
feeds	_	_	O
them	_	_	O
on	_	_	O
enriched	_	_	B-VAR
hay	_	_	I-VAR
and	_	_	O
chicken	_	_	B-VAR
scraps	_	_	I-VAR
.	_	_	O
Enriched	_	_	B-VAR
hay	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
200	_	_	B-PARAM
per	_	_	O
kilogram	_	_	O
while	_	_	O
chicken	_	_	B-VAR
scraps	_	_	I-VAR
cost	_	_	B-OBJ_NAME
$	_	_	O
350	_	_	B-PARAM
per	_	_	O
kilogram	_	_	O
.	_	_	O
Each	_	_	O
kilogram	_	_	O
of	_	_	O
enriched	_	_	B-VAR
hay	_	_	I-VAR
contains	_	_	O
0.3	_	_	B-PARAM
kilograms	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
0.1	_	_	B-PARAM
kilograms	_	_	O
of	_	_	O
vitamins	_	_	O
,	_	_	O
and	_	_	O
0.15	_	_	B-PARAM
kilograms	_	_	O
of	_	_	O
minerals	_	_	O
.	_	_	O
Each	_	_	O
kilogram	_	_	O
of	_	_	O
chicken	_	_	B-VAR
scraps	_	_	I-VAR
contains	_	_	O
0.6	_	_	B-PARAM
kilograms	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
0.2	_	_	B-PARAM
kilograms	_	_	O
of	_	_	O
vitamins	_	_	O
,	_	_	O
and	_	_	O
0.05	_	_	B-PARAM
kilograms	_	_	O
of	_	_	O
minerals	_	_	O
.	_	_	O
Each	_	_	O
cow	_	_	O
requires	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
1.5	_	_	B-LIMIT
kilograms	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
0.5	_	_	B-LIMIT
kilograms	_	_	O
of	_	_	O
minerals	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
each	_	_	O
cow	_	_	O
can	_	_	O
have	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
0.5	_	_	B-LIMIT
kilograms	_	_	O
of	_	_	O
vitamins	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
How	_	_	O
should	_	_	O
the	_	_	O
farmer	_	_	O
feed	_	_	O
his	_	_	O
cows	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
while	_	_	O
ensuring	_	_	O
the	_	_	O
cows	_	_	O
get	_	_	O
the	_	_	O
required	_	_	O
nutrition	_	_	O
?	_	_	O

A	_	_	O
bakery	_	_	O
makes	_	_	O
chocolate	_	_	B-VAR
and	_	_	O
blueberry	_	_	B-VAR
muffins	_	_	I-VAR
,	_	_	O
each	_	_	O
requiring	_	_	O
both	_	_	O
sugar	_	_	O
and	_	_	O
butter	_	_	O
.	_	_	O
The	_	_	O
bakery	_	_	O
has	_	_	O
6000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
sugar	_	_	O
and	_	_	O
4000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
butter	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
Chocolate	_	_	B-VAR
muffins	_	_	I-VAR
require	_	_	O
30	_	_	B-PARAM
grams	_	_	O
of	_	_	O
sugar	_	_	O
and	_	_	O
10	_	_	B-PARAM
grams	_	_	O
of	_	_	O
butter	_	_	O
,	_	_	O
while	_	_	O
blueberry	_	_	B-VAR
muffins	_	_	I-VAR
require	_	_	O
20	_	_	B-PARAM
grams	_	_	O
of	_	_	O
sugar	_	_	O
and	_	_	O
15	_	_	B-PARAM
grams	_	_	O
of	_	_	O
butter	_	_	O
.	_	_	O
Assuming	_	_	O
all	_	_	O
other	_	_	O
ingredients	_	_	O
are	_	_	O
available	_	_	O
,	_	_	O
what	_	_	O
is	_	_	O
the	_	_	O
maximum	_	_	B-OBJ_DIR
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
muffins	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
made	_	_	O
?	_	_	O

A	_	_	O
factory	_	_	O
makes	_	_	O
violins	_	_	B-VAR
and	_	_	O
harps	_	_	B-VAR
.	_	_	O
A	_	_	O
violin	_	_	B-VAR
takes	_	_	O
6	_	_	B-PARAM
hours	_	_	O
of	_	_	O
woodworking	_	_	O
time	_	_	O
and	_	_	O
2.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
assembling	_	_	O
time	_	_	O
.	_	_	O
A	_	_	O
harp	_	_	B-VAR
takes	_	_	O
2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
woodworking	_	_	O
time	_	_	O
and	_	_	O
10	_	_	B-PARAM
hours	_	_	O
of	_	_	O
assembling	_	_	O
time	_	_	O
.	_	_	O
The	_	_	O
factory	_	_	O
has	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
woodworking	_	_	O
time	_	_	O
and	_	_	O
150	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
assembling	_	_	O
time	_	_	O
available	_	_	O
per	_	_	O
day	_	_	O
among	_	_	O
all	_	_	O
the	_	_	O
workers	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
violin	_	_	B-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
harp	_	_	B-VAR
is	_	_	O
$	_	_	O
350	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
instrument	_	_	O
should	_	_	O
the	_	_	O
factory	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profits	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
smoothie	_	_	O
store	_	_	O
makes	_	_	O
fruit	_	_	B-VAR
and	_	_	O
vegetable	_	_	B-VAR
smoothies	_	_	I-VAR
.	_	_	O
It	_	_	O
takes	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
cutting	_	_	O
machine	_	_	O
and	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
blending	_	_	O
machine	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
fruit	_	_	B-VAR
smoothie	_	_	I-VAR
.	_	_	O
It	_	_	O
takes	_	_	O
7	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
cutting	_	_	O
machine	_	_	O
and	_	_	O
4	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
blending	_	_	O
machine	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
vegetable	_	_	B-VAR
smoothie	_	_	I-VAR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
fruit	_	_	B-VAR
smoothie	_	_	I-VAR
is	_	_	O
$	_	_	O
4	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
vegetable	_	_	B-VAR
smoothie	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
.	_	_	O
If	_	_	O
both	_	_	O
the	_	_	O
cutting	_	_	O
machine	_	_	O
and	_	_	O
blending	_	_	O
machine	_	_	O
are	_	_	O
available	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
400	_	_	B-LIMIT
minutes	_	_	O
per	_	_	O
day	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
smoothie	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
vehicle	_	_	O
company	_	_	O
makes	_	_	O
bikes	_	_	B-VAR
and	_	_	O
cars	_	_	B-VAR
,	_	_	O
each	_	_	O
requiring	_	_	O
use	_	_	O
of	_	_	O
an	_	_	O
assembly	_	_	O
machine	_	_	O
and	_	_	O
a	_	_	O
painting	_	_	O
machine	_	_	O
.	_	_	O
It	_	_	O
takes	_	_	O
1	_	_	B-PARAM
hour	_	_	O
on	_	_	O
the	_	_	O
assembly	_	_	O
machine	_	_	O
and	_	_	O
0.5	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
painting	_	_	O
machine	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
bike	_	_	B-VAR
.	_	_	O
On	_	_	O
the	_	_	O
other	_	_	O
hand	_	_	O
,	_	_	O
it	_	_	O
takes	_	_	O
3	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
assembly	_	_	O
machine	_	_	O
and	_	_	O
1	_	_	B-PARAM
hour	_	_	O
on	_	_	O
the	_	_	O
painting	_	_	O
machine	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
car	_	_	B-VAR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
bike	_	_	B-VAR
is	_	_	O
$	_	_	O
1000	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
car	_	_	B-VAR
is	_	_	O
$	_	_	O
3000	_	_	B-PARAM
.	_	_	O
The	_	_	O
assembly	_	_	O
machine	_	_	O
is	_	_	O
available	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
10	_	_	B-LIMIT
hours	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
the	_	_	O
painting	_	_	O
machine	_	_	O
is	_	_	O
available	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
8	_	_	B-LIMIT
hours	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
vehicle	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
make	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
chair	_	_	O
store	_	_	O
sells	_	_	O
leather	_	_	B-VAR
and	_	_	O
mesh	_	_	B-VAR
chairs	_	_	I-VAR
.	_	_	O
A	_	_	O
leather	_	_	B-VAR
chair	_	_	I-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
500	_	_	B-PARAM
and	_	_	O
a	_	_	O
mesh	_	_	B-VAR
chair	_	_	I-VAR
costs	_	_	O
the	_	_	O
stores	_	_	O
$	_	_	O
300	_	_	B-PARAM
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
leather	_	_	B-VAR
chair	_	_	I-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
250	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
mesh	_	_	B-VAR
chair	_	_	I-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
.	_	_	O
The	_	_	O
store	_	_	O
does	_	_	O
not	_	_	O
want	_	_	O
to	_	_	O
invest	_	_	O
more	_	_	B-CONST_DIR
that	_	_	I-CONST_DIR
$	_	_	O
50000	_	_	B-LIMIT
on	_	_	O
chairs	_	_	O
and	_	_	O
estimates	_	_	O
a	_	_	O
monthly	_	_	O
demand	_	_	O
of	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
125	_	_	B-LIMIT
chairs	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
chair	_	_	O
should	_	_	O
the	_	_	O
store	_	_	O
stock	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

David	_	_	O
has	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
liquid	_	_	O
supplementation	_	_	O
available	_	_	O
:	_	_	O
regular	_	_	B-VAR
and	_	_	O
premium	_	_	B-VAR
.	_	_	O
After	_	_	O
consulting	_	_	O
with	_	_	O
a	_	_	O
doctor	_	_	O
,	_	_	O
he	_	_	O
finds	_	_	O
that	_	_	O
he	_	_	O
needs	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
30	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
iron	_	_	O
and	_	_	O
50	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
calcium	_	_	O
.	_	_	O
Regular	_	_	B-VAR
supplementation	_	_	I-VAR
consists	_	_	O
of	_	_	O
20	_	_	B-PARAM
%	_	_	I-PARAM
iron	_	_	O
and	_	_	O
30	_	_	B-PARAM
%	_	_	I-PARAM
calcium	_	_	O
while	_	_	O
premium	_	_	B-VAR
supplementation	_	_	I-VAR
consists	_	_	O
of	_	_	O
25	_	_	B-PARAM
%	_	_	I-PARAM
iron	_	_	O
and	_	_	O
40	_	_	B-PARAM
%	_	_	I-PARAM
calcium	_	_	O
.	_	_	O
Regular	_	_	B-VAR
supplementation	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
0.04	_	_	B-PARAM
per	_	_	O
gram	_	_	O
while	_	_	O
premium	_	_	B-VAR
supplementation	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
0.08	_	_	B-PARAM
per	_	_	O
gram	_	_	O
.	_	_	O
How	_	_	O
much	_	_	O
of	_	_	O
each	_	_	O
supplementation	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
meet	_	_	O
his	_	_	O
requirements	_	_	O
and	_	_	O
minimize	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
paint	_	_	O
store	_	_	O
mixes	_	_	O
two	_	_	O
brands	_	_	O
of	_	_	O
paint	_	_	O
,	_	_	O
Ruby	_	_	B-VAR
and	_	_	O
Sapphire	_	_	B-VAR
,	_	_	O
to	_	_	O
create	_	_	O
a	_	_	O
new	_	_	O
mixture	_	_	O
of	_	_	O
paint	_	_	O
.	_	_	O
A	_	_	O
can	_	_	O
of	_	_	O
Ruby	_	_	B-VAR
paint	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
12	_	_	B-PARAM
and	_	_	O
a	_	_	O
can	_	_	O
of	_	_	O
Sapphire	_	_	B-VAR
paint	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
15	_	_	B-PARAM
.	_	_	O
A	_	_	O
can	_	_	O
of	_	_	O
Ruby	_	_	B-VAR
paint	_	_	I-VAR
contains	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
dye	_	_	O
,	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
thinner	_	_	O
,	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	O
.	_	_	O
A	_	_	O
can	_	_	O
of	_	_	O
Sapphire	_	_	B-VAR
paint	_	_	I-VAR
contains	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
dye	_	_	O
,	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
thinner	_	_	O
,	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	O
.	_	_	O
The	_	_	O
minimum	_	_	B-CONST_DIR
requirements	_	_	I-CONST_DIR
of	_	_	O
dye	_	_	O
,	_	_	O
thinner	_	_	O
,	_	_	O
and	_	_	O
water	_	_	O
for	_	_	O
the	_	_	O
new	_	_	O
mixture	_	_	O
are	_	_	O
15	_	_	B-LIMIT
units	_	_	O
,	_	_	O
20	_	_	B-LIMIT
units	_	_	O
,	_	_	O
and	_	_	O
18	_	_	B-LIMIT
units	_	_	O
respectively	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
cans	_	_	O
of	_	_	O
each	_	_	O
paint	_	_	O
brand	_	_	O
should	_	_	O
be	_	_	O
mixed	_	_	O
to	_	_	O
achieve	_	_	O
the	_	_	O
new	_	_	O
mixture	_	_	O
at	_	_	O
a	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
electronics	_	_	O
store	_	_	O
sells	_	_	O
two	_	_	O
web	_	_	O
cams	_	_	O
:	_	_	O
a	_	_	O
standard	_	_	B-VAR
definition	_	_	I-VAR
one	_	_	O
and	_	_	O
a	_	_	O
high	_	_	B-VAR
definition	_	_	I-VAR
one	_	_	O
.	_	_	O
The	_	_	O
standard	_	_	B-VAR
definition	_	_	I-VAR
web	_	_	O
-	_	_	O
cam	_	_	O
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
150	_	_	B-PARAM
and	_	_	O
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
100	_	_	B-PARAM
.	_	_	O
The	_	_	O
high	_	_	B-VAR
definition	_	_	I-VAR
web	_	_	O
-	_	_	O
cam	_	_	O
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
250	_	_	B-PARAM
and	_	_	O
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
125	_	_	B-PARAM
.	_	_	O
The	_	_	O
store	_	_	O
owner	_	_	O
does	_	_	O
not	_	_	O
want	_	_	O
to	_	_	O
invest	_	_	O
more	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
$	_	_	O
40000	_	_	B-LIMIT
in	_	_	O
web	_	_	O
-	_	_	O
cam	_	_	O
inventory	_	_	O
and	_	_	O
estimates	_	_	O
a	_	_	O
total	_	_	O
monthly	_	_	O
demand	_	_	O
of	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
275	_	_	B-LIMIT
web	_	_	O
-	_	_	O
cams	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
web	_	_	O
-	_	_	O
cams	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
should	_	_	O
be	_	_	O
stocked	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
farmer	_	_	O
has	_	_	B-CONST_DIR
200	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
on	_	_	O
which	_	_	O
he	_	_	O
grows	_	_	O
corn	_	_	B-VAR
and	_	_	O
cabbage	_	_	B-VAR
.	_	_	O
It	_	_	O
takes	_	_	O
1	_	_	B-PARAM
day	_	_	O
of	_	_	O
tractor	_	_	O
time	_	_	O
and	_	_	O
2	_	_	B-PARAM
days	_	_	O
of	_	_	O
hand	_	_	O
-	_	_	O
picking	_	_	O
time	_	_	O
per	_	_	O
acre	_	_	O
of	_	_	O
corn	_	_	B-VAR
.	_	_	O
It	_	_	O
takes	_	_	O
1.5	_	_	B-PARAM
days	_	_	O
of	_	_	O
tractor	_	_	O
time	_	_	O
and	_	_	O
3	_	_	B-PARAM
days	_	_	O
of	_	_	O
hand	_	_	O
-	_	_	O
picking	_	_	O
time	_	_	O
per	_	_	O
acre	_	_	O
of	_	_	O
cabbage	_	_	B-VAR
.	_	_	O
In	_	_	O
a	_	_	O
year	_	_	O
,	_	_	O
there	_	_	O
are	_	_	O
200	_	_	B-LIMIT
days	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
tractor	_	_	O
use	_	_	O
and	_	_	O
275	_	_	B-LIMIT
days	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
hand	_	_	O
-	_	_	O
picking	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
corn	_	_	B-VAR
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
cabbage	_	_	B-VAR
is	_	_	O
$	_	_	O
70	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
grown	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
fitness	_	_	O
trainer	_	_	O
has	_	_	O
decided	_	_	O
to	_	_	O
mix	_	_	O
two	_	_	O
brands	_	_	O
of	_	_	O
protein	_	_	O
drinks	_	_	O
to	_	_	O
create	_	_	O
a	_	_	O
new	_	_	O
mixture	_	_	O
.	_	_	O
The	_	_	O
Alpha	_	_	B-VAR
brand	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
5	_	_	B-PARAM
per	_	_	O
bottle	_	_	O
and	_	_	O
contains	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
carbs	_	_	O
,	_	_	O
and	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
The	_	_	O
Gamma	_	_	B-VAR
brand	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
8	_	_	B-PARAM
per	_	_	O
bottle	_	_	O
and	_	_	O
contains	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
carbs	_	_	O
,	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
The	_	_	O
trainer	_	_	O
wants	_	_	O
to	_	_	O
create	_	_	O
a	_	_	O
mixture	_	_	O
having	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
units	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
80	_	_	B-LIMIT
units	_	_	O
of	_	_	O
carbs	_	_	O
,	_	_	O
and	_	_	O
60	_	_	B-LIMIT
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
bottles	_	_	O
of	_	_	O
each	_	_	O
brand	_	_	O
drink	_	_	O
should	_	_	O
be	_	_	O
mixed	_	_	O
to	_	_	O
create	_	_	O
the	_	_	O
new	_	_	O
mixture	_	_	O
at	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
woodshop	_	_	O
makes	_	_	O
dining	_	_	B-VAR
tables	_	_	I-VAR
and	_	_	O
desks	_	_	B-VAR
.	_	_	O
Each	_	_	O
dining	_	_	B-VAR
table	_	_	I-VAR
requires	_	_	O
2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
woodworking	_	_	O
,	_	_	O
3	_	_	B-PARAM
boxes	_	_	O
of	_	_	O
nails	_	_	O
,	_	_	O
and	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
varnish	_	_	O
.	_	_	O
Each	_	_	O
desk	_	_	B-VAR
requires	_	_	O
3	_	_	B-PARAM
hours	_	_	O
of	_	_	O
woodworking	_	_	O
,	_	_	O
4	_	_	B-PARAM
boxes	_	_	O
of	_	_	O
nails	_	_	O
,	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
varnish	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
100	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
woodworking	_	_	O
available	_	_	B-CONST_DIR
,	_	_	O
75	_	_	B-LIMIT
boxes	_	_	O
of	_	_	O
nails	_	_	O
available	_	_	B-CONST_DIR
,	_	_	O
and	_	_	O
80	_	_	B-LIMIT
units	_	_	O
of	_	_	O
varnish	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
If	_	_	O
each	_	_	O
dining	_	_	B-VAR
table	_	_	I-VAR
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
350	_	_	B-PARAM
and	_	_	O
each	_	_	O
desk	_	_	B-VAR
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
400	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
paper	_	_	O
company	_	_	O
makes	_	_	O
lined	_	_	B-VAR
paper	_	_	I-VAR
and	_	_	O
graph	_	_	B-VAR
paper	_	_	I-VAR
.	_	_	O
All	_	_	O
paper	_	_	O
has	_	_	O
to	_	_	O
go	_	_	O
through	_	_	O
a	_	_	O
cutting	_	_	O
machine	_	_	O
and	_	_	O
a	_	_	O
line	_	_	O
-	_	_	O
printing	_	_	O
machine	_	_	O
.	_	_	O
A	_	_	O
ream	_	_	O
of	_	_	O
lined	_	_	B-VAR
paper	_	_	I-VAR
requires	_	_	O
2	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
cutting	_	_	O
machine	_	_	O
and	_	_	O
6	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
line	_	_	O
-	_	_	O
printing	_	_	O
machine	_	_	O
.	_	_	O
A	_	_	O
ream	_	_	O
of	_	_	O
graph	_	_	B-VAR
paper	_	_	I-VAR
requires	_	_	O
2	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
cutting	_	_	O
machine	_	_	O
and	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
line	_	_	O
-	_	_	O
printing	_	_	O
machine	_	_	O
.	_	_	O
In	_	_	O
a	_	_	O
week	_	_	O
,	_	_	O
each	_	_	O
machine	_	_	O
is	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
3500	_	_	B-LIMIT
minutes	_	_	O
.	_	_	O
There	_	_	O
is	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
11	_	_	B-PARAM
per	_	_	O
ream	_	_	O
of	_	_	O
lined	_	_	B-VAR
paper	_	_	I-VAR
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
13	_	_	B-PARAM
per	_	_	O
ream	_	_	O
of	_	_	O
graph	_	_	B-VAR
paper	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
reams	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Jake	_	_	O
and	_	_	O
Jill	_	_	O
own	_	_	O
a	_	_	O
bakery	_	_	O
where	_	_	O
they	_	_	O
sell	_	_	O
donuts	_	_	B-VAR
and	_	_	O
cookies	_	_	B-VAR
.	_	_	O
Each	_	_	O
batch	_	_	O
of	_	_	O
donuts	_	_	B-VAR
takes	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
Jake	_	_	O
's	_	_	O
time	_	_	O
and	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
Jill	_	_	O
's	_	_	O
time	_	_	O
.	_	_	O
Each	_	_	O
batch	_	_	O
of	_	_	O
cookies	_	_	B-VAR
takes	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
Jake	_	_	O
's	_	_	O
time	_	_	O
and	_	_	O
25	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
Jill	_	_	O
's	_	_	O
time	_	_	O
.	_	_	O
In	_	_	O
a	_	_	O
day	_	_	O
,	_	_	O
Jake	_	_	O
has	_	_	O
200	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
and	_	_	O
Jill	_	_	O
has	_	_	O
300	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
batch	_	_	O
of	_	_	O
donuts	_	_	B-VAR
is	_	_	O
$	_	_	O
20	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
batch	_	_	O
of	_	_	O
cookies	_	_	B-VAR
is	_	_	O
$	_	_	O
15	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
batches	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
peanut	_	_	O
farmer	_	_	O
has	_	_	O
to	_	_	O
send	_	_	O
his	_	_	O
product	_	_	O
to	_	_	O
the	_	_	O
city	_	_	O
.	_	_	O
He	_	_	O
can	_	_	O
transport	_	_	O
his	_	_	O
peanut	_	_	O
packages	_	_	O
on	_	_	O
the	_	_	O
train	_	_	B-VAR
which	_	_	O
can	_	_	O
take	_	_	O
80	_	_	B-PARAM
packages	_	_	B-OBJ_NAME
per	_	_	O
trip	_	_	O
or	_	_	O
by	_	_	O
truck	_	_	B-VAR
which	_	_	O
can	_	_	O
take	_	_	O
50	_	_	B-PARAM
packages	_	_	B-OBJ_NAME
per	_	_	O
trip	_	_	O
.	_	_	O
The	_	_	O
cost	_	_	O
per	_	_	O
train	_	_	B-VAR
trip	_	_	I-VAR
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	O
per	_	_	O
truck	_	_	B-VAR
trip	_	_	I-VAR
is	_	_	O
$	_	_	O
40	_	_	B-PARAM
.	_	_	O
He	_	_	O
wants	_	_	O
to	_	_	O
spend	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
3000	_	_	B-LIMIT
and	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
train	_	_	B-VAR
trips	_	_	I-VAR
must	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
truck	_	_	B-VAR
trips	_	_	I-VAR
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
peanut	_	_	I-OBJ_NAME
packages	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
transported	_	_	O
.	_	_	O

A	_	_	O
company	_	_	O
has	_	_	O
international	_	_	B-VAR
employees	_	_	I-VAR
earning	_	_	B-OBJ_NAME
$	_	_	O
500	_	_	B-PARAM
per	_	_	O
week	_	_	O
and	_	_	O
local	_	_	B-VAR
employees	_	_	I-VAR
earning	_	_	B-OBJ_NAME
$	_	_	O
1200	_	_	B-PARAM
per	_	_	O
week	_	_	O
.	_	_	O
The	_	_	O
projects	_	_	O
require	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
employees	_	_	O
,	_	_	O
of	_	_	O
whom	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
12	_	_	B-LIMIT
have	_	_	O
to	_	_	O
be	_	_	O
local	_	_	B-VAR
employees	_	_	I-VAR
.	_	_	O
Due	_	_	O
to	_	_	O
corporate	_	_	O
law	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
local	_	_	B-VAR
employees	_	_	I-VAR
should	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
a	_	_	O
third	_	_	B-PARAM
of	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
international	_	_	B-VAR
employees	_	_	I-VAR
.	_	_	O
It	_	_	O
is	_	_	O
also	_	_	O
required	_	_	O
to	_	_	O
keep	_	_	O
the	_	_	O
weekly	_	_	O
wage	_	_	O
bill	_	_	O
below	_	_	B-CONST_DIR
$	_	_	O
40000	_	_	B-LIMIT
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	B-OBJ_NAME
wage	_	_	I-OBJ_NAME
bill	_	_	I-OBJ_NAME
.	_	_	O

A	_	_	O
farmer	_	_	O
must	_	_	O
allocate	_	_	O
his	_	_	O
farming	_	_	O
equipment	_	_	O
between	_	_	O
his	_	_	O
two	_	_	O
farms	_	_	O
,	_	_	O
a	_	_	O
beet	_	_	B-VAR
farm	_	_	I-VAR
and	_	_	O
a	_	_	O
carrot	_	_	B-VAR
farm	_	_	I-VAR
.	_	_	O
The	_	_	O
revenue	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
beets	_	_	B-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
the	_	_	O
revenue	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
carrots	_	_	B-VAR
is	_	_	O
$	_	_	O
340	_	_	B-PARAM
.	_	_	O
He	_	_	O
has	_	_	O
one	_	_	O
tractor	_	_	O
,	_	_	O
one	_	_	O
plow	_	_	O
,	_	_	O
and	_	_	O
one	_	_	O
combine	_	_	O
.	_	_	O
Each	_	_	O
equipment	_	_	O
can	_	_	B-CONST_DIR
be	_	_	I-CONST_DIR
used	_	_	I-CONST_DIR
for	_	_	I-CONST_DIR
10	_	_	B-LIMIT
hours	_	_	O
a	_	_	O
day	_	_	O
divided	_	_	O
in	_	_	O
any	_	_	O
way	_	_	O
between	_	_	O
his	_	_	O
two	_	_	O
farms	_	_	O
.	_	_	O
On	_	_	O
his	_	_	O
beet	_	_	B-VAR
farm	_	_	I-VAR
,	_	_	O
harvesting	_	_	O
an	_	_	O
acre	_	_	O
of	_	_	O
beets	_	_	B-VAR
requires	_	_	O
0.6	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
tractor	_	_	O
,	_	_	O
0.3	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
plow	_	_	O
,	_	_	O
and	_	_	O
0.2	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
combine	_	_	O
.	_	_	O
On	_	_	O
his	_	_	O
carrot	_	_	B-VAR
farm	_	_	I-VAR
,	_	_	O
harvesting	_	_	O
an	_	_	O
acre	_	_	O
of	_	_	O
carrots	_	_	B-VAR
requires	_	_	O
0.7	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
tractor	_	_	O
,	_	_	O
0.25	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
plow	_	_	O
,	_	_	O
and	_	_	O
0.1	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
combine	_	_	O
.	_	_	O
How	_	_	O
should	_	_	O
the	_	_	O
farmer	_	_	O
allocate	_	_	O
his	_	_	O
equipment	_	_	O
between	_	_	O
his	_	_	O
farms	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
revenue	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
fishing	_	_	O
company	_	_	O
fishes	_	_	O
in	_	_	O
two	_	_	O
areas	_	_	O
of	_	_	O
the	_	_	O
world	_	_	O
,	_	_	O
the	_	_	O
Pacific	_	_	B-VAR
and	_	_	O
Atlantic	_	_	B-VAR
ocean	_	_	O
.	_	_	O
In	_	_	O
a	_	_	O
week	_	_	O
,	_	_	O
they	_	_	O
must	_	_	O
provide	_	_	B-CONST_DIR
18	_	_	B-LIMIT
tons	_	_	O
of	_	_	O
fish	_	_	O
,	_	_	O
10	_	_	B-LIMIT
tons	_	_	O
of	_	_	O
crab	_	_	O
,	_	_	O
and	_	_	O
5	_	_	B-LIMIT
tons	_	_	O
of	_	_	O
lobster	_	_	O
.	_	_	O
It	_	_	O
costs	_	_	B-OBJ_NAME
the	_	_	O
company	_	_	O
$	_	_	O
5000	_	_	B-PARAM
per	_	_	O
day	_	_	O
to	_	_	O
operate	_	_	O
in	_	_	O
the	_	_	O
Pacific	_	_	B-VAR
ocean	_	_	I-VAR
and	_	_	O
$	_	_	O
7000	_	_	B-PARAM
per	_	_	O
day	_	_	O
to	_	_	O
operate	_	_	O
in	_	_	O
the	_	_	O
Atlantic	_	_	B-VAR
ocean	_	_	I-VAR
.	_	_	O
In	_	_	O
a	_	_	O
day	_	_	O
's	_	_	O
operation	_	_	O
in	_	_	O
the	_	_	O
Pacific	_	_	B-VAR
ocean	_	_	I-VAR
,	_	_	O
the	_	_	O
company	_	_	O
can	_	_	O
catch	_	_	O
5	_	_	B-PARAM
tons	_	_	O
of	_	_	O
fish	_	_	O
,	_	_	O
2	_	_	B-PARAM
tons	_	_	O
of	_	_	O
crab	_	_	O
,	_	_	O
and	_	_	O
0.5	_	_	B-PARAM
tons	_	_	O
of	_	_	O
lobster	_	_	O
.	_	_	O
In	_	_	O
a	_	_	O
day	_	_	O
's	_	_	O
operation	_	_	O
in	_	_	O
the	_	_	O
Atlantic	_	_	B-VAR
ocean	_	_	I-VAR
,	_	_	O
the	_	_	O
company	_	_	O
can	_	_	O
catch	_	_	O
4	_	_	B-PARAM
tons	_	_	O
of	_	_	O
fish	_	_	O
,	_	_	O
3	_	_	B-PARAM
tons	_	_	O
of	_	_	O
crab	_	_	O
,	_	_	O
and	_	_	O
1	_	_	B-PARAM
ton	_	_	O
of	_	_	O
lobster	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
days	_	_	O
a	_	_	O
week	_	_	O
should	_	_	O
fishing	_	_	O
be	_	_	O
done	_	_	O
in	_	_	O
each	_	_	O
ocean	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

To	_	_	O
make	_	_	O
their	_	_	O
sausages	_	_	B-VAR
and	_	_	O
burger	_	_	B-VAR
patties	_	_	I-VAR
,	_	_	O
a	_	_	O
factory	_	_	O
uses	_	_	O
two	_	_	O
machines	_	_	O
,	_	_	O
a	_	_	O
meat	_	_	O
-	_	_	O
grinder	_	_	O
and	_	_	O
a	_	_	O
meat	_	_	O
-	_	_	O
packer	_	_	O
.	_	_	O
To	_	_	O
produce	_	_	O
one	_	_	O
batch	_	_	O
of	_	_	O
sausages	_	_	B-VAR
requires	_	_	O
2	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
meat	_	_	O
-	_	_	O
grinder	_	_	O
and	_	_	O
3	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
meat	_	_	O
-	_	_	O
packer	_	_	O
.	_	_	O
To	_	_	O
produce	_	_	O
one	_	_	O
batch	_	_	O
of	_	_	O
burger	_	_	B-VAR
patties	_	_	I-VAR
requires	_	_	O
4	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
meat	_	_	O
-	_	_	O
grinder	_	_	O
and	_	_	O
1.5	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
meat	_	_	O
-	_	_	O
packer	_	_	O
.	_	_	O
Each	_	_	O
machine	_	_	O
runs	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
3000	_	_	B-LIMIT
hours	_	_	O
per	_	_	O
year	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
batch	_	_	O
of	_	_	O
sausages	_	_	B-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
batch	_	_	O
of	_	_	O
burger	_	_	B-VAR
patties	_	_	I-VAR
is	_	_	O
$	_	_	O
250	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
batches	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
nut	_	_	O
farmer	_	_	O
has	_	_	B-CONST_DIR
80	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
on	_	_	O
which	_	_	O
he	_	_	O
grows	_	_	O
almonds	_	_	B-VAR
and	_	_	O
pecans	_	_	B-VAR
.	_	_	O
The	_	_	O
net	_	_	B-OBJ_NAME
revenue	_	_	I-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
almonds	_	_	B-VAR
is	_	_	O
$	_	_	O
500	_	_	B-PARAM
and	_	_	O
the	_	_	O
net	_	_	B-OBJ_NAME
revenue	_	_	I-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
pecans	_	_	B-VAR
is	_	_	O
$	_	_	O
600	_	_	B-PARAM
.	_	_	O
Each	_	_	O
acre	_	_	O
of	_	_	O
almonds	_	_	B-VAR
requires	_	_	O
1.5	_	_	B-PARAM
days	_	_	O
worth	_	_	O
of	_	_	O
labor	_	_	O
and	_	_	O
$	_	_	O
200	_	_	B-PARAM
in	_	_	O
maintenance	_	_	O
costs	_	_	O
.	_	_	O
Each	_	_	O
acre	_	_	O
of	_	_	O
pecans	_	_	B-VAR
requires	_	_	O
3	_	_	B-PARAM
days	_	_	O
worth	_	_	O
of	_	_	O
labor	_	_	O
and	_	_	O
$	_	_	O
250	_	_	B-PARAM
in	_	_	O
maintenance	_	_	O
costs	_	_	O
.	_	_	O
The	_	_	O
farmer	_	_	O
has	_	_	O
$	_	_	O
10000	_	_	B-LIMIT
available	_	_	B-CONST_DIR
to	_	_	O
spend	_	_	O
on	_	_	O
maintenance	_	_	O
costs	_	_	O
and	_	_	O
275	_	_	B-LIMIT
days	_	_	O
worth	_	_	O
of	_	_	O
labor	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
How	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
grown	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
net	_	_	B-OBJ_NAME
revenue	_	_	I-OBJ_NAME
?	_	_	O

John	_	_	O
has	_	_	O
pears	_	_	B-VAR
and	_	_	O
broccoli	_	_	B-VAR
to	_	_	O
eat	_	_	O
.	_	_	O
A	_	_	O
pound	_	_	O
of	_	_	O
pears	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
6	_	_	B-PARAM
and	_	_	O
contains	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
calcium	_	_	O
,	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
potassium	_	_	O
,	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
magnesium	_	_	O
per	_	_	O
pound	_	_	O
.	_	_	O
A	_	_	O
pound	_	_	O
of	_	_	O
broccoli	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
8	_	_	B-PARAM
and	_	_	O
contains	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
calcium	_	_	O
,	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
potassium	_	_	O
,	_	_	O
and	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
magnesium	_	_	O
per	_	_	O
pound	_	_	O
.	_	_	O
There	_	_	O
is	_	_	O
nothing	_	_	O
else	_	_	O
available	_	_	O
to	_	_	O
eat	_	_	O
and	_	_	O
John	_	_	O
must	_	_	O
meet	_	_	O
his	_	_	O
daily	_	_	O
requirements	_	_	O
of	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
15	_	_	B-LIMIT
units	_	_	O
of	_	_	O
calcium	_	_	O
,	_	_	O
20	_	_	B-LIMIT
units	_	_	O
of	_	_	O
potassium	_	_	O
,	_	_	O
and	_	_	O
17	_	_	B-LIMIT
units	_	_	O
of	_	_	O
magnesium	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
pounds	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
John	_	_	O
eat	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
cost	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
candy	_	_	O
store	_	_	O
has	_	_	B-CONST_DIR
30	_	_	B-LIMIT
kilograms	_	_	O
of	_	_	O
gummy	_	_	O
bears	_	_	O
and	_	_	O
25	_	_	B-LIMIT
kilograms	_	_	O
of	_	_	O
gummy	_	_	O
worms	_	_	O
.	_	_	O
They	_	_	O
sell	_	_	O
two	_	_	O
mixtures	_	_	O
of	_	_	O
these	_	_	O
gummies	_	_	O
:	_	_	O
mixture	_	_	B-VAR
A	_	_	I-VAR
and	_	_	O
mixture	_	_	B-VAR
B.	_	_	I-VAR
Mixture	_	_	B-VAR
A	_	_	I-VAR
is	_	_	O
75	_	_	B-PARAM
%	_	_	I-PARAM
gummy	_	_	O
bears	_	_	O
and	_	_	O
25	_	_	B-PARAM
%	_	_	I-PARAM
gummy	_	_	O
worms	_	_	O
.	_	_	O
Mixture	_	_	B-VAR
B	_	_	I-VAR
is	_	_	O
40	_	_	B-PARAM
%	_	_	I-PARAM
gummy	_	_	O
bears	_	_	O
and	_	_	O
60	_	_	B-PARAM
%	_	_	I-PARAM
gummy	_	_	O
worms	_	_	O
.	_	_	O
A	_	_	O
kilogram	_	_	O
of	_	_	O
mixture	_	_	B-VAR
A	_	_	I-VAR
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
30	_	_	B-PARAM
and	_	_	O
a	_	_	O
kilogram	_	_	O
of	_	_	O
mixture	_	_	B-VAR
B	_	_	I-VAR
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
40	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
kilograms	_	_	O
of	_	_	O
each	_	_	O
mixture	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Iron	_	_	O
and	_	_	O
zinc	_	_	O
are	_	_	O
found	_	_	O
in	_	_	O
elk	_	_	B-VAR
meat	_	_	I-VAR
and	_	_	O
bison	_	_	B-VAR
meat	_	_	I-VAR
.	_	_	O
A	_	_	O
serving	_	_	O
of	_	_	O
elk	_	_	B-VAR
meat	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
6	_	_	B-PARAM
and	_	_	O
contains	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
iron	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
zinc	_	_	O
.	_	_	O
A	_	_	O
serving	_	_	O
of	_	_	O
bison	_	_	B-VAR
meat	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
7	_	_	B-PARAM
and	_	_	O
contains	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
iron	_	_	O
and	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
zinc	_	_	O
.	_	_	O
If	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
units	_	_	O
of	_	_	O
iron	_	_	O
and	_	_	O
40	_	_	B-LIMIT
units	_	_	O
of	_	_	O
zinc	_	_	O
must	_	_	O
be	_	_	O
consumed	_	_	O
daily	_	_	O
,	_	_	O
formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
soup	_	_	O
store	_	_	O
sell	_	_	O
two	_	_	O
soups	_	_	O
:	_	_	O
a	_	_	O
crab	_	_	B-VAR
soup	_	_	I-VAR
and	_	_	O
a	_	_	O
lobster	_	_	B-VAR
soup	_	_	I-VAR
.	_	_	O
The	_	_	O
soups	_	_	O
are	_	_	O
made	_	_	O
using	_	_	O
water	_	_	O
,	_	_	O
crab	_	_	O
meat	_	_	O
,	_	_	O
and	_	_	O
lobster	_	_	O
meat	_	_	O
.	_	_	O
A	_	_	O
serving	_	_	O
of	_	_	O
crab	_	_	B-VAR
soup	_	_	I-VAR
requires	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	O
and	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
crab	_	_	O
meat	_	_	O
.	_	_	O
A	_	_	O
serving	_	_	O
of	_	_	O
lobster	_	_	B-VAR
soup	_	_	I-VAR
requires	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
lobster	_	_	O
meat	_	_	O
.	_	_	O
There	_	_	O
is	_	_	O
80	_	_	B-LIMIT
units	_	_	O
of	_	_	O
water	_	_	O
available	_	_	B-CONST_DIR
,	_	_	O
65	_	_	B-LIMIT
units	_	_	O
of	_	_	O
crab	_	_	O
meat	_	_	O
available	_	_	B-CONST_DIR
,	_	_	O
and	_	_	O
55	_	_	B-LIMIT
units	_	_	O
of	_	_	O
lobster	_	_	O
meat	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
serving	_	_	O
of	_	_	O
crab	_	_	B-VAR
soup	_	_	I-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
serving	_	_	O
of	_	_	O
lobster	_	_	B-VAR
soup	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
.	_	_	O
Formulate	_	_	O
as	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
.	_	_	O

Emma	_	_	O
makes	_	_	O
fancy	_	_	O
dresses	_	_	B-VAR
and	_	_	O
suits	_	_	B-VAR
in	_	_	O
her	_	_	O
shop	_	_	O
.	_	_	O
Both	_	_	O
of	_	_	O
these	_	_	O
items	_	_	O
require	_	_	O
use	_	_	O
of	_	_	O
a	_	_	O
sewing	_	_	O
machine	_	_	O
and	_	_	O
embroidery	_	_	O
machine	_	_	O
.	_	_	O
A	_	_	O
dress	_	_	B-VAR
requires	_	_	O
2	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
sewing	_	_	O
machine	_	_	O
and	_	_	O
4	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
embroidery	_	_	O
machine	_	_	O
.	_	_	O
A	_	_	O
suit	_	_	B-VAR
requires	_	_	O
1	_	_	B-PARAM
hour	_	_	O
on	_	_	O
the	_	_	O
sewing	_	_	O
machine	_	_	O
and	_	_	O
1	_	_	B-PARAM
hour	_	_	O
on	_	_	O
the	_	_	O
embroidery	_	_	O
machine	_	_	O
.	_	_	O
In	_	_	O
a	_	_	O
week	_	_	O
,	_	_	O
there	_	_	O
are	_	_	O
30	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
on	_	_	O
the	_	_	O
sewing	_	_	O
machine	_	_	O
and	_	_	O
50	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
on	_	_	O
the	_	_	O
embroidery	_	_	O
machine	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
dress	_	_	B-VAR
is	_	_	O
$	_	_	O
500	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
suit	_	_	B-VAR
is	_	_	O
$	_	_	O
800	_	_	B-PARAM
,	_	_	O
what	_	_	O
should	_	_	O
the	_	_	O
weekly	_	_	O
production	_	_	O
be	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
chocolate	_	_	O
company	_	_	O
makes	_	_	O
chocolate	_	_	B-VAR
bars	_	_	I-VAR
and	_	_	O
chocolate	_	_	B-VAR
wafers	_	_	I-VAR
.	_	_	O
Two	_	_	O
different	_	_	O
teams	_	_	O
produce	_	_	O
the	_	_	O
chocolate	_	_	B-VAR
bars	_	_	I-VAR
and	_	_	O
chocolate	_	_	B-VAR
wafers	_	_	I-VAR
.	_	_	O
The	_	_	O
chocolate	_	_	B-VAR
bar	_	_	I-VAR
team	_	_	O
has	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
daily	_	_	O
production	_	_	O
of	_	_	O
80	_	_	B-LIMIT
chocolate	_	_	B-VAR
bars	_	_	I-VAR
while	_	_	O
the	_	_	O
chocolate	_	_	B-VAR
wafer	_	_	I-VAR
team	_	_	O
has	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
daily	_	_	O
production	_	_	O
of	_	_	O
100	_	_	B-LIMIT
chocolate	_	_	B-VAR
wafers	_	_	I-VAR
.	_	_	O
However	_	_	O
both	_	_	O
bars	_	_	B-VAR
and	_	_	O
wafers	_	_	B-VAR
require	_	_	O
time	_	_	O
on	_	_	O
a	_	_	O
shared	_	_	O
packaging	_	_	O
machine	_	_	O
and	_	_	O
this	_	_	O
machine	_	_	O
can	_	_	O
process	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
125	_	_	B-LIMIT
chocolate	_	_	O
items	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
chocolate	_	_	B-VAR
bar	_	_	I-VAR
is	_	_	O
$	_	_	O
2	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
chocolate	_	_	B-VAR
wafer	_	_	I-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
make	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profits	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
pharmacist	_	_	O
wants	_	_	O
to	_	_	O
mix	_	_	O
two	_	_	O
drugs	_	_	O
in	_	_	O
such	_	_	O
a	_	_	O
way	_	_	O
to	_	_	O
create	_	_	O
a	_	_	O
mixture	_	_	O
that	_	_	O
contains	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
units	_	_	O
of	_	_	O
pain	_	_	O
killer	_	_	O
and	_	_	O
12	_	_	B-LIMIT
units	_	_	O
of	_	_	O
fever	_	_	O
reliever	_	_	O
.	_	_	O
The	_	_	O
amount	_	_	O
of	_	_	O
pain	_	_	O
killer	_	_	O
and	_	_	O
fever	_	_	O
reliever	_	_	O
in	_	_	O
drug	_	_	B-VAR
A	_	_	I-VAR
is	_	_	O
3	_	_	B-PARAM
units	_	_	O
/	_	_	O
mg	_	_	O
and	_	_	O
2.5	_	_	B-PARAM
units	_	_	O
/	_	_	O
mg	_	_	O
respectively	_	_	O
.	_	_	O
On	_	_	O
the	_	_	O
other	_	_	O
hand	_	_	O
,	_	_	O
the	_	_	O
amount	_	_	O
of	_	_	O
pain	_	_	O
killer	_	_	O
and	_	_	O
fever	_	_	O
reliever	_	_	O
in	_	_	O
drug	_	_	B-VAR
B	_	_	I-VAR
is	_	_	O
2	_	_	B-PARAM
units	_	_	O
/	_	_	O
mg	_	_	O
and	_	_	O
3.5	_	_	B-PARAM
units	_	_	O
/	_	_	O
mg	_	_	O
respectively	_	_	O
.	_	_	O
It	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
0.50	_	_	B-PARAM
per	_	_	O
mg	_	_	O
to	_	_	O
purchase	_	_	O
drug	_	_	B-VAR
A	_	_	I-VAR
and	_	_	O
$	_	_	O
0.30	_	_	B-PARAM
per	_	_	O
mg	_	_	O
to	_	_	O
purchase	_	_	O
drug	_	_	B-VAR
B.	_	_	I-VAR
Formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
of	_	_	O
such	_	_	O
a	_	_	O
mixture	_	_	O
.	_	_	O

A	_	_	O
florist	_	_	O
has	_	_	B-CONST_DIR
40	_	_	B-LIMIT
acres	_	_	O
to	_	_	O
grow	_	_	O
sunflowers	_	_	B-VAR
and	_	_	O
roses	_	_	B-VAR
.	_	_	O
To	_	_	O
ensure	_	_	O
the	_	_	O
flowers	_	_	O
grow	_	_	O
,	_	_	O
the	_	_	O
florist	_	_	O
must	_	_	O
use	_	_	O
plant	_	_	O
nutrition	_	_	O
to	_	_	O
feed	_	_	O
the	_	_	O
flowers	_	_	O
.	_	_	O
Sunflowers	_	_	B-VAR
require	_	_	O
5	_	_	B-PARAM
kg	_	_	O
of	_	_	O
plant	_	_	O
nutrition	_	_	O
per	_	_	O
acre	_	_	O
while	_	_	O
roses	_	_	B-VAR
require	_	_	O
8	_	_	B-PARAM
kg	_	_	O
of	_	_	O
plant	_	_	O
nutrition	_	_	O
per	_	_	O
acre	_	_	O
.	_	_	O
Due	_	_	O
to	_	_	O
the	_	_	O
high	_	_	O
cost	_	_	O
of	_	_	O
the	_	_	O
plant	_	_	O
nutrition	_	_	O
,	_	_	O
the	_	_	O
florist	_	_	O
wants	_	_	O
to	_	_	O
use	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
230	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
plant	_	_	O
nutrition	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
sunflowers	_	_	B-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
roses	_	_	B-VAR
is	_	_	O
$	_	_	O
375	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
florist	_	_	O
grow	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
phone	_	_	O
company	_	_	O
makes	_	_	O
two	_	_	O
phone	_	_	O
models	_	_	O
:	_	_	O
a	_	_	O
touchscreen	_	_	B-VAR
phone	_	_	I-VAR
and	_	_	O
a	_	_	O
flip	_	_	B-VAR
phone	_	_	I-VAR
.	_	_	O
Each	_	_	O
touchscreen	_	_	B-VAR
phone	_	_	I-VAR
requires	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
hardware	_	_	O
setup	_	_	O
and	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
software	_	_	O
verification	_	_	O
.	_	_	O
Each	_	_	O
flip	_	_	B-VAR
phone	_	_	I-VAR
requires	_	_	O
80	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
hardware	_	_	O
setup	_	_	O
and	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
software	_	_	O
verification	_	_	O
.	_	_	O
The	_	_	O
maximum	_	_	B-CONST_DIR
available	_	_	O
time	_	_	O
for	_	_	O
hardware	_	_	O
setup	_	_	O
is	_	_	O
5000	_	_	B-LIMIT
minutes	_	_	O
and	_	_	O
the	_	_	O
maximum	_	_	B-CONST_DIR
available	_	_	O
time	_	_	O
for	_	_	O
software	_	_	O
verification	_	_	O
is	_	_	O
3750	_	_	B-LIMIT
minutes	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
company	_	_	O
makes	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
150	_	_	B-PARAM
per	_	_	O
touchscreen	_	_	B-VAR
phone	_	_	I-VAR
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
200	_	_	B-PARAM
per	_	_	O
flip	_	_	B-VAR
phone	_	_	I-VAR
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
actor	_	_	O
needs	_	_	O
to	_	_	O
gain	_	_	O
weight	_	_	O
for	_	_	O
a	_	_	O
role	_	_	O
and	_	_	O
decides	_	_	O
to	_	_	O
eat	_	_	O
only	_	_	O
pizza	_	_	B-VAR
and	_	_	O
donuts	_	_	B-VAR
.	_	_	O
He	_	_	O
wants	_	_	O
to	_	_	O
eat	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
3000	_	_	B-LIMIT
calories	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
200	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
fat	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
Each	_	_	O
pizza	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
4	_	_	B-PARAM
and	_	_	O
contains	_	_	O
300	_	_	B-PARAM
calories	_	_	O
and	_	_	O
10	_	_	B-PARAM
grams	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
Each	_	_	O
donut	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
2	_	_	B-PARAM
and	_	_	O
contains	_	_	O
200	_	_	B-PARAM
calories	_	_	O
and	_	_	O
7	_	_	B-PARAM
grams	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
actor	_	_	O
eat	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
rich	_	_	O
lawyer	_	_	O
has	_	_	O
$	_	_	O
1000000	_	_	B-LIMIT
available	_	_	B-CONST_DIR
for	_	_	O
investment	_	_	O
.	_	_	O
He	_	_	O
wants	_	_	O
to	_	_	O
invest	_	_	O
in	_	_	O
the	_	_	O
gold	_	_	B-VAR
,	_	_	O
diamond	_	_	B-VAR
,	_	_	O
ruby	_	_	B-VAR
,	_	_	O
and	_	_	O
sapphire	_	_	B-VAR
industries	_	_	O
.	_	_	O
The	_	_	O
annual	_	_	O
rate	_	_	O
of	_	_	O
return	_	_	B-OBJ_NAME
for	_	_	O
each	_	_	O
industry	_	_	O
is	_	_	O
known	_	_	O
to	_	_	O
be	_	_	O
:	_	_	O
gold	_	_	B-VAR
,	_	_	O
3	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
diamond	_	_	B-VAR
,	_	_	O
5	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
ruby	_	_	B-VAR
,	_	_	O
6	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
sapphire	_	_	B-VAR
10	_	_	B-PARAM
%	_	_	I-PARAM
.	_	_	O
To	_	_	O
make	_	_	O
his	_	_	O
investments	_	_	O
more	_	_	O
spread	_	_	O
out	_	_	O
,	_	_	O
he	_	_	O
wants	_	_	O
to	_	_	O
ensure	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
sapphire	_	_	B-VAR
industry	_	_	I-VAR
does	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
gold	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
Also	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
diamond	_	_	B-VAR
industry	_	_	I-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
ruby	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
Finally	_	_	O
,	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
40	_	_	B-LIMIT
%	_	_	I-LIMIT
can	_	_	O
be	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
sapphire	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
How	_	_	O
should	_	_	O
the	_	_	O
lawyer	_	_	O
invest	_	_	O
his	_	_	O
money	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
return	_	_	B-OBJ_NAME
?	_	_	O

In	_	_	O
order	_	_	O
to	_	_	O
get	_	_	O
some	_	_	O
extra	_	_	O
amino	_	_	O
acids	_	_	O
,	_	_	O
Cindy	_	_	O
drinks	_	_	O
orange	_	_	B-VAR
juice	_	_	I-VAR
and	_	_	O
apple	_	_	B-VAR
juice	_	_	I-VAR
.	_	_	O
A	_	_	O
glass	_	_	O
of	_	_	O
orange	_	_	B-VAR
juice	_	_	I-VAR
contains	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
Lysine	_	_	O
,	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
Alanine	_	_	O
,	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
Methionine	_	_	O
,	_	_	O
and	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
Glycine	_	_	B-OBJ_NAME
.	_	_	O
A	_	_	O
glass	_	_	O
of	_	_	O
apple	_	_	B-VAR
juice	_	_	I-VAR
contains	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
Lysine	_	_	O
,	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
Alanine	_	_	O
,	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
Methionine	_	_	O
,	_	_	O
and	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
Glycine	_	_	B-OBJ_NAME
.	_	_	O
She	_	_	O
requires	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
units	_	_	O
of	_	_	O
Lysine	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
40	_	_	B-LIMIT
units	_	_	O
of	_	_	O
Alanine	_	_	O
,	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
50	_	_	B-LIMIT
units	_	_	O
of	_	_	O
Methionine	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
glasses	_	_	O
of	_	_	O
each	_	_	O
juice	_	_	O
should	_	_	O
she	_	_	O
drink	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
Glycine	_	_	I-OBJ_NAME
she	_	_	O
gets	_	_	O
.	_	_	O

A	_	_	O
laundromat	_	_	O
mixes	_	_	O
cans	_	_	O
of	_	_	O
product	_	_	O
from	_	_	O
two	_	_	O
companies	_	_	O
,	_	_	O
Omega	_	_	B-VAR
and	_	_	O
Omini	_	_	B-VAR
,	_	_	O
to	_	_	O
create	_	_	O
a	_	_	O
new	_	_	O
mixture	_	_	O
.	_	_	O
A	_	_	O
can	_	_	O
from	_	_	O
Omega	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
30	_	_	B-PARAM
while	_	_	O
a	_	_	O
can	_	_	O
from	_	_	O
Omini	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
40	_	_	B-PARAM
.	_	_	O
A	_	_	O
can	_	_	O
from	_	_	O
Omega	_	_	B-VAR
contains	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	O
,	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
detergent	_	_	O
,	_	_	O
and	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
bleach	_	_	O
.	_	_	O
A	_	_	O
can	_	_	O
from	_	_	O
Omini	_	_	B-VAR
contains	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	O
,	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
detergent	_	_	O
,	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
bleach	_	_	O
.	_	_	O
The	_	_	O
new	_	_	O
mixture	_	_	O
must	_	_	O
contain	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
units	_	_	O
of	_	_	O
water	_	_	O
,	_	_	O
35	_	_	B-LIMIT
units	_	_	O
of	_	_	O
detergent	_	_	O
,	_	_	O
and	_	_	O
40	_	_	B-LIMIT
units	_	_	O
of	_	_	O
bleach	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
cans	_	_	O
from	_	_	O
each	_	_	O
brand	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
create	_	_	O
the	_	_	O
mixture	_	_	O
at	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
circuit	_	_	O
board	_	_	O
company	_	_	O
makes	_	_	O
small	_	_	B-VAR
and	_	_	O
large	_	_	B-VAR
circuit	_	_	I-VAR
boards	_	_	I-VAR
for	_	_	O
customers	_	_	O
.	_	_	O
Both	_	_	O
circuit	_	_	O
boards	_	_	O
requires	_	_	O
time	_	_	O
on	_	_	O
a	_	_	O
drilling	_	_	O
machine	_	_	O
and	_	_	O
a	_	_	O
printing	_	_	O
machine	_	_	O
.	_	_	O
Each	_	_	O
small	_	_	B-VAR
circuit	_	_	I-VAR
board	_	_	I-VAR
takes	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
drilling	_	_	O
machine	_	_	O
,	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
printing	_	_	O
machine	_	_	O
and	_	_	O
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
5	_	_	B-PARAM
.	_	_	O
Each	_	_	O
large	_	_	B-VAR
circuit	_	_	I-VAR
board	_	_	I-VAR
takes	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
drilling	_	_	O
machine	_	_	O
,	_	_	O
18	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
printing	_	_	O
machine	_	_	O
,	_	_	O
and	_	_	O
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
7	_	_	B-PARAM
.	_	_	O
If	_	_	O
both	_	_	O
machines	_	_	O
are	_	_	O
available	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
600	_	_	B-LIMIT
minutes	_	_	O
a	_	_	O
day	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
circuit	_	_	O
board	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
costume	_	_	O
store	_	_	O
sells	_	_	O
policeman	_	_	B-VAR
costumes	_	_	I-VAR
and	_	_	O
fireman	_	_	B-VAR
costumes	_	_	I-VAR
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
3000	_	_	B-LIMIT
and	_	_	O
each	_	_	O
policeman	_	_	B-VAR
costume	_	_	I-VAR
costs	_	_	O
$	_	_	O
10	_	_	B-PARAM
and	_	_	O
each	_	_	O
fireman	_	_	B-VAR
costume	_	_	I-VAR
costs	_	_	O
$	_	_	O
15	_	_	B-PARAM
.	_	_	O
The	_	_	O
monthly	_	_	O
demand	_	_	O
for	_	_	O
both	_	_	O
costumes	_	_	O
will	_	_	O
not	_	_	B-CONST_DIR
exceed	_	_	I-CONST_DIR
280	_	_	B-LIMIT
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
policeman	_	_	B-VAR
costume	_	_	I-VAR
is	_	_	O
$	_	_	O
8	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
fireman	_	_	B-VAR
costume	_	_	I-VAR
is	_	_	O
$	_	_	O
10	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
store	_	_	O
stock	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
sandwich	_	_	O
store	_	_	O
makes	_	_	O
large	_	_	B-VAR
and	_	_	O
small	_	_	B-VAR
sandwiches	_	_	O
.	_	_	O
Each	_	_	O
large	_	_	B-VAR
sandwich	_	_	I-VAR
takes	_	_	O
4	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
preparation	_	_	O
and	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
toasting	_	_	O
.	_	_	O
Each	_	_	O
small	_	_	B-VAR
sandwich	_	_	I-VAR
takes	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
preparation	_	_	O
and	_	_	O
4	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
toasting	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
1000	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
preparation	_	_	O
and	_	_	O
1200	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
toasting	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
large	_	_	B-VAR
sandwich	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
small	_	_	B-VAR
sandwich	_	_	I-VAR
is	_	_	O
$	_	_	O
3.50	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
bus	_	_	O
can	_	_	O
carry	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
80	_	_	B-LIMIT
people	_	_	O
and	_	_	O
sells	_	_	O
adult	_	_	B-VAR
ticket	_	_	I-VAR
and	_	_	O
children	_	_	B-VAR
's	_	_	I-VAR
tickets	_	_	I-VAR
.	_	_	O
A	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
3	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
adult	_	_	B-VAR
ticket	_	_	I-VAR
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
1	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
children	_	_	B-VAR
's	_	_	I-VAR
ticket	_	_	I-VAR
.	_	_	O
The	_	_	O
bus	_	_	O
reserves	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
15	_	_	B-LIMIT
tickets	_	_	O
for	_	_	O
children	_	_	B-VAR
.	_	_	O
However	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
tickets	_	_	O
sold	_	_	O
are	_	_	O
adult	_	_	B-VAR
tickets	_	_	I-VAR
than	_	_	O
children	_	_	B-VAR
's	_	_	I-VAR
ticket	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
ticket	_	_	O
should	_	_	O
be	_	_	O
sold	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
engineering	_	_	O
company	_	_	O
makes	_	_	O
small	_	_	B-VAR
and	_	_	O
large	_	_	B-VAR
PCB	_	_	O
's	_	_	O
.	_	_	O
A	_	_	O
small	_	_	B-VAR
PCB	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
silicon	_	_	O
while	_	_	O
a	_	_	O
large	_	_	B-VAR
PCB	_	_	I-VAR
requires	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
silicon	_	_	O
.	_	_	O
A	_	_	O
small	_	_	B-VAR
PCB	_	_	I-VAR
requires	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
design	_	_	O
and	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
soldering	_	_	O
while	_	_	O
a	_	_	O
large	_	_	B-VAR
PCB	_	_	I-VAR
requires	_	_	O
40	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
design	_	_	O
and	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
soldering	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
250	_	_	B-LIMIT
units	_	_	O
of	_	_	O
silicon	_	_	O
,	_	_	O
800	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
design	_	_	O
time	_	_	O
,	_	_	O
and	_	_	O
600	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
soldering	_	_	O
time	_	_	O
.	_	_	O
They	_	_	O
also	_	_	O
want	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
5	_	_	B-LIMIT
small	_	_	B-VAR
PCB	_	_	I-VAR
's	_	_	O
and	_	_	O
6	_	_	B-LIMIT
large	_	_	B-VAR
PCB	_	_	I-VAR
's	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
small	_	_	B-VAR
PCB	_	_	I-VAR
is	_	_	O
$	_	_	O
20	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
large	_	_	B-VAR
PCB	_	_	I-VAR
is	_	_	O
$	_	_	O
35	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
candy	_	_	O
company	_	_	O
wants	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
special	_	_	O
mix	_	_	O
using	_	_	O
sour	_	_	B-VAR
cherry	_	_	I-VAR
candies	_	_	I-VAR
and	_	_	O
sour	_	_	B-VAR
peach	_	_	I-VAR
candies	_	_	I-VAR
.	_	_	O
Each	_	_	O
sour	_	_	B-VAR
cherry	_	_	I-VAR
candy	_	_	I-VAR
has	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
citric	_	_	O
acid	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
sugar	_	_	O
.	_	_	O
Each	_	_	O
sour	_	_	B-VAR
peach	_	_	I-VAR
candy	_	_	I-VAR
has	_	_	O
1	_	_	B-PARAM
units	_	_	O
of	_	_	O
citric	_	_	O
acid	_	_	O
and	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
sugar	_	_	O
.	_	_	O
The	_	_	O
special	_	_	O
mix	_	_	O
must	_	_	O
contain	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
units	_	_	O
of	_	_	O
citric	_	_	O
acid	_	_	O
and	_	_	O
60	_	_	B-LIMIT
units	_	_	O
of	_	_	O
sugar	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
there	_	_	O
can	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
10	_	_	B-LIMIT
sour	_	_	B-VAR
cherry	_	_	I-VAR
candies	_	_	I-VAR
in	_	_	O
the	_	_	O
mixture	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
sour	_	_	B-VAR
cherry	_	_	I-VAR
candy	_	_	I-VAR
is	_	_	O
$	_	_	O
0.10	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
sour	_	_	B-VAR
peach	_	_	I-VAR
candy	_	_	I-VAR
is	_	_	O
$	_	_	O
0.12	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
in	_	_	O
the	_	_	O
mixture	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
company	_	_	O
sells	_	_	O
almond	_	_	B-VAR
and	_	_	O
cashews	_	_	B-VAR
in	_	_	O
small	_	_	O
tins	_	_	O
.	_	_	O
Each	_	_	O
almond	_	_	B-VAR
tin	_	_	I-VAR
takes	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
fill	_	_	O
and	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
label	_	_	O
.	_	_	O
Each	_	_	O
cashew	_	_	B-VAR
tin	_	_	I-VAR
takes	_	_	O
4	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
fill	_	_	O
and	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
label	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
400	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
filling	_	_	O
and	_	_	O
500	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
labelling	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
almond	_	_	B-VAR
tin	_	_	I-VAR
is	_	_	O
$	_	_	O
10	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
cashew	_	_	B-VAR
tin	_	_	I-VAR
is	_	_	O
$	_	_	O
15	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
aquarium	_	_	O
feeds	_	_	O
their	_	_	O
large	_	_	O
animals	_	_	O
with	_	_	O
smaller	_	_	O
fish	_	_	O
by	_	_	O
making	_	_	O
a	_	_	O
mixture	_	_	O
from	_	_	O
two	_	_	O
bags	_	_	O
.	_	_	O
Bag	_	_	B-VAR
A	_	_	I-VAR
contains	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
sardines	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
anchovies	_	_	O
per	_	_	O
bag	_	_	O
.	_	_	O
Bag	_	_	B-VAR
B	_	_	I-VAR
contains	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
sardines	_	_	O
and	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
anchovies	_	_	O
per	_	_	O
bag	_	_	O
.	_	_	O
The	_	_	O
mixture	_	_	O
must	_	_	O
contain	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
units	_	_	O
of	_	_	O
sardines	_	_	O
and	_	_	O
25	_	_	B-LIMIT
units	_	_	O
of	_	_	O
anchovies	_	_	O
.	_	_	O
Bag	_	_	B-VAR
A	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
4	_	_	B-PARAM
per	_	_	O
bag	_	_	O
and	_	_	O
Bag	_	_	B-VAR
B	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
6	_	_	B-PARAM
per	_	_	O
bag	_	_	O
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
for	_	_	O
the	_	_	O
mixture	_	_	O
.	_	_	O

A	_	_	O
pizza	_	_	O
store	_	_	O
makes	_	_	O
cheese	_	_	B-VAR
and	_	_	O
pepperoni	_	_	B-VAR
pizza	_	_	I-VAR
.	_	_	O
Each	_	_	O
cheese	_	_	B-VAR
pizza	_	_	I-VAR
requires	_	_	O
30	_	_	B-PARAM
grams	_	_	O
of	_	_	O
flour	_	_	O
,	_	_	O
50	_	_	B-PARAM
grams	_	_	O
of	_	_	O
cheese	_	_	O
,	_	_	O
and	_	_	O
40	_	_	B-PARAM
grams	_	_	O
of	_	_	O
sauce	_	_	O
.	_	_	O
Each	_	_	O
pepperoni	_	_	B-VAR
pizza	_	_	I-VAR
requires	_	_	O
40	_	_	B-PARAM
grams	_	_	O
of	_	_	O
flour	_	_	O
,	_	_	O
20	_	_	B-PARAM
grams	_	_	O
of	_	_	O
cheese	_	_	O
,	_	_	O
and	_	_	O
30	_	_	B-PARAM
grams	_	_	O
of	_	_	O
sauce	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
3000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
flour	_	_	O
,	_	_	O
4000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
cheese	_	_	O
,	_	_	O
and	_	_	O
5000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
sauce	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
cheese	_	_	B-VAR
pizza	_	_	I-VAR
is	_	_	O
$	_	_	O
7	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
pepperoni	_	_	B-VAR
pizza	_	_	I-VAR
is	_	_	O
$	_	_	O
9	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
company	_	_	O
installs	_	_	O
washing	_	_	B-VAR
machines	_	_	I-VAR
and	_	_	O
dryers	_	_	B-VAR
in	_	_	O
houses	_	_	O
.	_	_	O
Each	_	_	O
washing	_	_	B-VAR
machine	_	_	I-VAR
takes	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
plumber	_	_	O
time	_	_	O
and	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
electrician	_	_	O
time	_	_	O
.	_	_	O
Each	_	_	O
dryer	_	_	B-VAR
takes	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
plumber	_	_	O
time	_	_	O
and	_	_	O
25	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
electrician	_	_	O
time	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
2000	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
plumber	_	_	O
time	_	_	O
and	_	_	O
3000	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
electrician	_	_	O
time	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
washing	_	_	B-VAR
machine	_	_	I-VAR
installation	_	_	O
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
dryer	_	_	B-VAR
installation	_	_	O
is	_	_	O
$	_	_	O
150	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
installed	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
company	_	_	O
hand	_	_	O
fills	_	_	O
shampoo	_	_	B-VAR
and	_	_	O
conditioner	_	_	B-VAR
bottles	_	_	O
.	_	_	O
Each	_	_	O
shampoo	_	_	B-VAR
bottle	_	_	I-VAR
takes	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
fill	_	_	O
and	_	_	O
each	_	_	O
conditioner	_	_	B-VAR
bottle	_	_	I-VAR
takes	_	_	O
4	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
fill	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
must	_	_	O
fill	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
shampoo	_	_	B-VAR
bottles	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
conditioner	_	_	B-VAR
bottles	_	_	I-VAR
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
300	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
shampoo	_	_	B-VAR
bottle	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
conditioner	_	_	B-VAR
bottle	_	_	I-VAR
is	_	_	O
$	_	_	O
6	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
filled	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
woodshop	_	_	O
makes	_	_	O
dining	_	_	B-VAR
tables	_	_	I-VAR
and	_	_	O
bed	_	_	B-VAR
frames	_	_	I-VAR
using	_	_	O
oak	_	_	O
and	_	_	O
mahogany	_	_	O
wood	_	_	O
.	_	_	O
Each	_	_	O
dining	_	_	B-VAR
table	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
oak	_	_	O
wood	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
mahogany	_	_	O
wood	_	_	O
.	_	_	O
Each	_	_	O
bed	_	_	B-VAR
frame	_	_	I-VAR
requires	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
oak	_	_	O
wood	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
mahogany	_	_	O
wood	_	_	O
.	_	_	O
The	_	_	O
woodshop	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
300	_	_	B-LIMIT
units	_	_	O
of	_	_	O
oak	_	_	O
wood	_	_	O
and	_	_	O
400	_	_	B-LIMIT
units	_	_	O
of	_	_	O
mahogany	_	_	O
wood	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
dining	_	_	B-VAR
table	_	_	I-VAR
is	_	_	O
$	_	_	O
300	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
bed	_	_	B-VAR
frame	_	_	I-VAR
is	_	_	O
$	_	_	O
400	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

You	_	_	O
need	_	_	O
to	_	_	O
buy	_	_	O
shelves	_	_	O
to	_	_	O
store	_	_	O
your	_	_	O
action	_	_	O
figures	_	_	O
.	_	_	O
A	_	_	O
small	_	_	B-VAR
shelf	_	_	I-VAR
takes	_	_	O
3	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
of	_	_	O
space	_	_	O
and	_	_	O
costs	_	_	O
$	_	_	O
50	_	_	B-PARAM
.	_	_	O
A	_	_	O
large	_	_	B-VAR
shelf	_	_	I-VAR
takes	_	_	O
6	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
and	_	_	O
costs	_	_	O
$	_	_	O
80	_	_	B-PARAM
.	_	_	O
You	_	_	O
have	_	_	O
100	_	_	B-LIMIT
sq	_	_	O
ft	_	_	O
of	_	_	O
space	_	_	O
available	_	_	B-CONST_DIR
and	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
1250	_	_	B-LIMIT
.	_	_	O
If	_	_	O
the	_	_	O
small	_	_	B-VAR
shelf	_	_	I-VAR
can	_	_	O
hold	_	_	O
20	_	_	B-PARAM
action	_	_	B-OBJ_NAME
figures	_	_	I-OBJ_NAME
and	_	_	O
a	_	_	O
large	_	_	B-VAR
shelf	_	_	I-VAR
can	_	_	O
hold	_	_	O
30	_	_	B-PARAM
action	_	_	B-OBJ_NAME
figures	_	_	I-OBJ_NAME
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
you	_	_	O
buy	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
action	_	_	I-OBJ_NAME
figures	_	_	I-OBJ_NAME
you	_	_	O
can	_	_	O
store	_	_	O
.	_	_	O

Your	_	_	O
client	_	_	O
has	_	_	O
$	_	_	O
60,000	_	_	B-LIMIT
available	_	_	B-CONST_DIR
to	_	_	O
invest	_	_	O
for	_	_	O
a	_	_	O
1	_	_	O
year	_	_	O
term	_	_	O
.	_	_	O
The	_	_	O
money	_	_	O
can	_	_	O
be	_	_	O
placed	_	_	O
in	_	_	O
a	_	_	O
trust	_	_	B-VAR
yielding	_	_	O
a	_	_	O
2	_	_	B-PARAM
%	_	_	O
return	_	_	B-OBJ_NAME
or	_	_	O
in	_	_	O
a	_	_	O
savings	_	_	B-VAR
account	_	_	I-VAR
yielding	_	_	O
a	_	_	O
3	_	_	B-PARAM
%	_	_	O
return	_	_	B-OBJ_NAME
.	_	_	O
Based	_	_	O
on	_	_	O
your	_	_	O
experience	_	_	O
,	_	_	O
you	_	_	O
advise	_	_	O
your	_	_	O
client	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
15	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
investment	_	_	O
be	_	_	O
placed	_	_	O
in	_	_	O
the	_	_	O
trust	_	_	B-VAR
and	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
80	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
investment	_	_	O
be	_	_	O
placed	_	_	O
in	_	_	O
the	_	_	O
savings	_	_	B-VAR
account	_	_	I-VAR
.	_	_	O
How	_	_	O
much	_	_	O
should	_	_	O
your	_	_	O
client	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
so	_	_	O
as	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
return	_	_	B-OBJ_NAME
on	_	_	O
investment	_	_	O
?	_	_	O

A	_	_	O
landscaper	_	_	O
provides	_	_	O
3	_	_	O
landscaping	_	_	O
layouts	_	_	O
using	_	_	O
different	_	_	O
amounts	_	_	O
of	_	_	O
rock	_	_	O
,	_	_	O
mulch	_	_	O
,	_	_	O
and	_	_	O
grass	_	_	O
.	_	_	O
He	_	_	O
has	_	_	B-CONST_DIR
1200	_	_	B-LIMIT
units	_	_	O
of	_	_	O
rock	_	_	O
,	_	_	O
700	_	_	B-LIMIT
units	_	_	O
of	_	_	O
mulch	_	_	O
,	_	_	O
and	_	_	O
2000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
grass	_	_	O
.	_	_	O
A	_	_	O
type	_	_	B-VAR
A	_	_	I-VAR
layout	_	_	I-VAR
has	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
rock	_	_	O
,	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
mulch	_	_	O
,	_	_	O
and	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
grass	_	_	O
.	_	_	O
A	_	_	O
type	_	_	B-VAR
B	_	_	I-VAR
layout	_	_	I-VAR
has	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
rock	_	_	O
,	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
mulch	_	_	O
,	_	_	O
and	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
grass	_	_	O
.	_	_	O
A	_	_	O
type	_	_	B-VAR
C	_	_	I-VAR
layout	_	_	I-VAR
has	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
rock	_	_	O
,	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
mulch	_	_	O
,	_	_	O
and	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
grass	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
for	_	_	O
each	_	_	O
type	_	_	B-VAR
A	_	_	I-VAR
layout	_	_	I-VAR
,	_	_	O
$	_	_	O
175	_	_	B-PARAM
for	_	_	O
each	_	_	O
type	_	_	B-VAR
B	_	_	I-VAR
layout	_	_	I-VAR
,	_	_	O
and	_	_	O
$	_	_	O
225	_	_	B-PARAM
for	_	_	O
each	_	_	O
type	_	_	B-VAR
C	_	_	I-VAR
layout	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
layouts	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
toy	_	_	O
company	_	_	O
makes	_	_	O
toys	_	_	O
and	_	_	O
knows	_	_	O
that	_	_	O
most	_	_	O
of	_	_	O
their	_	_	O
customers	_	_	O
are	_	_	O
young	_	_	O
boys	_	_	O
and	_	_	O
girls	_	_	O
.	_	_	O
To	_	_	O
reach	_	_	O
these	_	_	O
groups	_	_	O
,	_	_	O
the	_	_	O
company	_	_	O
has	_	_	O
decided	_	_	O
to	_	_	O
purchase	_	_	O
commercial	_	_	O
spots	_	_	O
on	_	_	O
cartoons	_	_	B-VAR
and	_	_	O
kids	_	_	B-VAR
-	_	_	I-VAR
movies	_	_	I-VAR
.	_	_	O
Each	_	_	O
cartoon	_	_	B-VAR
is	_	_	O
seen	_	_	O
by	_	_	O
2	_	_	B-PARAM
millions	_	_	O
young	_	_	O
boys	_	_	O
and	_	_	O
1	_	_	B-PARAM
million	_	_	O
young	_	_	O
girls	_	_	O
.	_	_	O
Each	_	_	O
kids	_	_	B-VAR
-	_	_	I-VAR
movie	_	_	I-VAR
is	_	_	O
seen	_	_	O
by	_	_	O
4	_	_	B-PARAM
million	_	_	O
young	_	_	O
boys	_	_	O
and	_	_	O
6	_	_	B-PARAM
million	_	_	O
young	_	_	O
girls	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
wants	_	_	O
their	_	_	O
commercials	_	_	O
to	_	_	O
be	_	_	O
seen	_	_	O
by	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
million	_	_	O
young	_	_	O
boys	_	_	O
and	_	_	O
40	_	_	B-LIMIT
million	_	_	O
young	_	_	O
girls	_	_	O
.	_	_	O
If	_	_	O
a	_	_	O
commercial	_	_	O
during	_	_	O
a	_	_	O
cartoon	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
5000	_	_	B-PARAM
and	_	_	O
a	_	_	O
commercial	_	_	O
during	_	_	O
a	_	_	O
kids	_	_	B-VAR
-	_	_	I-VAR
movie	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
12000	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
purchased	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
?	_	_	O

Lisa	_	_	O
can	_	_	O
invest	_	_	O
in	_	_	O
NFTs	_	_	B-VAR
and	_	_	O
crypto	_	_	B-VAR
-	_	_	I-VAR
currency	_	_	I-VAR
up	_	_	B-CONST_DIR
to	_	_	I-CONST_DIR
$	_	_	O
5000	_	_	B-LIMIT
.	_	_	O
Each	_	_	O
dollar	_	_	O
invested	_	_	O
in	_	_	O
NFTs	_	_	B-VAR
yields	_	_	O
$	_	_	O
0.30	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
,	_	_	O
and	_	_	O
each	_	_	O
dollar	_	_	O
invested	_	_	O
in	_	_	O
a	_	_	O
crypto	_	_	B-VAR
-	_	_	I-VAR
currency	_	_	I-VAR
yields	_	_	O
$	_	_	O
0.40	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
.	_	_	O
A	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
25	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
all	_	_	O
money	_	_	O
invested	_	_	O
must	_	_	O
be	_	_	O
in	_	_	O
NFTs	_	_	B-VAR
,	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
$	_	_	O
2300	_	_	B-LIMIT
must	_	_	O
be	_	_	O
in	_	_	O
crypto	_	_	B-VAR
-	_	_	I-VAR
currency	_	_	I-VAR
.	_	_	O
How	_	_	O
can	_	_	O
Lisa	_	_	O
maximize	_	_	B-OBJ_DIR
her	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
vendor	_	_	O
sells	_	_	O
coffee	_	_	B-VAR
and	_	_	O
hot	_	_	B-VAR
chocolate	_	_	I-VAR
during	_	_	O
ice	_	_	O
hockey	_	_	O
games	_	_	O
.	_	_	O
To	_	_	O
stay	_	_	O
in	_	_	O
business	_	_	O
,	_	_	O
he	_	_	O
must	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
40	_	_	B-LIMIT
coffees	_	_	B-VAR
and	_	_	O
20	_	_	B-LIMIT
hot	_	_	B-VAR
chocolates	_	_	I-VAR
,	_	_	O
but	_	_	O
can	_	_	O
not	_	_	B-CONST_DIR
make	_	_	I-CONST_DIR
more	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
60	_	_	B-LIMIT
coffees	_	_	B-VAR
or	_	_	O
35	_	_	B-LIMIT
hot	_	_	B-VAR
chocolates	_	_	I-VAR
.	_	_	O
The	_	_	O
vendor	_	_	O
also	_	_	O
ca	_	_	O
n't	_	_	B-CONST_DIR
make	_	_	I-CONST_DIR
more	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
75	_	_	B-LIMIT
items	_	_	O
total	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
on	_	_	O
a	_	_	O
coffee	_	_	B-VAR
is	_	_	O
$	_	_	O
0.22	_	_	B-PARAM
,	_	_	O
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
on	_	_	O
a	_	_	O
hot	_	_	B-VAR
chocolate	_	_	I-VAR
is	_	_	O
$	_	_	O
0.14	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
item	_	_	O
should	_	_	O
he	_	_	O
sell	_	_	O
to	_	_	O
make	_	_	O
the	_	_	O
maximum	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
store	_	_	O
sells	_	_	O
two	_	_	O
different	_	_	O
scents	_	_	O
of	_	_	O
hand	_	_	O
lotion	_	_	O
,	_	_	O
Eucalyptus	_	_	B-VAR
and	_	_	O
Citrus	_	_	B-VAR
.	_	_	O
The	_	_	O
store	_	_	O
owner	_	_	O
pays	_	_	O
$	_	_	O
6	_	_	B-PARAM
for	_	_	O
a	_	_	O
bottle	_	_	O
of	_	_	O
Eucalyptus	_	_	B-VAR
lotion	_	_	I-VAR
and	_	_	O
$	_	_	O
8	_	_	B-PARAM
for	_	_	O
a	_	_	O
bottle	_	_	O
of	_	_	O
Citrus	_	_	B-VAR
lotion	_	_	I-VAR
.	_	_	O
A	_	_	O
bottle	_	_	O
of	_	_	O
Eucalyptus	_	_	B-VAR
lotion	_	_	I-VAR
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
1	_	_	B-PARAM
while	_	_	O
a	_	_	O
bottle	_	_	O
of	_	_	O
Citrus	_	_	B-VAR
lotion	_	_	I-VAR
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
4	_	_	B-PARAM
.	_	_	O
The	_	_	O
store	_	_	O
owner	_	_	O
estimates	_	_	O
that	_	_	O
no	_	_	B-CONST_DIR
more	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
1500	_	_	B-LIMIT
bottles	_	_	O
of	_	_	O
lotion	_	_	O
will	_	_	O
be	_	_	O
sold	_	_	O
every	_	_	O
month	_	_	O
and	_	_	O
she	_	_	O
does	_	_	O
not	_	_	O
plan	_	_	O
to	_	_	O
invest	_	_	O
more	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
$	_	_	O
10000	_	_	B-LIMIT
in	_	_	O
inventory	_	_	O
for	_	_	O
these	_	_	O
lotions	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
bottles	_	_	O
of	_	_	O
each	_	_	O
lotion	_	_	O
should	_	_	O
be	_	_	O
stocked	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
her	_	_	O
total	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
candy	_	_	O
company	_	_	O
makes	_	_	O
3	_	_	O
different	_	_	O
sized	_	_	O
gift	_	_	O
boxes	_	_	O
:	_	_	O
small	_	_	O
,	_	_	O
medium	_	_	O
,	_	_	O
and	_	_	O
large	_	_	O
.	_	_	O
These	_	_	O
gift	_	_	O
boxes	_	_	O
are	_	_	O
made	_	_	O
by	_	_	O
their	_	_	O
mall	_	_	B-VAR
kiosk	_	_	I-VAR
and	_	_	O
flagship	_	_	B-VAR
store	_	_	I-VAR
location	_	_	O
.	_	_	O
The	_	_	O
mall	_	_	B-VAR
kiosk	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
150	_	_	B-PARAM
to	_	_	O
operate	_	_	O
per	_	_	O
hour	_	_	O
and	_	_	O
can	_	_	O
make	_	_	O
5	_	_	B-PARAM
small	_	_	O
gift	_	_	O
boxes	_	_	O
,	_	_	O
6	_	_	B-PARAM
medium	_	_	O
gift	_	_	O
boxes	_	_	O
,	_	_	O
and	_	_	O
2	_	_	B-PARAM
large	_	_	O
gift	_	_	O
boxes	_	_	O
in	_	_	O
that	_	_	O
hour	_	_	O
.	_	_	O
The	_	_	O
flagship	_	_	B-VAR
store	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
500	_	_	B-PARAM
to	_	_	O
operate	_	_	O
per	_	_	O
hour	_	_	O
and	_	_	O
can	_	_	O
make	_	_	O
10	_	_	B-PARAM
small	_	_	O
gift	_	_	O
boxes	_	_	O
,	_	_	O
15	_	_	B-PARAM
medium	_	_	O
gift	_	_	O
boxes	_	_	O
,	_	_	O
and	_	_	O
9	_	_	B-PARAM
large	_	_	O
gift	_	_	O
boxes	_	_	O
in	_	_	O
that	_	_	O
hour	_	_	O
.	_	_	O
To	_	_	O
meet	_	_	O
demands	_	_	O
,	_	_	O
the	_	_	O
company	_	_	O
must	_	_	O
make	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
80	_	_	B-LIMIT
small	_	_	O
gift	_	_	O
boxes	_	_	O
,	_	_	O
100	_	_	B-LIMIT
medium	_	_	O
gift	_	_	O
boxes	_	_	O
,	_	_	O
and	_	_	O
50	_	_	B-LIMIT
large	_	_	O
gift	_	_	O
boxes	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
lighting	_	_	O
company	_	_	O
makes	_	_	O
2	_	_	O
types	_	_	O
of	_	_	O
lightbulbs	_	_	O
,	_	_	O
LED	_	_	B-VAR
and	_	_	O
Halogen	_	_	B-VAR
.	_	_	O
Each	_	_	O
type	_	_	O
of	_	_	O
lightbulb	_	_	O
requires	_	_	O
time	_	_	O
on	_	_	O
a	_	_	O
plastics	_	_	O
machine	_	_	O
and	_	_	O
a	_	_	O
wiring	_	_	O
machine	_	_	O
.	_	_	O
It	_	_	O
takes	_	_	O
6	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
plastics	_	_	O
machine	_	_	O
and	_	_	O
12	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
wiring	_	_	O
machine	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
package	_	_	O
of	_	_	O
LED	_	_	B-VAR
lightbulbs	_	_	I-VAR
.	_	_	O
On	_	_	O
the	_	_	O
other	_	_	O
hand	_	_	O
,	_	_	O
it	_	_	O
takes	_	_	O
9	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
plastics	_	_	O
machine	_	_	O
and	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
wiring	_	_	O
machine	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
package	_	_	O
of	_	_	O
Halogen	_	_	B-VAR
lightbulbs	_	_	I-VAR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
package	_	_	O
of	_	_	O
LED	_	_	B-VAR
lightbulbs	_	_	I-VAR
is	_	_	O
$	_	_	O
30	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
package	_	_	O
of	_	_	O
Halogen	_	_	B-VAR
lightbulbs	_	_	I-VAR
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
.	_	_	O
If	_	_	O
both	_	_	O
machines	_	_	O
are	_	_	O
available	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
500	_	_	B-LIMIT
minutes	_	_	O
per	_	_	O
day	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
packages	_	_	O
of	_	_	O
each	_	_	O
lightbulb	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
student	_	_	O
group	_	_	O
makes	_	_	O
chocolate	_	_	B-VAR
chip	_	_	I-VAR
and	_	_	O
oatmeal	_	_	B-VAR
cookies	_	_	I-VAR
.	_	_	O
To	_	_	O
make	_	_	O
a	_	_	O
batch	_	_	O
of	_	_	O
chocolate	_	_	B-VAR
chip	_	_	I-VAR
cookies	_	_	I-VAR
,	_	_	O
it	_	_	O
take	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
gather	_	_	O
the	_	_	O
ingredients	_	_	O
,	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
mix	_	_	O
them	_	_	O
,	_	_	O
and	_	_	O
50	_	_	B-PARAM
minutes	_	_	O
for	_	_	O
baking	_	_	O
.	_	_	O
To	_	_	O
make	_	_	O
a	_	_	O
batch	_	_	O
of	_	_	O
oatmeal	_	_	B-VAR
cookies	_	_	I-VAR
,	_	_	O
it	_	_	O
takes	_	_	O
8	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
gather	_	_	O
the	_	_	O
ingredients	_	_	O
,	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
mix	_	_	O
them	_	_	O
,	_	_	O
and	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
for	_	_	O
baking	_	_	O
.	_	_	O
Per	_	_	O
week	_	_	O
,	_	_	O
the	_	_	O
group	_	_	O
has	_	_	B-CONST_DIR
1000	_	_	B-LIMIT
minutes	_	_	O
to	_	_	O
gather	_	_	O
ingredients	_	_	O
,	_	_	O
1200	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
mixing	_	_	O
,	_	_	O
and	_	_	O
3000	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
baking	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
batch	_	_	O
of	_	_	O
chocolate	_	_	B-VAR
chip	_	_	I-VAR
cookies	_	_	I-VAR
is	_	_	O
$	_	_	O
12	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
batch	_	_	O
of	_	_	O
oatmeal	_	_	B-VAR
cookies	_	_	I-VAR
is	_	_	O
$	_	_	O
15	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
batches	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Jane	_	_	O
has	_	_	B-CONST_DIR
a	_	_	O
field	_	_	O
of	_	_	O
200	_	_	B-LIMIT
acres	_	_	O
to	_	_	O
grow	_	_	O
tulips	_	_	B-VAR
and	_	_	O
daffodils	_	_	B-VAR
.	_	_	O
The	_	_	O
bulbs	_	_	O
for	_	_	O
tulips	_	_	B-VAR
cost	_	_	O
$	_	_	O
10	_	_	B-PARAM
per	_	_	O
acre	_	_	O
while	_	_	O
the	_	_	O
bulbs	_	_	O
for	_	_	O
daffodils	_	_	B-VAR
cost	_	_	O
$	_	_	O
5	_	_	B-PARAM
per	_	_	O
acre	_	_	O
.	_	_	O
Jane	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
1500	_	_	B-LIMIT
to	_	_	O
spend	_	_	O
on	_	_	O
bulbs	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
tulips	_	_	B-VAR
is	_	_	O
$	_	_	O
325	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
daffodils	_	_	B-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
grown	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
factory	_	_	O
uses	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
apples	_	_	O
,	_	_	O
green	_	_	B-VAR
and	_	_	O
red	_	_	B-VAR
,	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
large	_	_	O
batch	_	_	O
of	_	_	O
pie	_	_	O
filling	_	_	O
.	_	_	O
Green	_	_	B-VAR
apples	_	_	I-VAR
consist	_	_	O
of	_	_	O
5	_	_	B-PARAM
%	_	_	I-PARAM
sugar	_	_	O
and	_	_	O
16	_	_	B-PARAM
%	_	_	I-PARAM
fiber	_	_	O
and	_	_	O
red	_	_	B-VAR
apples	_	_	I-VAR
consists	_	_	O
of	_	_	O
25	_	_	B-PARAM
%	_	_	I-PARAM
sugar	_	_	O
and	_	_	O
8	_	_	B-PARAM
%	_	_	I-PARAM
fiber	_	_	O
.	_	_	O
They	_	_	O
need	_	_	O
to	_	_	O
make	_	_	O
sure	_	_	O
the	_	_	O
filling	_	_	O
has	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
12	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
sugar	_	_	O
and	_	_	O
5	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
fiber	_	_	O
.	_	_	O
If	_	_	O
green	_	_	B-VAR
apples	_	_	I-VAR
cost	_	_	B-OBJ_NAME
$	_	_	O
9	_	_	B-PARAM
per	_	_	O
kg	_	_	O
and	_	_	O
red	_	_	B-VAR
apples	_	_	I-VAR
cost	_	_	B-OBJ_NAME
$	_	_	O
7	_	_	B-PARAM
per	_	_	O
kg	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
kg	_	_	O
of	_	_	O
each	_	_	O
apple	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
make	_	_	O
the	_	_	O
filling	_	_	O
at	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
?	_	_	O
What	_	_	O
is	_	_	O
the	_	_	O
minimum	_	_	O
cost	_	_	O
?	_	_	O

A	_	_	O
collector	_	_	O
's	_	_	O
shop	_	_	O
sells	_	_	O
rocks	_	_	O
in	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
shapes	_	_	O
,	_	_	O
oval	_	_	B-VAR
and	_	_	O
rectangular	_	_	B-VAR
.	_	_	O
Oval	_	_	B-VAR
rocks	_	_	I-VAR
require	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
washing	_	_	O
and	_	_	O
12	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
polishing	_	_	O
.	_	_	O
Rectangular	_	_	B-VAR
rocks	_	_	I-VAR
require	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
washing	_	_	O
and	_	_	O
12	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
polishing	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
oval	_	_	B-VAR
rock	_	_	I-VAR
is	_	_	O
$	_	_	O
7	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
rectangular	_	_	B-VAR
rock	_	_	I-VAR
is	_	_	O
$	_	_	O
9	_	_	B-PARAM
.	_	_	O
If	_	_	O
there	_	_	O
are	_	_	O
2000	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
washing	_	_	O
and	_	_	O
2500	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
polishing	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
rocks	_	_	O
of	_	_	O
each	_	_	O
shape	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

You	_	_	O
have	_	_	O
two	_	_	O
sodas	_	_	O
that	_	_	O
contain	_	_	O
caffeine	_	_	O
and	_	_	O
sugar	_	_	O
.	_	_	O
Soda	_	_	B-VAR
1	_	_	I-VAR
contains	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
caffeine	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
sugar	_	_	O
per	_	_	O
can	_	_	O
.	_	_	O
Soda	_	_	B-VAR
2	_	_	I-VAR
contains	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
caffeine	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
sugar	_	_	O
per	_	_	O
can	_	_	O
.	_	_	O
You	_	_	O
must	_	_	O
consume	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
units	_	_	O
of	_	_	O
caffeine	_	_	O
and	_	_	O
40	_	_	B-LIMIT
units	_	_	O
of	_	_	O
sugar	_	_	O
.	_	_	O
If	_	_	O
a	_	_	O
can	_	_	O
of	_	_	O
soda	_	_	B-VAR
1	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
a	_	_	O
can	_	_	O
of	_	_	O
soda	_	_	B-VAR
2	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
7	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
you	_	_	O
buy	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

You	_	_	O
have	_	_	B-CONST_DIR
30	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
on	_	_	O
which	_	_	O
you	_	_	O
grow	_	_	O
peaches	_	_	B-VAR
and	_	_	O
nectarines	_	_	B-VAR
.	_	_	O
Each	_	_	O
acre	_	_	O
of	_	_	O
peaches	_	_	B-VAR
requires	_	_	O
$	_	_	O
40	_	_	B-PARAM
worth	_	_	O
of	_	_	O
bug	_	_	O
-	_	_	O
spray	_	_	O
and	_	_	O
50	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
time	_	_	O
to	_	_	O
spray	_	_	O
the	_	_	O
bug	_	_	O
-	_	_	O
spray	_	_	O
.	_	_	O
Each	_	_	O
acre	_	_	O
of	_	_	O
nectarines	_	_	B-VAR
requires	_	_	O
$	_	_	O
50	_	_	B-PARAM
worth	_	_	O
of	_	_	O
bug	_	_	O
-	_	_	O
spray	_	_	O
and	_	_	O
70	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
time	_	_	O
to	_	_	O
spray	_	_	O
the	_	_	O
bug	_	_	O
-	_	_	O
spray	_	_	O
.	_	_	O
You	_	_	O
have	_	_	O
available	_	_	B-CONST_DIR
$	_	_	O
1350	_	_	B-LIMIT
to	_	_	O
spend	_	_	O
on	_	_	O
bug	_	_	O
-	_	_	O
spray	_	_	O
and	_	_	O
2000	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
to	_	_	O
spray	_	_	O
the	_	_	O
bug	_	_	O
-	_	_	O
spray	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
peaches	_	_	B-VAR
is	_	_	O
$	_	_	O
300	_	_	B-PARAM
and	_	_	O
he	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
nectarines	_	_	B-VAR
is	_	_	O
$	_	_	O
350	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
grown	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
street	_	_	O
vendor	_	_	O
sells	_	_	O
fried	_	_	B-VAR
fish	_	_	I-VAR
and	_	_	O
fried	_	_	B-VAR
chicken	_	_	I-VAR
.	_	_	O
Each	_	_	O
piece	_	_	O
of	_	_	O
fried	_	_	B-VAR
fish	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
batter	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
oil	_	_	O
.	_	_	O
Each	_	_	O
piece	_	_	O
of	_	_	O
fried	_	_	B-VAR
chicken	_	_	I-VAR
requires	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
batter	_	_	O
and	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
oil	_	_	O
.	_	_	O
The	_	_	O
vendor	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
400	_	_	B-LIMIT
units	_	_	O
of	_	_	O
batter	_	_	O
and	_	_	O
500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
oil	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
revenue	_	_	B-OBJ_NAME
per	_	_	O
piece	_	_	O
of	_	_	O
fried	_	_	B-VAR
fish	_	_	I-VAR
is	_	_	O
$	_	_	O
4	_	_	B-PARAM
and	_	_	O
the	_	_	O
revenue	_	_	B-OBJ_NAME
per	_	_	O
piece	_	_	O
of	_	_	O
fried	_	_	B-VAR
chicken	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
revenue	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
furniture	_	_	O
company	_	_	O
makes	_	_	O
chairs	_	_	B-VAR
and	_	_	O
shelves	_	_	B-VAR
.	_	_	O
Each	_	_	O
chair	_	_	B-VAR
requires	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
assembly	_	_	O
and	_	_	O
50	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
painting	_	_	O
.	_	_	O
Each	_	_	O
shelf	_	_	B-VAR
requires	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
assembly	_	_	O
and	_	_	O
60	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
painting	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
3000	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
assembly	_	_	O
and	_	_	O
4000	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
painting	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
chair	_	_	B-VAR
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
shelf	_	_	B-VAR
is	_	_	O
$	_	_	O
55	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
artist	_	_	O
uses	_	_	O
clay	_	_	O
to	_	_	O
make	_	_	O
both	_	_	O
mini	_	_	B-VAR
elephants	_	_	I-VAR
and	_	_	O
lions	_	_	B-VAR
.	_	_	O
Each	_	_	O
mini	_	_	B-VAR
elephant	_	_	I-VAR
requires	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
clay	_	_	O
and	_	_	O
each	_	_	O
mini	_	_	B-VAR
lion	_	_	I-VAR
requires	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
clay	_	_	O
.	_	_	O
The	_	_	O
artist	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
300	_	_	B-LIMIT
units	_	_	O
of	_	_	O
clay	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
due	_	_	O
to	_	_	O
time	_	_	O
constraints	_	_	O
,	_	_	O
the	_	_	O
artist	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
33	_	_	B-LIMIT
animals	_	_	O
total	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
mini	_	_	B-VAR
elephant	_	_	I-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
mini	_	_	B-VAR
lion	_	_	I-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
45	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
artist	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

In	_	_	O
an	_	_	O
arcade	_	_	O
shooting	_	_	O
game	_	_	O
,	_	_	O
each	_	_	O
deer	_	_	B-VAR
shot	_	_	O
is	_	_	O
4	_	_	B-PARAM
points	_	_	B-OBJ_NAME
and	_	_	O
each	_	_	O
bear	_	_	B-VAR
shot	_	_	O
is	_	_	O
10	_	_	B-PARAM
points	_	_	B-OBJ_NAME
You	_	_	O
must	_	_	O
shoot	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
deer	_	_	B-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
2	_	_	B-LIMIT
bears	_	_	B-VAR
to	_	_	O
pass	_	_	O
the	_	_	O
level	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
you	_	_	O
can	_	_	O
shoot	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
10	_	_	B-LIMIT
deer	_	_	B-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
5	_	_	B-LIMIT
bears	_	_	B-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
you	_	_	O
only	_	_	B-CONST_DIR
have	_	_	O
enough	_	_	O
bullets	_	_	O
to	_	_	O
shoot	_	_	O
12	_	_	B-LIMIT
animals	_	_	O
total	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
animal	_	_	O
should	_	_	O
you	_	_	O
shoot	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
your	_	_	O
points	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
fisherman	_	_	O
must	_	_	O
catch	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
small	_	_	O
fish	_	_	O
and	_	_	O
15	_	_	B-LIMIT
large	_	_	O
fish	_	_	O
.	_	_	O
He	_	_	O
visits	_	_	O
two	_	_	O
lakes	_	_	O
.	_	_	O
For	_	_	O
each	_	_	O
hour	_	_	O
at	_	_	O
lake	_	_	B-VAR
1	_	_	I-VAR
he	_	_	O
spends	_	_	O
,	_	_	O
he	_	_	O
can	_	_	O
catch	_	_	O
5	_	_	B-PARAM
small	_	_	O
fish	_	_	O
and	_	_	O
3	_	_	B-PARAM
large	_	_	O
fish	_	_	O
.	_	_	O
For	_	_	O
each	_	_	O
hour	_	_	O
at	_	_	O
lake	_	_	B-VAR
2	_	_	I-VAR
he	_	_	O
spends	_	_	O
,	_	_	O
he	_	_	O
can	_	_	O
catch	_	_	O
7	_	_	B-PARAM
small	_	_	O
fish	_	_	O
and	_	_	O
2	_	_	B-PARAM
large	_	_	O
fish	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
hours	_	_	O
should	_	_	O
he	_	_	O
spend	_	_	O
at	_	_	O
each	_	_	O
lake	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
time	_	_	I-OBJ_NAME
he	_	_	O
spends	_	_	O
at	_	_	O
both	_	_	O
lakes	_	_	O
fishing	_	_	O
?	_	_	O

A	_	_	O
store	_	_	O
sells	_	_	O
hot	_	_	O
sauce	_	_	O
in	_	_	O
large	_	_	B-VAR
and	_	_	O
small	_	_	B-VAR
bottles	_	_	I-VAR
.	_	_	O
Each	_	_	O
large	_	_	B-VAR
bottle	_	_	I-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
3	_	_	B-PARAM
and	_	_	O
each	_	_	O
small	_	_	B-VAR
bottle	_	_	I-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
2	_	_	B-PARAM
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
1000	_	_	B-LIMIT
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
each	_	_	O
large	_	_	B-VAR
bottle	_	_	I-VAR
takes	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
shelf	_	_	O
space	_	_	O
while	_	_	O
each	_	_	O
small	_	_	B-VAR
bottle	_	_	I-VAR
takes	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
shelf	_	_	O
space	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
shelf	_	_	O
space	_	_	O
.	_	_	O
Also	_	_	O
the	_	_	O
store	_	_	O
wants	_	_	O
to	_	_	O
make	_	_	O
sure	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
all	_	_	O
stock	_	_	O
is	_	_	O
small	_	_	B-VAR
bottles	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
large	_	_	B-VAR
bottle	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
small	_	_	B-VAR
bottle	_	_	I-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
store	_	_	O
keep	_	_	O
in	_	_	O
stock	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
small	_	_	O
candy	_	_	O
store	_	_	O
hand	_	_	O
makes	_	_	O
hard	_	_	O
candy	_	_	O
.	_	_	O
Each	_	_	O
packet	_	_	O
of	_	_	O
lemon	_	_	B-VAR
candy	_	_	I-VAR
takes	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
make	_	_	O
and	_	_	O
each	_	_	O
packet	_	_	O
of	_	_	O
cherry	_	_	B-VAR
candy	_	_	I-VAR
takes	_	_	O
25	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
make	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
3000	_	_	B-LIMIT
minutes	_	_	O
to	_	_	O
make	_	_	O
the	_	_	O
packets	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
they	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
lemon	_	_	B-VAR
candy	_	_	I-VAR
packets	_	_	O
and	_	_	O
80	_	_	B-LIMIT
cherry	_	_	B-VAR
candy	_	_	I-VAR
packets	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
packet	_	_	O
of	_	_	O
lemon	_	_	B-VAR
candy	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
packet	_	_	O
of	_	_	O
cherry	_	_	B-VAR
candy	_	_	I-VAR
is	_	_	O
$	_	_	O
7	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
small	_	_	O
pharmacy	_	_	O
weighs	_	_	O
and	_	_	O
packages	_	_	O
their	_	_	O
medication	_	_	O
.	_	_	O
Each	_	_	O
bottle	_	_	O
of	_	_	O
pills	_	_	B-VAR
takes	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
weighing	_	_	O
and	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
packaging	_	_	O
.	_	_	O
Each	_	_	O
bottle	_	_	O
of	_	_	O
cream	_	_	B-VAR
takes	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
weighing	_	_	O
and	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
packaging	_	_	O
.	_	_	O
The	_	_	O
pharmacy	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
4000	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
weighing	_	_	O
and	_	_	O
3000	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
packaging	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
bottle	_	_	O
of	_	_	O
pills	_	_	B-VAR
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
bottle	_	_	O
of	_	_	O
cream	_	_	B-VAR
is	_	_	O
$	_	_	O
60	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
pharmacy	_	_	O
prepare	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
appliance	_	_	O
store	_	_	O
sells	_	_	O
microwaves	_	_	B-VAR
and	_	_	O
vents	_	_	B-VAR
.	_	_	O
A	_	_	O
microwave	_	_	B-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
300	_	_	B-PARAM
and	_	_	O
a	_	_	O
vent	_	_	B-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
400	_	_	B-PARAM
.	_	_	O
The	_	_	O
store	_	_	O
can	_	_	O
spend	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
20000	_	_	B-LIMIT
.	_	_	O
The	_	_	O
store	_	_	O
sells	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
microwaves	_	_	B-VAR
but	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
65	_	_	B-LIMIT
microwaves	_	_	B-VAR
.	_	_	O
Also	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
vents	_	_	B-VAR
sold	_	_	O
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
a	_	_	O
third	_	_	B-PARAM
of	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
microwaves	_	_	B-VAR
sold	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
microwave	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
vent	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
300	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
store	_	_	O
buy	_	_	O
and	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
man	_	_	O
insists	_	_	O
he	_	_	O
can	_	_	O
meet	_	_	O
his	_	_	O
calorie	_	_	O
and	_	_	O
protein	_	_	O
requirements	_	_	O
from	_	_	O
eating	_	_	O
burgers	_	_	B-VAR
and	_	_	O
fries	_	_	B-VAR
.	_	_	O
He	_	_	O
wants	_	_	O
to	_	_	O
get	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3000	_	_	B-LIMIT
calories	_	_	O
and	_	_	O
150	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
protein	_	_	O
.	_	_	O
Each	_	_	O
burger	_	_	B-VAR
contains	_	_	O
500	_	_	B-PARAM
calories	_	_	O
and	_	_	O
30	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
while	_	_	O
each	_	_	O
order	_	_	O
of	_	_	O
fries	_	_	B-VAR
contains	_	_	O
300	_	_	B-PARAM
calories	_	_	O
and	_	_	O
5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
burger	_	_	B-VAR
is	_	_	O
$	_	_	O
7	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
order	_	_	O
of	_	_	O
fries	_	_	B-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
eat	_	_	O
to	_	_	O
meet	_	_	O
his	_	_	O
requirements	_	_	O
at	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
company	_	_	O
makes	_	_	O
hoodies	_	_	B-VAR
and	_	_	O
sweaters	_	_	B-VAR
.	_	_	O
Each	_	_	O
hoodie	_	_	B-VAR
requires	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
fabric	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
dye	_	_	O
.	_	_	O
Each	_	_	O
sweater	_	_	B-VAR
requires	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
fabric	_	_	O
and	_	_	O
1.5	_	_	B-PARAM
units	_	_	O
of	_	_	O
dye	_	_	O
.	_	_	O
At	_	_	O
the	_	_	O
company	_	_	O
,	_	_	O
there	_	_	O
are	_	_	O
500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
fabric	_	_	O
available	_	_	B-CONST_DIR
and	_	_	O
300	_	_	B-LIMIT
units	_	_	O
of	_	_	O
dye	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
hoodie	_	_	B-VAR
is	_	_	O
$	_	_	O
20	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
sweater	_	_	B-VAR
is	_	_	O
$	_	_	O
15	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
woman	_	_	O
owns	_	_	O
two	_	_	O
chocolate	_	_	O
shops	_	_	O
.	_	_	O
Running	_	_	O
shop	_	_	B-VAR
1	_	_	I-VAR
for	_	_	O
an	_	_	O
hour	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
makes	_	_	O
5	_	_	B-PARAM
milk	_	_	O
chocolate	_	_	O
bars	_	_	O
,	_	_	O
8	_	_	B-PARAM
dark	_	_	O
chocolate	_	_	O
bars	_	_	O
,	_	_	O
and	_	_	O
6	_	_	B-PARAM
white	_	_	O
chocolate	_	_	O
bars	_	_	O
.	_	_	O
Running	_	_	O
shop	_	_	B-VAR
2	_	_	I-VAR
for	_	_	O
an	_	_	O
hour	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
75	_	_	B-PARAM
and	_	_	O
makes	_	_	O
8	_	_	B-PARAM
milk	_	_	O
chocolate	_	_	O
bars	_	_	O
,	_	_	O
7	_	_	B-PARAM
dark	_	_	O
chocolate	_	_	O
bars	_	_	O
,	_	_	O
and	_	_	O
4	_	_	B-PARAM
white	_	_	O
chocolate	_	_	O
bars	_	_	O
.	_	_	O
To	_	_	O
meet	_	_	O
demand	_	_	O
,	_	_	O
she	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
milk	_	_	O
chocolate	_	_	O
bars	_	_	O
,	_	_	O
60	_	_	B-LIMIT
dark	_	_	O
chocolate	_	_	O
bars	_	_	O
,	_	_	O
and	_	_	O
30	_	_	B-LIMIT
white	_	_	O
chocolate	_	_	O
bars	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
hours	_	_	O
should	_	_	O
she	_	_	O
run	_	_	O
each	_	_	O
shop	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
kitchen	_	_	O
company	_	_	O
makes	_	_	O
spoons	_	_	B-VAR
,	_	_	O
forks	_	_	B-VAR
,	_	_	O
and	_	_	O
knives	_	_	B-VAR
with	_	_	O
rubber	_	_	O
handles	_	_	O
.	_	_	O
Each	_	_	O
spoon	_	_	B-VAR
requires	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
steel	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
rubber	_	_	O
.	_	_	O
Each	_	_	O
fork	_	_	B-VAR
requires	_	_	O
1.5	_	_	B-PARAM
units	_	_	O
of	_	_	O
steel	_	_	O
and	_	_	O
1.5	_	_	B-PARAM
units	_	_	O
of	_	_	O
rubber	_	_	O
.	_	_	O
Each	_	_	O
knife	_	_	B-VAR
requires	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
steel	_	_	O
and	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
rubber	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
400	_	_	B-LIMIT
units	_	_	O
of	_	_	O
steel	_	_	O
and	_	_	O
500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
rubber	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
revenue	_	_	B-OBJ_NAME
per	_	_	O
spoon	_	_	B-VAR
is	_	_	O
$	_	_	O
2	_	_	B-PARAM
,	_	_	O
the	_	_	O
revenue	_	_	B-OBJ_NAME
per	_	_	O
fork	_	_	B-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
,	_	_	O
and	_	_	O
the	_	_	O
revenue	_	_	B-OBJ_NAME
per	_	_	O
knife	_	_	B-VAR
is	_	_	O
$	_	_	O
4	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
revenue	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
doctor	_	_	O
prescribed	_	_	O
two	_	_	O
pills	_	_	O
to	_	_	O
a	_	_	O
patient	_	_	O
.	_	_	O
Pill	_	_	B-VAR
A	_	_	I-VAR
contains	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
muscle	_	_	O
relaxant	_	_	O
,	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
anxiety	_	_	O
medication	_	_	O
,	_	_	O
and	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
pain	_	_	O
reliever	_	_	O
per	_	_	O
pill	_	_	O
.	_	_	O
Pill	_	_	B-VAR
B	_	_	I-VAR
contains	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
muscle	_	_	O
relaxant	_	_	O
,	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
anxiety	_	_	O
medication	_	_	O
,	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
pain	_	_	O
reliever	_	_	O
per	_	_	O
pill	_	_	O
.	_	_	O
Pill	_	_	B-VAR
A	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
3	_	_	B-PARAM
per	_	_	O
pill	_	_	O
while	_	_	O
pill	_	_	B-VAR
B	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
5	_	_	B-PARAM
per	_	_	O
pill	_	_	O
.	_	_	O
The	_	_	O
patient	_	_	O
must	_	_	O
get	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
units	_	_	O
of	_	_	O
muscle	_	_	O
relaxant	_	_	O
,	_	_	O
15	_	_	B-LIMIT
units	_	_	O
of	_	_	O
anxiety	_	_	O
medication	_	_	O
,	_	_	O
and	_	_	O
20	_	_	B-LIMIT
units	_	_	O
of	_	_	O
pain	_	_	O
reliever	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
pill	_	_	O
should	_	_	O
he	_	_	O
buy	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
cost	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
diner	_	_	O
makes	_	_	O
packaged	_	_	O
lunches	_	_	O
.	_	_	O
The	_	_	O
meat	_	_	B-VAR
option	_	_	I-VAR
takes	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
prepare	_	_	O
and	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
package	_	_	O
.	_	_	O
The	_	_	O
veggie	_	_	B-VAR
option	_	_	I-VAR
takes	_	_	O
4	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
prepare	_	_	O
and	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
package	_	_	O
.	_	_	O
The	_	_	O
diner	_	_	O
has	_	_	O
500	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
preparations	_	_	O
and	_	_	O
400	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
packaging	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
meat	_	_	B-VAR
lunch	_	_	I-VAR
is	_	_	O
$	_	_	O
8	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
veggie	_	_	B-VAR
lunch	_	_	I-VAR
is	_	_	O
$	_	_	O
6	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
diner	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
smoothie	_	_	O
store	_	_	O
sells	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
smoothies	_	_	O
-	_	_	O
a	_	_	O
small	_	_	B-VAR
and	_	_	O
a	_	_	O
large	_	_	B-VAR
size	_	_	I-VAR
.	_	_	O
Both	_	_	O
contain	_	_	O
only	_	_	O
ice	_	_	O
cream	_	_	O
and	_	_	O
peanut	_	_	O
butter	_	_	O
.	_	_	O
Each	_	_	O
small	_	_	B-VAR
smoothie	_	_	I-VAR
requires	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
ice	_	_	O
cream	_	_	O
and	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
peanut	_	_	O
butter	_	_	O
.	_	_	O
Each	_	_	O
large	_	_	B-VAR
smoothie	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
ice	_	_	O
cream	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
peanut	_	_	O
butter	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
only	_	_	O
has	_	_	O
a	_	_	O
total	_	_	B-CONST_DIR
of	_	_	O
20	_	_	B-LIMIT
units	_	_	O
of	_	_	O
ice	_	_	O
cream	_	_	O
and	_	_	O
18	_	_	B-LIMIT
units	_	_	O
of	_	_	O
peanut	_	_	O
butter	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
small	_	_	B-VAR
smoothie	_	_	I-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
large	_	_	B-VAR
smoothie	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
store	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
farmer	_	_	O
has	_	_	B-CONST_DIR
50	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
on	_	_	O
which	_	_	O
he	_	_	O
grows	_	_	O
lettuce	_	_	B-VAR
and	_	_	O
spinach	_	_	B-VAR
.	_	_	O
Per	_	_	O
acre	_	_	O
of	_	_	O
lettuce	_	_	B-VAR
,	_	_	O
it	_	_	O
cost	_	_	O
$	_	_	O
10	_	_	B-PARAM
in	_	_	O
watering	_	_	O
costs	_	_	O
and	_	_	O
2	_	_	B-PARAM
days	_	_	O
of	_	_	O
picking	_	_	O
time	_	_	O
.	_	_	O
Per	_	_	O
acre	_	_	O
of	_	_	O
spinach	_	_	B-VAR
,	_	_	O
it	_	_	O
costs	_	_	O
$	_	_	O
12	_	_	B-PARAM
in	_	_	O
watering	_	_	O
costs	_	_	O
and	_	_	O
1	_	_	B-PARAM
day	_	_	O
of	_	_	O
picking	_	_	O
time	_	_	O
.	_	_	O
The	_	_	O
farmer	_	_	O
has	_	_	O
a	_	_	O
total	_	_	O
of	_	_	O
$	_	_	O
5000	_	_	B-LIMIT
available	_	_	B-CONST_DIR
for	_	_	O
watering	_	_	O
costs	_	_	O
and	_	_	O
300	_	_	B-LIMIT
days	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
picking	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
lettuce	_	_	B-VAR
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
spinach	_	_	B-VAR
is	_	_	O
$	_	_	O
55	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
grown	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
small	_	_	O
factory	_	_	O
makes	_	_	O
plush	_	_	O
toys	_	_	O
in	_	_	O
a	_	_	O
small	_	_	B-VAR
and	_	_	O
large	_	_	B-VAR
size	_	_	O
using	_	_	O
cotton	_	_	O
.	_	_	O
To	_	_	O
make	_	_	O
a	_	_	O
small	_	_	B-VAR
plush	_	_	I-VAR
requires	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
cotton	_	_	O
and	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
worker	_	_	O
time	_	_	O
.	_	_	O
To	_	_	O
make	_	_	O
a	_	_	O
large	_	_	B-VAR
plush	_	_	I-VAR
requires	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
cotton	_	_	O
and	_	_	O
12	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
worker	_	_	O
time	_	_	O
.	_	_	O
In	_	_	O
a	_	_	O
day	_	_	O
,	_	_	O
there	_	_	O
are	_	_	O
250	_	_	B-LIMIT
units	_	_	O
of	_	_	O
cotton	_	_	O
available	_	_	B-CONST_DIR
and	_	_	O
500	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
worker	_	_	O
time	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
small	_	_	B-VAR
plush	_	_	I-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
large	_	_	B-VAR
plush	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
company	_	_	O
decides	_	_	O
to	_	_	O
advertise	_	_	O
their	_	_	O
movie	_	_	O
with	_	_	O
posters	_	_	O
in	_	_	O
3	_	_	O
malls	_	_	O
:	_	_	O
the	_	_	O
northside	_	_	B-VAR
mall	_	_	I-VAR
,	_	_	O
the	_	_	O
southside	_	_	B-VAR
mall	_	_	I-VAR
,	_	_	O
and	_	_	O
the	_	_	O
central	_	_	B-VAR
mall	_	_	I-VAR
.	_	_	O
The	_	_	O
cost	_	_	O
for	_	_	O
placing	_	_	O
a	_	_	O
poster	_	_	O
and	_	_	O
the	_	_	O
expected	_	_	O
viewership	_	_	O
is	_	_	O
given	_	_	O
.	_	_	O
At	_	_	O
the	_	_	O
northside	_	_	B-VAR
mall	_	_	I-VAR
,	_	_	O
a	_	_	O
poster	_	_	O
costs	_	_	O
$	_	_	O
500	_	_	B-PARAM
and	_	_	O
attracts	_	_	O
20000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
At	_	_	O
the	_	_	O
southside	_	_	B-VAR
mall	_	_	I-VAR
,	_	_	O
a	_	_	O
poster	_	_	O
costs	_	_	O
$	_	_	O
1000	_	_	B-PARAM
and	_	_	O
attracts	_	_	O
50000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
At	_	_	O
the	_	_	O
central	_	_	B-VAR
mall	_	_	I-VAR
,	_	_	O
a	_	_	O
poster	_	_	O
costs	_	_	O
$	_	_	O
800	_	_	B-PARAM
and	_	_	O
attracts	_	_	O
40000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
southside	_	_	B-VAR
mall	_	_	I-VAR
limits	_	_	B-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
posters	_	_	O
from	_	_	O
a	_	_	O
company	_	_	O
to	_	_	O
5	_	_	B-LIMIT
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
the	_	_	O
company	_	_	O
decides	_	_	O
to	_	_	O
make	_	_	O
sure	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
a	_	_	O
third	_	_	B-LIMIT
of	_	_	O
the	_	_	O
posters	_	_	O
be	_	_	O
placed	_	_	O
at	_	_	O
the	_	_	O
central	_	_	B-VAR
mall	_	_	I-VAR
.	_	_	O
Finally	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
posters	_	_	O
should	_	_	O
be	_	_	O
placed	_	_	O
at	_	_	O
the	_	_	O
northside	_	_	B-VAR
mall	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
weekly	_	_	O
budget	_	_	B-CONST_DIR
is	_	_	O
$	_	_	O
30000	_	_	B-LIMIT
,	_	_	O
how	_	_	O
many	_	_	O
posters	_	_	O
should	_	_	O
be	_	_	O
placed	_	_	O
in	_	_	O
each	_	_	O
location	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
viewership	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
bath	_	_	O
store	_	_	O
makes	_	_	O
rubber	_	_	B-VAR
ducks	_	_	I-VAR
and	_	_	O
toy	_	_	B-VAR
boats	_	_	I-VAR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
rubber	_	_	B-VAR
duck	_	_	I-VAR
is	_	_	O
$	_	_	O
2	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
toy	_	_	B-VAR
boat	_	_	I-VAR
is	_	_	O
$	_	_	O
4	_	_	B-PARAM
.	_	_	O
Each	_	_	O
rubber	_	_	B-VAR
ducks	_	_	I-VAR
take	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
preparation	_	_	O
and	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
testing	_	_	O
to	_	_	O
make	_	_	O
.	_	_	O
Each	_	_	O
toy	_	_	B-VAR
boat	_	_	I-VAR
takes	_	_	O
8	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
preparation	_	_	O
and	_	_	O
2	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
testing	_	_	O
.	_	_	O
In	_	_	O
a	_	_	O
week	_	_	O
,	_	_	O
there	_	_	O
are	_	_	O
1000	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
preparation	_	_	O
and	_	_	O
700	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
testing	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
bath	_	_	O
store	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
electronics	_	_	O
repair	_	_	O
shop	_	_	O
fixes	_	_	O
old	_	_	O
phones	_	_	B-VAR
and	_	_	O
laptops	_	_	B-VAR
.	_	_	O
Each	_	_	O
phone	_	_	B-VAR
requires	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
inspection	_	_	O
and	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
fixing	_	_	O
.	_	_	O
Each	_	_	O
laptop	_	_	B-VAR
requires	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
inspection	_	_	O
and	_	_	O
50	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
fixing	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
makes	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
50	_	_	B-PARAM
per	_	_	O
phone	_	_	B-VAR
repaired	_	_	O
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
60	_	_	B-PARAM
per	_	_	O
laptop	_	_	B-VAR
repaired	_	_	O
.	_	_	O
If	_	_	O
there	_	_	O
are	_	_	O
6000	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
inspection	_	_	O
and	_	_	O
7000	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
fixing	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
shop	_	_	O
repair	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
patient	_	_	O
with	_	_	O
weak	_	_	O
bones	_	_	O
has	_	_	O
been	_	_	O
told	_	_	O
to	_	_	O
drink	_	_	O
milk	_	_	B-VAR
and	_	_	O
eat	_	_	O
cheese	_	_	B-VAR
in	_	_	O
order	_	_	O
to	_	_	O
meet	_	_	O
his	_	_	O
calcium	_	_	O
and	_	_	O
vitamin	_	_	O
D	_	_	O
requirements	_	_	O
.	_	_	O
In	_	_	O
one	_	_	O
serving	_	_	O
of	_	_	O
milk	_	_	B-VAR
,	_	_	O
there	_	_	O
are	_	_	O
10	_	_	B-PARAM
grams	_	_	O
of	_	_	O
calcium	_	_	O
and	_	_	O
5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
Vitamin	_	_	O
D.	_	_	O
In	_	_	O
one	_	_	O
serving	_	_	O
of	_	_	O
cheese	_	_	B-VAR
,	_	_	O
there	_	_	O
are	_	_	O
8	_	_	B-PARAM
grams	_	_	O
of	_	_	O
calcium	_	_	O
and	_	_	O
6	_	_	B-PARAM
grams	_	_	O
of	_	_	O
vitamin	_	_	O
D.	_	_	O
The	_	_	O
patient	_	_	O
must	_	_	O
get	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
calcium	_	_	O
and	_	_	O
80	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
Vitamin	_	_	O
D	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
If	_	_	O
a	_	_	O
serving	_	_	O
of	_	_	O
milk	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
2	_	_	B-PARAM
and	_	_	O
a	_	_	O
serving	_	_	O
of	_	_	O
cheese	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
4	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
servings	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
patient	_	_	O
eat	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
young	_	_	O
man	_	_	O
eats	_	_	O
carrots	_	_	B-VAR
and	_	_	O
spinach	_	_	B-VAR
to	_	_	O
meet	_	_	O
his	_	_	O
biotin	_	_	O
and	_	_	O
folate	_	_	O
needs	_	_	O
.	_	_	O
He	_	_	O
wants	_	_	O
to	_	_	O
make	_	_	O
sure	_	_	O
he	_	_	O
eats	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
20	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
each	_	_	O
biotin	_	_	O
and	_	_	O
folate	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
One	_	_	O
cup	_	_	O
of	_	_	O
carrots	_	_	B-VAR
contains	_	_	O
1	_	_	B-PARAM
gram	_	_	O
of	_	_	O
biotin	_	_	O
and	_	_	O
3	_	_	B-PARAM
grams	_	_	O
of	_	_	O
folate	_	_	O
.	_	_	O
One	_	_	O
cup	_	_	O
of	_	_	O
spinach	_	_	B-VAR
contain	_	_	O
2	_	_	B-PARAM
grams	_	_	O
of	_	_	O
biotin	_	_	O
and	_	_	O
1.5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
folate	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
cup	_	_	O
of	_	_	O
carrots	_	_	B-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
cup	_	_	O
of	_	_	O
spinach	_	_	B-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
cups	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
consume	_	_	O
to	_	_	O
meet	_	_	O
his	_	_	O
requirements	_	_	O
at	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
sandwich	_	_	O
store	_	_	O
sells	_	_	O
tuna	_	_	B-VAR
salad	_	_	I-VAR
and	_	_	O
chicken	_	_	B-VAR
salad	_	_	I-VAR
sandwiches	_	_	I-VAR
.	_	_	O
Both	_	_	O
sandwiches	_	_	O
require	_	_	O
time	_	_	O
to	_	_	O
mix	_	_	O
the	_	_	O
ingredients	_	_	O
and	_	_	O
time	_	_	O
to	_	_	O
put	_	_	O
together	_	_	O
the	_	_	O
sandwich	_	_	O
.	_	_	O
To	_	_	O
make	_	_	O
a	_	_	O
tuna	_	_	B-VAR
salad	_	_	I-VAR
sandwich	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
mix	_	_	O
the	_	_	O
ingredients	_	_	O
and	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
put	_	_	O
together	_	_	O
the	_	_	O
sandwich	_	_	O
.	_	_	O
To	_	_	O
make	_	_	O
a	_	_	O
chicken	_	_	B-VAR
salad	_	_	I-VAR
sandwich	_	_	I-VAR
requires	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
mix	_	_	O
the	_	_	O
ingredients	_	_	O
and	_	_	O
6	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
put	_	_	O
together	_	_	O
the	_	_	O
sandwich	_	_	O
.	_	_	O
In	_	_	O
a	_	_	O
day	_	_	O
,	_	_	O
there	_	_	O
are	_	_	O
300	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
mixing	_	_	O
the	_	_	O
ingredients	_	_	O
and	_	_	O
400	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
putting	_	_	O
together	_	_	O
sandwiches	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
tuna	_	_	B-VAR
salad	_	_	I-VAR
sandwich	_	_	I-VAR
is	_	_	O
$	_	_	O
2	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
chicken	_	_	B-VAR
salad	_	_	I-VAR
sandwich	_	_	I-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
syrup	_	_	O
factory	_	_	O
makes	_	_	O
chocolate	_	_	B-VAR
and	_	_	O
caramel	_	_	B-VAR
syrup	_	_	I-VAR
.	_	_	O
They	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
15	_	_	B-LIMIT
tons	_	_	O
of	_	_	O
each	_	_	O
per	_	_	O
week	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
they	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
2	_	_	B-LIMIT
tons	_	_	O
of	_	_	O
chocolate	_	_	B-VAR
syrup	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-LIMIT
tons	_	_	O
of	_	_	O
caramel	_	_	B-VAR
syrup	_	_	I-VAR
per	_	_	O
week	_	_	O
.	_	_	O
Each	_	_	O
ton	_	_	O
of	_	_	O
chocolate	_	_	B-VAR
and	_	_	O
caramel	_	_	B-VAR
syrup	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
heating	_	_	O
machine	_	_	O
.	_	_	O
The	_	_	O
heating	_	_	O
machine	_	_	O
is	_	_	O
available	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
50	_	_	B-LIMIT
hours	_	_	O
per	_	_	O
week	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
ton	_	_	O
of	_	_	O
chocolate	_	_	B-VAR
syrup	_	_	I-VAR
is	_	_	O
$	_	_	O
500	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
ton	_	_	O
of	_	_	O
caramel	_	_	B-VAR
syrup	_	_	I-VAR
is	_	_	O
$	_	_	O
350	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
tons	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
gardener	_	_	O
has	_	_	B-CONST_DIR
30	_	_	B-LIMIT
acres	_	_	O
to	_	_	O
grow	_	_	O
peas	_	_	B-VAR
and	_	_	O
beans	_	_	B-VAR
.	_	_	O
Each	_	_	O
acre	_	_	O
of	_	_	O
peas	_	_	B-VAR
requires	_	_	O
$	_	_	O
30	_	_	B-PARAM
of	_	_	O
bug	_	_	O
-	_	_	O
spray	_	_	O
and	_	_	O
2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
care	_	_	O
-	_	_	O
taking	_	_	O
.	_	_	O
Each	_	_	O
acre	_	_	O
of	_	_	O
beans	_	_	B-VAR
requires	_	_	O
$	_	_	O
50	_	_	B-PARAM
of	_	_	O
bug	_	_	O
-	_	_	O
spray	_	_	O
and	_	_	O
1.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
care	_	_	O
-	_	_	O
taking	_	_	O
.	_	_	O
The	_	_	O
gardener	_	_	O
has	_	_	O
at	_	_	O
most	_	_	O
$	_	_	O
1300	_	_	B-LIMIT
available	_	_	B-CONST_DIR
to	_	_	O
spend	_	_	O
on	_	_	O
bug	_	_	O
-	_	_	O
spray	_	_	O
and	_	_	O
50	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
to	_	_	O
spend	_	_	O
on	_	_	O
care	_	_	O
-	_	_	O
taking	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
peas	_	_	B-VAR
is	_	_	O
$	_	_	O
100	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
beans	_	_	B-VAR
is	_	_	O
$	_	_	O
160	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
gardener	_	_	O
grow	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
man	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
50000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
his	_	_	O
son	_	_	B-VAR
's	_	_	I-VAR
company	_	_	I-VAR
and	_	_	O
his	_	_	O
friend	_	_	B-VAR
's	_	_	I-VAR
company	_	_	I-VAR
.	_	_	O
He	_	_	O
has	_	_	O
decided	_	_	O
that	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
his	_	_	O
son	_	_	B-VAR
's	_	_	I-VAR
company	_	_	I-VAR
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	O
as	_	_	O
much	_	_	O
as	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
his	_	_	O
friend	_	_	B-VAR
's	_	_	I-VAR
company	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
he	_	_	O
has	_	_	O
also	_	_	O
decided	_	_	O
to	_	_	O
invest	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
40000	_	_	B-LIMIT
in	_	_	O
his	_	_	O
son	_	_	B-VAR
's	_	_	I-VAR
company	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
investments	_	_	O
earn	_	_	B-OBJ_NAME
8	_	_	B-PARAM
%	_	_	I-PARAM
in	_	_	O
his	_	_	O
son	_	_	B-VAR
's	_	_	I-VAR
company	_	_	I-VAR
and	_	_	O
the	_	_	O
investments	_	_	O
earn	_	_	B-OBJ_NAME
10	_	_	B-PARAM
%	_	_	I-PARAM
in	_	_	O
his	_	_	O
friend	_	_	B-VAR
's	_	_	I-VAR
company	_	_	I-VAR
,	_	_	O
how	_	_	O
much	_	_	O
money	_	_	O
should	_	_	O
he	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
earnings	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
glass	_	_	O
artist	_	_	O
makes	_	_	O
glass	_	_	B-VAR
dogs	_	_	I-VAR
and	_	_	O
cats	_	_	B-VAR
.	_	_	O
Each	_	_	O
piece	_	_	O
requires	_	_	O
time	_	_	O
heating	_	_	O
,	_	_	O
molding	_	_	O
,	_	_	O
and	_	_	O
cooling	_	_	O
.	_	_	O
A	_	_	O
glass	_	_	B-VAR
dog	_	_	I-VAR
requires	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
heating	_	_	O
,	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
molding	_	_	O
,	_	_	O
and	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
cooling	_	_	O
.	_	_	O
A	_	_	O
glass	_	_	B-VAR
cat	_	_	I-VAR
requires	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
heating	_	_	O
,	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
molding	_	_	O
,	_	_	O
and	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
cooling	_	_	O
.	_	_	O
In	_	_	O
his	_	_	O
shop	_	_	O
,	_	_	O
he	_	_	O
has	_	_	O
1000	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
heating	_	_	O
,	_	_	O
1500	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
molding	_	_	O
,	_	_	O
and	_	_	O
1200	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
cooling	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
glass	_	_	B-VAR
dog	_	_	I-VAR
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
glass	_	_	B-VAR
cat	_	_	I-VAR
is	_	_	O
$	_	_	O
40	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
profits	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
seafood	_	_	O
market	_	_	O
sells	_	_	O
scallops	_	_	O
,	_	_	O
mussels	_	_	O
,	_	_	O
and	_	_	O
oysters	_	_	O
in	_	_	O
packages	_	_	O
named	_	_	O
seafood	_	_	B-VAR
medley	_	_	I-VAR
one	_	_	I-VAR
and	_	_	O
seafood	_	_	B-VAR
medley	_	_	I-VAR
two	_	_	I-VAR
.	_	_	O
A	_	_	O
package	_	_	O
of	_	_	O
seafood	_	_	B-VAR
medley	_	_	I-VAR
one	_	_	I-VAR
contains	_	_	O
20	_	_	B-PARAM
grams	_	_	O
of	_	_	O
scallops	_	_	O
,	_	_	O
30	_	_	B-PARAM
grams	_	_	O
of	_	_	O
mussels	_	_	O
,	_	_	O
and	_	_	O
50	_	_	B-PARAM
grams	_	_	O
of	_	_	O
oysters	_	_	O
.	_	_	O
A	_	_	O
package	_	_	O
of	_	_	O
seafood	_	_	B-VAR
medley	_	_	I-VAR
two	_	_	I-VAR
contains	_	_	O
40	_	_	B-PARAM
grams	_	_	O
of	_	_	O
scallops	_	_	O
,	_	_	O
40	_	_	B-PARAM
grams	_	_	O
of	_	_	O
mussels	_	_	O
,	_	_	O
and	_	_	O
20	_	_	B-PARAM
grams	_	_	O
of	_	_	O
oysters	_	_	O
.	_	_	O
The	_	_	O
market	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
10000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
scallops	_	_	O
,	_	_	O
12000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
mussels	_	_	O
,	_	_	O
and	_	_	O
11000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
oysters	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
package	_	_	O
of	_	_	O
seafood	_	_	B-VAR
medley	_	_	I-VAR
one	_	_	I-VAR
is	_	_	O
$	_	_	O
20	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
package	_	_	O
of	_	_	O
seafood	_	_	B-VAR
medley	_	_	I-VAR
two	_	_	I-VAR
is	_	_	O
$	_	_	O
25	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
sold	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
office	_	_	O
is	_	_	O
purchasing	_	_	O
two	_	_	O
different	_	_	O
printers	_	_	O
for	_	_	O
their	_	_	O
entire	_	_	O
office	_	_	O
.	_	_	O
Printer	_	_	B-VAR
A	_	_	I-VAR
can	_	_	O
print	_	_	O
10	_	_	B-PARAM
sheets	_	_	O
per	_	_	O
minute	_	_	O
,	_	_	O
requires	_	_	O
3	_	_	B-PARAM
ink	_	_	O
cartridges	_	_	O
per	_	_	O
year	_	_	O
,	_	_	O
and	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
500	_	_	B-PARAM
.	_	_	O
Printer	_	_	B-VAR
B	_	_	I-VAR
can	_	_	O
print	_	_	O
30	_	_	B-PARAM
sheets	_	_	O
per	_	_	O
minute	_	_	O
,	_	_	O
requires	_	_	O
8	_	_	B-PARAM
ink	_	_	O
cartridges	_	_	O
per	_	_	O
year	_	_	O
,	_	_	O
and	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
1200	_	_	B-PARAM
.	_	_	O
The	_	_	O
office	_	_	O
wants	_	_	O
to	_	_	O
make	_	_	O
sure	_	_	O
they	_	_	O
can	_	_	O
print	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
sheets	_	_	O
per	_	_	O
minute	_	_	O
total	_	_	O
and	_	_	O
that	_	_	O
they	_	_	O
use	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
27	_	_	B-LIMIT
ink	_	_	O
cartridges	_	_	O
per	_	_	O
year	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
printer	_	_	O
should	_	_	O
be	_	_	O
purchased	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
grocery	_	_	O
store	_	_	O
wants	_	_	O
to	_	_	O
sell	_	_	O
their	_	_	O
bulk	_	_	O
quantities	_	_	O
of	_	_	O
almonds	_	_	O
,	_	_	O
pecans	_	_	O
,	_	_	O
and	_	_	O
pistachios	_	_	O
.	_	_	O
They	_	_	O
have	_	_	B-CONST_DIR
1000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
almonds	_	_	O
,	_	_	O
1200	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
pecans	_	_	O
,	_	_	O
and	_	_	O
1100	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
pistachios	_	_	O
.	_	_	O
Mixture	_	_	B-VAR
1	_	_	I-VAR
contains	_	_	O
20	_	_	B-PARAM
grams	_	_	O
of	_	_	O
almonds	_	_	O
,	_	_	O
30	_	_	B-PARAM
grams	_	_	O
of	_	_	O
pecans	_	_	O
,	_	_	O
and	_	_	O
10	_	_	B-PARAM
grams	_	_	O
of	_	_	O
pistachios	_	_	O
.	_	_	O
Mixture	_	_	B-VAR
2	_	_	I-VAR
contains	_	_	O
15	_	_	B-PARAM
grams	_	_	O
of	_	_	O
almonds	_	_	O
,	_	_	O
20	_	_	B-PARAM
grams	_	_	O
of	_	_	O
pecans	_	_	O
,	_	_	O
and	_	_	O
25	_	_	B-PARAM
grams	_	_	O
of	_	_	O
pistachios	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
mixture	_	_	B-VAR
1	_	_	I-VAR
is	_	_	O
$	_	_	O
10	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
mixture	_	_	B-VAR
2	_	_	I-VAR
is	_	_	O
$	_	_	O
12	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
store	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
small	_	_	O
bakery	_	_	O
has	_	_	B-CONST_DIR
1000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
batter	_	_	O
and	_	_	O
800	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
milk	_	_	O
to	_	_	O
make	_	_	O
their	_	_	O
soft	_	_	B-VAR
,	_	_	O
smooth	_	_	B-VAR
,	_	_	O
and	_	_	O
crunchy	_	_	B-VAR
cake	_	_	O
-	_	_	O
pops	_	_	O
.	_	_	O
A	_	_	O
soft	_	_	B-VAR
cake	_	_	I-VAR
-	_	_	I-VAR
pop	_	_	I-VAR
needs	_	_	O
20	_	_	B-PARAM
grams	_	_	O
of	_	_	O
batter	_	_	O
and	_	_	O
10	_	_	B-PARAM
grams	_	_	O
of	_	_	O
milk	_	_	O
.	_	_	O
A	_	_	O
smooth	_	_	B-VAR
cake	_	_	I-VAR
-	_	_	I-VAR
pop	_	_	I-VAR
requires	_	_	O
15	_	_	B-PARAM
grams	_	_	O
of	_	_	O
batter	_	_	O
and	_	_	O
15	_	_	B-PARAM
grams	_	_	O
of	_	_	O
milk	_	_	O
.	_	_	O
A	_	_	O
crunchy	_	_	B-VAR
cake	_	_	I-VAR
-	_	_	I-VAR
pop	_	_	I-VAR
requires	_	_	O
12	_	_	B-PARAM
grams	_	_	O
of	_	_	O
batter	_	_	O
and	_	_	O
18	_	_	B-PARAM
grams	_	_	O
of	_	_	O
milk	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
soft	_	_	B-VAR
cake	_	_	I-VAR
-	_	_	I-VAR
pop	_	_	I-VAR
is	_	_	O
$	_	_	O
4	_	_	B-PARAM
,	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
smooth	_	_	B-VAR
cake	_	_	I-VAR
-	_	_	I-VAR
pop	_	_	I-VAR
is	_	_	O
$	_	_	O
6	_	_	B-PARAM
,	_	_	O
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
crunchy	_	_	B-VAR
cake	_	_	I-VAR
-	_	_	I-VAR
pop	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
bakery	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
their	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
factory	_	_	O
sells	_	_	O
fabric	_	_	O
in	_	_	O
two	_	_	O
packages	_	_	O
.	_	_	O
Package	_	_	B-VAR
1	_	_	I-VAR
contains	_	_	O
20	_	_	B-PARAM
meters	_	_	O
of	_	_	O
blue	_	_	O
fabric	_	_	O
and	_	_	O
30	_	_	B-PARAM
meters	_	_	O
of	_	_	O
red	_	_	O
fabric	_	_	O
.	_	_	O
Package	_	_	B-VAR
2	_	_	I-VAR
contains	_	_	O
40	_	_	B-PARAM
meters	_	_	O
of	_	_	O
blue	_	_	O
fabric	_	_	O
and	_	_	O
40	_	_	B-PARAM
meters	_	_	O
of	_	_	O
red	_	_	O
fabric	_	_	O
.	_	_	O
The	_	_	O
factory	_	_	O
has	_	_	B-CONST_DIR
10000	_	_	B-LIMIT
meters	_	_	O
of	_	_	O
blue	_	_	O
fabric	_	_	O
and	_	_	O
12000	_	_	B-LIMIT
meters	_	_	O
of	_	_	O
red	_	_	O
fabric	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
package	_	_	B-VAR
1	_	_	I-VAR
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
package	_	_	B-VAR
2	_	_	I-VAR
is	_	_	O
$	_	_	O
70	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
package	_	_	O
should	_	_	O
they	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
aquarium	_	_	O
feeds	_	_	O
their	_	_	O
seals	_	_	O
using	_	_	O
sardines	_	_	B-VAR
and	_	_	O
tuna	_	_	B-VAR
.	_	_	O
Each	_	_	O
packet	_	_	O
of	_	_	O
sardines	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
15	_	_	B-PARAM
while	_	_	O
each	_	_	O
packet	_	_	O
of	_	_	O
tuna	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
18	_	_	B-PARAM
.	_	_	O
Each	_	_	O
packet	_	_	O
of	_	_	O
sardines	_	_	B-VAR
contains	_	_	O
4	_	_	B-PARAM
grams	_	_	O
of	_	_	O
fat	_	_	O
,	_	_	O
12	_	_	B-PARAM
grams	_	_	O
of	_	_	O
essential	_	_	O
fatty	_	_	O
acids	_	_	O
,	_	_	O
and	_	_	O
10	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
.	_	_	O
Each	_	_	O
packet	_	_	O
of	_	_	O
tuna	_	_	B-VAR
contains	_	_	O
6	_	_	B-PARAM
grams	_	_	O
of	_	_	O
fat	_	_	O
,	_	_	O
10	_	_	B-PARAM
grams	_	_	O
of	_	_	O
essential	_	_	O
fatty	_	_	O
acids	_	_	O
,	_	_	O
and	_	_	O
7	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
.	_	_	O
The	_	_	O
aquarium	_	_	O
needs	_	_	O
in	_	_	B-CONST_DIR
total	_	_	I-CONST_DIR
800	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
fat	_	_	O
,	_	_	O
1200	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
essential	_	_	O
fatty	_	_	O
acids	_	_	O
,	_	_	O
and	_	_	O
700	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
protein	_	_	O
to	_	_	O
feed	_	_	O
their	_	_	O
seals	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
packet	_	_	O
should	_	_	O
they	_	_	O
buy	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
man	_	_	O
takes	_	_	O
two	_	_	O
supplements	_	_	O
to	_	_	O
get	_	_	O
his	_	_	O
keratin	_	_	O
and	_	_	O
calcium	_	_	O
requirements	_	_	O
.	_	_	O
He	_	_	O
needs	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
12	_	_	B-LIMIT
units	_	_	O
of	_	_	O
keratin	_	_	O
and	_	_	O
20	_	_	B-LIMIT
units	_	_	O
of	_	_	O
calcium	_	_	O
.	_	_	O
Per	_	_	O
serving	_	_	O
,	_	_	O
supplement	_	_	B-VAR
A	_	_	I-VAR
contains	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
keratin	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
calcium	_	_	O
.	_	_	O
Per	_	_	O
serving	_	_	O
,	_	_	O
supplement	_	_	B-VAR
B	_	_	I-VAR
contains	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
keratin	_	_	O
and	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
calcium	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
serving	_	_	O
for	_	_	O
supplement	_	_	B-VAR
A	_	_	I-VAR
is	_	_	O
$	_	_	O
2	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
serving	_	_	O
of	_	_	O
supplement	_	_	B-VAR
B	_	_	I-VAR
is	_	_	O
$	_	_	O
4	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
supplement	_	_	O
should	_	_	O
he	_	_	O
take	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
cost	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
store	_	_	O
sells	_	_	O
two	_	_	O
bowls	_	_	O
of	_	_	O
ramen	_	_	O
.	_	_	O
Bowl	_	_	B-VAR
1	_	_	I-VAR
requires	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
broth	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
toppings	_	_	O
.	_	_	O
Bowl	_	_	B-VAR
2	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
broth	_	_	O
and	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
toppings	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
300	_	_	B-LIMIT
units	_	_	O
of	_	_	O
broth	_	_	O
and	_	_	O
250	_	_	B-LIMIT
units	_	_	O
of	_	_	O
toppings	_	_	O
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
bowls	_	_	I-OBJ_NAME
of	_	_	O
either	_	_	O
type	_	_	O
that	_	_	O
can	_	_	O
be	_	_	O
made	_	_	O
.	_	_	O

A	_	_	O
gift	_	_	O
wrapping	_	_	O
kiosk	_	_	O
wraps	_	_	O
small	_	_	B-VAR
and	_	_	O
large	_	_	B-VAR
gifts	_	_	O
.	_	_	O
Small	_	_	B-VAR
gifts	_	_	I-VAR
take	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
worker	_	_	O
time	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
wrapping	_	_	O
paper	_	_	O
.	_	_	O
Large	_	_	B-VAR
gifts	_	_	I-VAR
take	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
worker	_	_	O
time	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
wrapping	_	_	O
paper	_	_	O
.	_	_	O
The	_	_	O
kiosk	_	_	O
has	_	_	O
720	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
worker	_	_	O
time	_	_	O
available	_	_	B-CONST_DIR
and	_	_	O
150	_	_	B-LIMIT
units	_	_	O
of	_	_	O
wrapping	_	_	O
paper	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
small	_	_	B-VAR
gift	_	_	I-VAR
wrapped	_	_	O
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
large	_	_	B-VAR
gift	_	_	I-VAR
wrapped	_	_	O
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
wrap	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
restaurant	_	_	O
cleans	_	_	O
and	_	_	O
cuts	_	_	O
both	_	_	O
small	_	_	B-VAR
fish	_	_	I-VAR
and	_	_	O
large	_	_	B-VAR
fish	_	_	I-VAR
.	_	_	O
Each	_	_	O
small	_	_	B-VAR
fish	_	_	I-VAR
take	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
cleaning	_	_	O
and	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
cutting	_	_	O
.	_	_	O
Each	_	_	O
large	_	_	B-VAR
fish	_	_	I-VAR
takes	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
cleaning	_	_	O
and	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
cutting	_	_	O
.	_	_	O
The	_	_	O
restaurant	_	_	O
has	_	_	O
500	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
cleaning	_	_	O
and	_	_	O
700	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
cutting	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
small	_	_	B-VAR
fish	_	_	I-VAR
is	_	_	O
$	_	_	O
8	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
large	_	_	B-VAR
fish	_	_	I-VAR
is	_	_	O
$	_	_	O
11	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
fish	_	_	O
size	_	_	O
should	_	_	O
the	_	_	O
restaurant	_	_	O
clean	_	_	O
and	_	_	O
cut	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
factory	_	_	O
makes	_	_	O
soccer	_	_	B-VAR
balls	_	_	I-VAR
and	_	_	O
basket	_	_	B-VAR
balls	_	_	I-VAR
.	_	_	O
Soccer	_	_	B-VAR
balls	_	_	I-VAR
take	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
manufacturing	_	_	O
machine	_	_	O
and	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
fill	_	_	O
with	_	_	O
air	_	_	O
.	_	_	O
Basket	_	_	B-VAR
balls	_	_	I-VAR
take	_	_	O
7	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
manufacturing	_	_	O
machine	_	_	O
and	_	_	O
4	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
fill	_	_	O
with	_	_	O
air	_	_	O
.	_	_	O
The	_	_	O
factory	_	_	O
can	_	_	O
run	_	_	O
the	_	_	O
manufacturing	_	_	O
machine	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
700	_	_	B-LIMIT
minutes	_	_	O
and	_	_	O
they	_	_	O
have	_	_	O
500	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
filling	_	_	O
the	_	_	O
balls	_	_	O
with	_	_	O
air	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
soccer	_	_	B-VAR
ball	_	_	I-VAR
is	_	_	O
$	_	_	O
4	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
basket	_	_	B-VAR
all	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
ball	_	_	O
should	_	_	O
the	_	_	O
factory	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
coffee	_	_	O
shop	_	_	O
makes	_	_	O
large	_	_	B-VAR
and	_	_	O
small	_	_	B-VAR
coffees	_	_	O
.	_	_	O
A	_	_	O
large	_	_	B-VAR
coffee	_	_	I-VAR
takes	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
coffee	_	_	O
beans	_	_	O
and	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
milk	_	_	O
.	_	_	O
A	_	_	O
small	_	_	B-VAR
coffee	_	_	I-VAR
takes	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
coffee	_	_	O
beans	_	_	O
and	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
milk	_	_	O
.	_	_	O
The	_	_	O
shop	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
1000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
coffee	_	_	O
beans	_	_	O
and	_	_	O
1500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
milk	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
large	_	_	B-VAR
coffee	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
small	_	_	B-VAR
coffee	_	_	I-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
company	_	_	O
sells	_	_	O
tennis	_	_	B-VAR
rackets	_	_	I-VAR
and	_	_	O
badminton	_	_	B-VAR
rackets	_	_	I-VAR
.	_	_	O
Each	_	_	O
tennis	_	_	B-VAR
racket	_	_	I-VAR
takes	_	_	O
12	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
mold	_	_	O
and	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
string	_	_	O
.	_	_	O
Each	_	_	O
badminton	_	_	B-VAR
racket	_	_	I-VAR
takes	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
mold	_	_	O
and	_	_	O
12	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
string	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
3000	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
molding	_	_	O
and	_	_	O
3500	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
stringing	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
tennis	_	_	B-VAR
racket	_	_	I-VAR
is	_	_	O
$	_	_	O
20	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
badminton	_	_	B-VAR
racket	_	_	I-VAR
is	_	_	O
$	_	_	O
17	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
boy	_	_	O
buys	_	_	O
and	_	_	O
sells	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
sneakers	_	_	O
.	_	_	O
Brand	_	_	B-VAR
A	_	_	I-VAR
sneakers	_	_	I-VAR
cost	_	_	O
him	_	_	O
$	_	_	O
100	_	_	B-PARAM
each	_	_	O
and	_	_	O
Brand	_	_	B-VAR
B	_	_	I-VAR
sneakers	_	_	I-VAR
cost	_	_	O
his	_	_	O
$	_	_	O
150	_	_	B-PARAM
each	_	_	O
.	_	_	O
He	_	_	O
can	_	_	B-CONST_DIR
spend	_	_	I-CONST_DIR
a	_	_	I-CONST_DIR
total	_	_	I-CONST_DIR
of	_	_	O
$	_	_	O
2000	_	_	B-LIMIT
.	_	_	O
He	_	_	O
can	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
15	_	_	B-LIMIT
sneakers	_	_	O
total	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
Brand	_	_	B-VAR
A	_	_	I-VAR
sneaker	_	_	I-VAR
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
Brand	_	_	B-VAR
B	_	_	I-VAR
sneaker	_	_	I-VAR
is	_	_	O
$	_	_	O
75	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
buy	_	_	O
and	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
baker	_	_	O
melts	_	_	O
milk	_	_	B-VAR
and	_	_	O
dark	_	_	B-VAR
chocolate	_	_	O
together	_	_	O
to	_	_	O
create	_	_	O
a	_	_	O
new	_	_	O
mixture	_	_	O
.	_	_	O
The	_	_	O
mixture	_	_	O
must	_	_	O
contain	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
120	_	_	B-LIMIT
units	_	_	O
of	_	_	O
cacao	_	_	O
and	_	_	O
80	_	_	B-LIMIT
units	_	_	O
of	_	_	O
sugar	_	_	O
.	_	_	O
Each	_	_	O
milk	_	_	B-VAR
chocolate	_	_	I-VAR
piece	_	_	I-VAR
contains	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
cacao	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
sugar	_	_	O
.	_	_	O
Each	_	_	O
dark	_	_	B-VAR
chocolate	_	_	I-VAR
piece	_	_	I-VAR
contains	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
cacao	_	_	O
and	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
sugar	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
milk	_	_	B-VAR
chocolate	_	_	I-VAR
piece	_	_	I-VAR
is	_	_	O
$	_	_	O
0.50	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
dark	_	_	B-VAR
chocolate	_	_	I-VAR
piece	_	_	I-VAR
is	_	_	O
$	_	_	O
0.75	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
baker	_	_	O
buy	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
breakfast	_	_	O
place	_	_	O
mixes	_	_	O
two	_	_	O
pancake	_	_	O
mixes	_	_	O
to	_	_	O
get	_	_	O
the	_	_	O
perfect	_	_	O
consistency	_	_	O
.	_	_	O
Mix	_	_	B-VAR
A	_	_	I-VAR
contains	_	_	O
10	_	_	B-PARAM
%	_	_	I-PARAM
sugar	_	_	O
and	_	_	O
60	_	_	B-PARAM
%	_	_	I-PARAM
flour	_	_	O
.	_	_	O
Mix	_	_	B-VAR
B	_	_	I-VAR
contains	_	_	O
15	_	_	B-PARAM
%	_	_	I-PARAM
sugar	_	_	O
and	_	_	O
50	_	_	B-PARAM
%	_	_	I-PARAM
flour	_	_	O
.	_	_	O
The	_	_	O
final	_	_	O
mixture	_	_	O
needs	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
sugar	_	_	O
and	_	_	O
50	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
flour	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
kg	_	_	O
of	_	_	O
Mix	_	_	B-VAR
A	_	_	I-VAR
is	_	_	O
$	_	_	O
20	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
kg	_	_	O
of	_	_	O
Mix	_	_	B-VAR
B	_	_	I-VAR
is	_	_	O
$	_	_	O
25	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
kg	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
breakfast	_	_	O
place	_	_	O
buy	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
man	_	_	O
is	_	_	O
watching	_	_	O
his	_	_	O
sugar	_	_	O
and	_	_	O
fat	_	_	O
intake	_	_	O
.	_	_	O
He	_	_	O
drinks	_	_	O
two	_	_	O
smoothies	_	_	O
.	_	_	O
Each	_	_	O
cup	_	_	O
of	_	_	O
smoothie	_	_	B-VAR
A	_	_	I-VAR
contains	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
carbs	_	_	O
,	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	O
,	_	_	O
and	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
sugar	_	_	B-OBJ_NAME
.	_	_	O
Each	_	_	O
cup	_	_	O
of	_	_	O
smoothie	_	_	B-VAR
B	_	_	I-VAR
contains	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
30	_	_	B-PARAM
units	_	_	O
of	_	_	O
carbs	_	_	O
,	_	_	O
25	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	O
,	_	_	O
and	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
sugar	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
man	_	_	O
needs	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
150	_	_	B-LIMIT
units	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
200	_	_	B-LIMIT
units	_	_	O
of	_	_	O
carbs	_	_	O
.	_	_	O
However	_	_	O
we	_	_	O
wants	_	_	O
to	_	_	O
consume	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
185	_	_	B-LIMIT
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
cups	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
drink	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
sugar	_	_	B-OBJ_NAME
intake	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
pharmacist	_	_	O
mixes	_	_	O
two	_	_	O
different	_	_	O
medications	_	_	O
.	_	_	O
One	_	_	O
unit	_	_	O
of	_	_	O
medication	_	_	B-VAR
A	_	_	I-VAR
contains	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
cough	_	_	O
relief	_	_	O
,	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
pain	_	_	O
relief	_	_	O
,	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
fever	_	_	O
relief	_	_	O
.	_	_	O
One	_	_	O
unit	_	_	O
of	_	_	O
medication	_	_	B-VAR
B	_	_	I-VAR
contains	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
cough	_	_	O
relief	_	_	O
,	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
pain	_	_	O
relief	_	_	O
,	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
fever	_	_	O
relief	_	_	O
.	_	_	O
The	_	_	O
new	_	_	O
mixture	_	_	O
must	_	_	O
contain	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
units	_	_	O
of	_	_	O
cough	_	_	O
relief	_	_	O
,	_	_	O
25	_	_	B-LIMIT
units	_	_	O
of	_	_	O
pain	_	_	O
relief	_	_	O
,	_	_	O
and	_	_	O
30	_	_	B-LIMIT
units	_	_	O
of	_	_	O
fever	_	_	O
relief	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
unit	_	_	O
of	_	_	O
medication	_	_	B-VAR
A	_	_	I-VAR
is	_	_	O
$	_	_	O
1	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
unit	_	_	O
of	_	_	O
medication	_	_	B-VAR
B	_	_	I-VAR
is	_	_	O
$	_	_	O
2	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
mixed	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
Ferris	_	_	O
wheel	_	_	O
can	_	_	O
take	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
250	_	_	B-LIMIT
people	_	_	O
.	_	_	O
A	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
50	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
premium	_	_	B-VAR
ticket	_	_	I-VAR
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
30	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
regular	_	_	B-VAR
ticket	_	_	I-VAR
.	_	_	O
There	_	_	O
are	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
50	_	_	B-LIMIT
premium	_	_	B-VAR
tickets	_	_	I-VAR
available	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
people	_	_	O
prefer	_	_	O
to	_	_	O
buy	_	_	O
regular	_	_	B-VAR
tickets	_	_	I-VAR
than	_	_	O
premium	_	_	B-VAR
tickets	_	_	I-VAR
.	_	_	O
How	_	_	O
any	_	_	O
of	_	_	O
each	_	_	O
ticket	_	_	O
should	_	_	O
be	_	_	O
sold	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
fruit	_	_	O
farmer	_	_	O
has	_	_	B-CONST_DIR
80	_	_	B-LIMIT
acres	_	_	O
to	_	_	O
grow	_	_	O
peaches	_	_	B-VAR
and	_	_	O
nectarines	_	_	B-VAR
.	_	_	O
Peaches	_	_	B-VAR
take	_	_	O
3	_	_	B-PARAM
hours	_	_	O
to	_	_	O
plant	_	_	O
per	_	_	O
acre	_	_	O
while	_	_	O
nectarines	_	_	B-VAR
take	_	_	O
4.5	_	_	B-PARAM
hours	_	_	O
to	_	_	O
plant	_	_	O
per	_	_	O
acre	_	_	O
.	_	_	O
Peaches	_	_	B-VAR
take	_	_	O
2	_	_	B-PARAM
hours	_	_	O
to	_	_	O
water	_	_	O
per	_	_	O
acre	_	_	O
while	_	_	O
nectarines	_	_	B-VAR
take	_	_	O
3	_	_	B-PARAM
hours	_	_	O
to	_	_	O
water	_	_	O
per	_	_	O
acre	_	_	O
.	_	_	O
The	_	_	O
farmer	_	_	O
has	_	_	O
300	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
planting	_	_	O
and	_	_	O
250	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
watering	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
peaches	_	_	B-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
nectarines	_	_	B-VAR
is	_	_	O
$	_	_	O
175	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
grown	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
bagel	_	_	O
company	_	_	O
mixes	_	_	O
two	_	_	O
bags	_	_	O
of	_	_	O
everything	_	_	O
seasoning	_	_	O
,	_	_	O
an	_	_	O
ordinary	_	_	B-VAR
bag	_	_	I-VAR
and	_	_	O
a	_	_	O
special	_	_	B-VAR
bag	_	_	I-VAR
,	_	_	O
to	_	_	O
make	_	_	O
their	_	_	O
house	_	_	O
mix	_	_	O
.	_	_	O
The	_	_	O
ordinary	_	_	B-VAR
bag	_	_	I-VAR
contains	_	_	O
5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
sesame	_	_	O
seeds	_	_	O
,	_	_	O
8	_	_	B-PARAM
grams	_	_	O
of	_	_	O
onions	_	_	O
powder	_	_	O
,	_	_	O
and	_	_	O
7	_	_	B-PARAM
grams	_	_	O
of	_	_	O
garlic	_	_	O
powder	_	_	O
.	_	_	O
The	_	_	O
special	_	_	B-VAR
bag	_	_	I-VAR
contains	_	_	O
10	_	_	B-PARAM
grams	_	_	O
of	_	_	O
sesame	_	_	O
seeds	_	_	O
,	_	_	O
6	_	_	B-PARAM
grams	_	_	O
of	_	_	O
onion	_	_	O
powder	_	_	O
,	_	_	O
and	_	_	O
8	_	_	B-PARAM
grams	_	_	O
of	_	_	O
garlic	_	_	O
powder	_	_	O
.	_	_	O
They	_	_	O
want	_	_	O
their	_	_	O
house	_	_	O
mix	_	_	O
to	_	_	O
contain	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
sesame	_	_	O
seeds	_	_	O
,	_	_	O
60	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
onion	_	_	O
powder	_	_	O
,	_	_	O
and	_	_	O
65	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
garlic	_	_	O
powder	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
ordinary	_	_	B-VAR
bag	_	_	I-VAR
is	_	_	O
$	_	_	O
10	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
special	_	_	B-VAR
bag	_	_	I-VAR
is	_	_	O
$	_	_	O
12	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
mix	_	_	O
to	_	_	O
create	_	_	O
their	_	_	O
house	_	_	O
mix	_	_	O
at	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
video	_	_	O
game	_	_	O
store	_	_	O
sells	_	_	O
regular	_	_	B-VAR
games	_	_	I-VAR
and	_	_	O
collector	_	_	B-VAR
's	_	_	I-VAR
edition	_	_	I-VAR
games	_	_	I-VAR
.	_	_	O
Each	_	_	O
regular	_	_	B-VAR
game	_	_	I-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
30	_	_	B-PARAM
while	_	_	O
each	_	_	O
collector	_	_	B-VAR
's	_	_	I-VAR
edition	_	_	I-VAR
game	_	_	I-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
50	_	_	B-PARAM
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
regular	_	_	B-VAR
game	_	_	I-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
20	_	_	B-PARAM
while	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
collector	_	_	B-VAR
's	_	_	I-VAR
edition	_	_	I-VAR
game	_	_	I-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
30	_	_	B-PARAM
.	_	_	O
The	_	_	O
store	_	_	O
can	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
video	_	_	O
games	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
per	_	_	O
month	_	_	O
and	_	_	O
wants	_	_	O
to	_	_	O
spend	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
4000	_	_	B-LIMIT
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
store	_	_	O
stock	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
restaurant	_	_	O
makes	_	_	O
chicken	_	_	B-VAR
and	_	_	O
goat	_	_	B-VAR
curry	_	_	O
.	_	_	O
One	_	_	O
serving	_	_	O
of	_	_	O
chicken	_	_	B-VAR
curry	_	_	I-VAR
requires	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
tomatoes	_	_	O
,	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
curry	_	_	O
paste	_	_	O
,	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	O
.	_	_	O
One	_	_	O
serving	_	_	O
of	_	_	O
goat	_	_	B-VAR
curry	_	_	I-VAR
requires	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
tomatoes	_	_	O
,	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
curry	_	_	O
paste	_	_	O
,	_	_	O
and	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
water	_	_	O
.	_	_	O
The	_	_	O
restaurant	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
20	_	_	B-LIMIT
units	_	_	O
of	_	_	O
tomatoes	_	_	O
,	_	_	O
30	_	_	B-LIMIT
units	_	_	O
of	_	_	O
curry	_	_	O
paste	_	_	O
,	_	_	O
and	_	_	O
25	_	_	B-LIMIT
units	_	_	O
of	_	_	O
water	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
serving	_	_	O
of	_	_	O
chicken	_	_	B-VAR
curry	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
serving	_	_	O
of	_	_	O
goat	_	_	B-VAR
curry	_	_	I-VAR
is	_	_	O
$	_	_	O
7	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
smoothies	_	_	O
store	_	_	O
makes	_	_	O
blueberry	_	_	B-VAR
and	_	_	O
chocolate	_	_	B-VAR
smoothies	_	_	I-VAR
.	_	_	O
All	_	_	O
smoothies	_	_	O
have	_	_	O
to	_	_	O
go	_	_	O
through	_	_	O
a	_	_	O
preparation	_	_	O
phase	_	_	O
and	_	_	O
a	_	_	O
blending	_	_	O
phase	_	_	O
.	_	_	O
A	_	_	O
blueberry	_	_	B-VAR
smoothies	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
preparation	_	_	O
and	_	_	O
2	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
blending	_	_	O
.	_	_	O
A	_	_	O
chocolate	_	_	B-VAR
smoothie	_	_	I-VAR
requires	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
preparation	_	_	O
and	_	_	O
1	_	_	B-PARAM
minute	_	_	O
of	_	_	O
blending	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
1000	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
preparation	_	_	O
and	_	_	O
750	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
blending	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
blueberry	_	_	B-VAR
smoothie	_	_	I-VAR
is	_	_	O
$	_	_	O
2	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
chocolate	_	_	B-VAR
smoothie	_	_	I-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

John	_	_	O
and	_	_	O
William	_	_	O
run	_	_	O
a	_	_	O
woodshop	_	_	O
where	_	_	O
they	_	_	O
make	_	_	O
chairs	_	_	B-VAR
and	_	_	O
nightstands	_	_	B-VAR
.	_	_	O
Each	_	_	O
chair	_	_	B-VAR
takes	_	_	O
2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
John	_	_	O
's	_	_	O
time	_	_	O
and	_	_	O
4	_	_	B-PARAM
hours	_	_	O
of	_	_	O
William	_	_	O
's	_	_	O
time	_	_	O
.	_	_	O
Each	_	_	O
nightstand	_	_	B-VAR
takes	_	_	O
5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
John	_	_	O
's	_	_	O
time	_	_	O
and	_	_	O
4	_	_	B-PARAM
hours	_	_	O
of	_	_	O
William	_	_	O
's	_	_	O
time	_	_	O
.	_	_	O
In	_	_	O
a	_	_	O
week	_	_	O
,	_	_	O
John	_	_	O
has	_	_	O
30	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
and	_	_	O
William	_	_	O
has	_	_	O
40	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
If	_	_	O
they	_	_	O
get	_	_	O
$	_	_	O
300	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
per	_	_	O
chair	_	_	B-VAR
sold	_	_	O
and	_	_	O
$	_	_	O
500	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
per	_	_	O
nightstand	_	_	B-VAR
sold	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profits	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
man	_	_	O
wants	_	_	O
to	_	_	O
sell	_	_	O
his	_	_	O
berries	_	_	O
at	_	_	O
the	_	_	O
market	_	_	O
down	_	_	O
the	_	_	O
river	_	_	O
.	_	_	O
He	_	_	O
can	_	_	O
either	_	_	O
use	_	_	O
a	_	_	O
boat	_	_	B-VAR
to	_	_	O
carry	_	_	O
it	_	_	O
down	_	_	O
stream	_	_	O
or	_	_	O
have	_	_	O
his	_	_	O
neighbor	_	_	B-VAR
carry	_	_	O
it	_	_	O
.	_	_	O
A	_	_	O
boat	_	_	B-VAR
can	_	_	O
take	_	_	O
200	_	_	B-PARAM
units	_	_	O
of	_	_	O
berries	_	_	B-OBJ_NAME
per	_	_	O
trip	_	_	O
and	_	_	O
cost	_	_	O
$	_	_	O
30	_	_	B-PARAM
per	_	_	O
trip	_	_	O
.	_	_	O
His	_	_	O
neighbor	_	_	B-VAR
can	_	_	O
take	_	_	O
40	_	_	B-PARAM
units	_	_	O
of	_	_	O
berries	_	_	B-OBJ_NAME
per	_	_	O
trip	_	_	O
and	_	_	O
costs	_	_	O
$	_	_	O
8	_	_	B-PARAM
.	_	_	O
The	_	_	O
man	_	_	O
does	_	_	O
not	_	_	B-CONST_DIR
want	_	_	I-CONST_DIR
to	_	_	I-CONST_DIR
spend	_	_	I-CONST_DIR
more	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
$	_	_	O
500	_	_	B-LIMIT
and	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
boat	_	_	B-VAR
trips	_	_	O
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
trips	_	_	O
his	_	_	O
neighbor	_	_	B-VAR
does	_	_	O
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
berries	_	_	I-OBJ_NAME
he	_	_	O
can	_	_	O
transport	_	_	O
to	_	_	O
the	_	_	O
market	_	_	O
?	_	_	O

A	_	_	O
snow	_	_	O
removal	_	_	O
company	_	_	O
uses	_	_	O
their	_	_	O
equipment	_	_	O
in	_	_	O
two	_	_	O
cities	_	_	O
and	_	_	O
gets	_	_	O
paid	_	_	O
per	_	_	O
kilogram	_	_	O
of	_	_	O
snow	_	_	O
they	_	_	O
remove	_	_	O
.	_	_	O
In	_	_	O
the	_	_	O
northern	_	_	B-VAR
city	_	_	I-VAR
,	_	_	O
the	_	_	O
net	_	_	B-OBJ_NAME
revenue	_	_	I-OBJ_NAME
per	_	_	O
kilogram	_	_	O
of	_	_	O
snow	_	_	O
is	_	_	O
$	_	_	O
2	_	_	B-PARAM
.	_	_	O
In	_	_	O
the	_	_	O
southern	_	_	B-VAR
city	_	_	I-VAR
,	_	_	O
the	_	_	O
net	_	_	B-OBJ_NAME
revenue	_	_	I-OBJ_NAME
per	_	_	O
kilogram	_	_	O
of	_	_	O
snow	_	_	O
is	_	_	O
$	_	_	O
1.50	_	_	B-PARAM
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
one	_	_	O
snow	_	_	O
plow	_	_	O
,	_	_	O
one	_	_	O
truck	_	_	O
,	_	_	O
and	_	_	O
one	_	_	O
shovel	_	_	O
.	_	_	O
Each	_	_	O
item	_	_	O
can	_	_	O
be	_	_	O
used	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
500	_	_	B-LIMIT
minutes	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
At	_	_	O
the	_	_	O
northern	_	_	B-VAR
city	_	_	I-VAR
,	_	_	O
to	_	_	O
remove	_	_	O
1	_	_	O
kilogram	_	_	O
of	_	_	O
snow	_	_	O
requires	_	_	O
2	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
snow	_	_	O
plow	_	_	O
,	_	_	O
1	_	_	B-PARAM
minute	_	_	O
on	_	_	O
the	_	_	O
truck	_	_	O
,	_	_	O
and	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
with	_	_	O
the	_	_	O
shovel	_	_	O
.	_	_	O
At	_	_	O
the	_	_	O
southern	_	_	B-VAR
city	_	_	I-VAR
,	_	_	O
to	_	_	O
remove	_	_	O
1	_	_	O
kilogram	_	_	O
of	_	_	O
snow	_	_	O
requires	_	_	O
1	_	_	B-PARAM
minute	_	_	O
on	_	_	O
the	_	_	O
snow	_	_	O
plow	_	_	O
,	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
truck	_	_	O
,	_	_	O
and	_	_	O
2	_	_	B-PARAM
minutes	_	_	O
with	_	_	O
the	_	_	O
shovel	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
kilograms	_	_	O
of	_	_	O
snow	_	_	O
should	_	_	O
be	_	_	O
removed	_	_	O
from	_	_	O
each	_	_	O
city	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
fruit	_	_	O
farmer	_	_	O
has	_	_	O
two	_	_	O
small	_	_	O
farms	_	_	O
where	_	_	O
he	_	_	O
grows	_	_	O
apples	_	_	O
,	_	_	O
oranges	_	_	O
,	_	_	O
and	_	_	O
pears	_	_	O
.	_	_	O
It	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
500	_	_	B-PARAM
per	_	_	O
day	_	_	O
to	_	_	O
operate	_	_	O
farm	_	_	B-VAR
1	_	_	I-VAR
and	_	_	O
$	_	_	O
400	_	_	B-PARAM
per	_	_	O
day	_	_	O
to	_	_	O
operate	_	_	O
farm	_	_	B-VAR
2	_	_	I-VAR
.	_	_	O
In	_	_	O
a	_	_	O
day	_	_	O
,	_	_	O
farm	_	_	B-VAR
1	_	_	I-VAR
yields	_	_	O
10	_	_	B-PARAM
apples	_	_	O
,	_	_	O
15	_	_	B-PARAM
oranges	_	_	O
,	_	_	O
and	_	_	O
5	_	_	B-PARAM
pears	_	_	O
.	_	_	O
In	_	_	O
a	_	_	O
day	_	_	O
,	_	_	O
farm	_	_	B-VAR
2	_	_	I-VAR
yields	_	_	O
7	_	_	B-PARAM
apples	_	_	O
,	_	_	O
8	_	_	B-PARAM
oranges	_	_	O
,	_	_	O
and	_	_	O
9	_	_	B-PARAM
pears	_	_	O
.	_	_	O
The	_	_	O
farmer	_	_	O
must	_	_	O
provide	_	_	B-CONST_DIR
50	_	_	B-LIMIT
apples	_	_	O
,	_	_	O
60	_	_	B-LIMIT
oranges	_	_	O
,	_	_	O
and	_	_	O
55	_	_	B-LIMIT
pears	_	_	O
to	_	_	O
the	_	_	O
market	_	_	O
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
farmer	_	_	O
's	_	_	O
cost	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
caviar	_	_	O
company	_	_	O
makes	_	_	O
caviar	_	_	O
in	_	_	O
two	_	_	O
different	_	_	O
locations	_	_	O
,	_	_	O
an	_	_	O
eastern	_	_	B-VAR
location	_	_	I-VAR
and	_	_	O
a	_	_	O
western	_	_	B-VAR
location	_	_	I-VAR
.	_	_	O
After	_	_	O
harvesting	_	_	O
the	_	_	O
caviar	_	_	O
from	_	_	O
the	_	_	O
fish	_	_	O
,	_	_	O
they	_	_	O
are	_	_	O
labelled	_	_	O
as	_	_	O
cheap	_	_	O
,	_	_	O
regular	_	_	O
,	_	_	O
or	_	_	O
expensive	_	_	O
.	_	_	O
The	_	_	O
eastern	_	_	B-VAR
location	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
1000	_	_	B-PARAM
to	_	_	O
operate	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
produces	_	_	O
5	_	_	B-PARAM
tons	_	_	O
of	_	_	O
cheap	_	_	O
caviar	_	_	O
,	_	_	O
7	_	_	B-PARAM
tons	_	_	O
of	_	_	O
regular	_	_	O
caviar	_	_	O
,	_	_	O
and	_	_	O
1	_	_	B-PARAM
ton	_	_	O
of	_	_	O
expensive	_	_	O
caviar	_	_	O
.	_	_	O
The	_	_	O
western	_	_	B-VAR
location	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
2000	_	_	B-PARAM
to	_	_	O
operate	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
produces	_	_	O
2	_	_	B-PARAM
tons	_	_	O
of	_	_	O
cheap	_	_	O
caviar	_	_	O
,	_	_	O
6	_	_	B-PARAM
tons	_	_	O
of	_	_	O
regular	_	_	O
caviar	_	_	O
,	_	_	O
and	_	_	O
4	_	_	B-PARAM
tons	_	_	O
of	_	_	O
expensive	_	_	O
caviar	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
is	_	_	O
also	_	_	O
under	_	_	O
contract	_	_	O
to	_	_	O
provide	_	_	B-CONST_DIR
25	_	_	B-LIMIT
tons	_	_	O
of	_	_	O
cheap	_	_	O
caviar	_	_	O
,	_	_	O
35	_	_	B-LIMIT
tons	_	_	O
of	_	_	O
regular	_	_	O
caviar	_	_	O
,	_	_	O
and	_	_	O
15	_	_	B-LIMIT
tons	_	_	O
of	_	_	O
expensive	_	_	O
caviar	_	_	O
per	_	_	O
week	_	_	O
to	_	_	O
a	_	_	O
distribution	_	_	O
company	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
days	_	_	O
per	_	_	O
week	_	_	O
should	_	_	O
each	_	_	O
location	_	_	O
operate	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

Jake	_	_	O
uses	_	_	O
two	_	_	O
3D	_	_	O
-	_	_	O
printers	_	_	O
,	_	_	O
Printer	_	_	O
A	_	_	O
and	_	_	O
Printer	_	_	O
B	_	_	O
,	_	_	O
to	_	_	O
make	_	_	O
his	_	_	O
superhero	_	_	B-VAR
and	_	_	O
cartoon	_	_	B-VAR
figurines	_	_	I-VAR
.	_	_	O
To	_	_	O
make	_	_	O
one	_	_	O
superhero	_	_	B-VAR
figurine	_	_	I-VAR
requires	_	_	O
5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
time	_	_	O
on	_	_	O
Printer	_	_	O
A	_	_	O
and	_	_	O
4	_	_	B-PARAM
hours	_	_	O
of	_	_	O
time	_	_	O
on	_	_	O
Printer	_	_	O
B.	_	_	O
To	_	_	O
make	_	_	O
one	_	_	O
cartoon	_	_	B-VAR
figurine	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
hours	_	_	O
on	_	_	O
Printer	_	_	O
A	_	_	O
and	_	_	O
7	_	_	B-PARAM
hours	_	_	O
on	_	_	O
Printer	_	_	O
B.	_	_	O
Each	_	_	O
machine	_	_	O
can	_	_	O
run	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
1000	_	_	B-LIMIT
hours	_	_	O
.	_	_	O
If	_	_	O
Jake	_	_	O
makes	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
10	_	_	B-PARAM
per	_	_	O
superhero	_	_	B-VAR
figurine	_	_	I-VAR
and	_	_	O
$	_	_	O
8	_	_	B-PARAM
per	_	_	O
cartoon	_	_	B-VAR
figurine	_	_	I-VAR
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

After	_	_	O
a	_	_	O
good	_	_	O
workout	_	_	O
,	_	_	O
Jason	_	_	O
makes	_	_	O
sure	_	_	O
he	_	_	O
gets	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
units	_	_	O
of	_	_	O
calcium	_	_	O
,	_	_	O
15	_	_	B-LIMIT
units	_	_	O
of	_	_	O
potassium	_	_	O
,	_	_	O
and	_	_	O
13	_	_	B-LIMIT
units	_	_	O
of	_	_	O
magnesium	_	_	O
.	_	_	O
In	_	_	O
order	_	_	O
to	_	_	O
do	_	_	O
so	_	_	O
,	_	_	O
Jason	_	_	O
can	_	_	O
drink	_	_	O
a	_	_	O
sports	_	_	B-VAR
drink	_	_	I-VAR
or	_	_	O
coconut	_	_	B-VAR
water	_	_	I-VAR
.	_	_	O
The	_	_	O
sports	_	_	B-VAR
drink	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
5	_	_	B-PARAM
per	_	_	O
bottle	_	_	O
and	_	_	O
contains	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
calcium	_	_	O
,	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
potassium	_	_	O
,	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
magnesium	_	_	O
.	_	_	O
Coconut	_	_	B-VAR
water	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
3	_	_	B-PARAM
per	_	_	O
bottle	_	_	O
and	_	_	O
contains	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
calcium	_	_	O
,	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
potassium	_	_	O
,	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
magnesium	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
bottle	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
Jason	_	_	O
drink	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
cost	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
store	_	_	O
sells	_	_	O
honey	_	_	O
-	_	_	O
roasted	_	_	O
almonds	_	_	O
and	_	_	O
chocolate	_	_	O
-	_	_	O
covered	_	_	O
almonds	_	_	O
in	_	_	O
bulk	_	_	O
.	_	_	O
The	_	_	O
first	_	_	B-VAR
mix	_	_	I-VAR
contains	_	_	O
30	_	_	B-PARAM
%	_	_	I-PARAM
honey	_	_	O
-	_	_	O
roasted	_	_	O
almonds	_	_	O
and	_	_	O
70	_	_	B-PARAM
%	_	_	I-PARAM
chocolate	_	_	O
-	_	_	O
covered	_	_	O
almonds	_	_	O
.	_	_	O
The	_	_	O
second	_	_	B-VAR
mix	_	_	I-VAR
contains	_	_	O
40	_	_	B-PARAM
%	_	_	I-PARAM
honey	_	_	O
-	_	_	O
roasted	_	_	O
almonds	_	_	O
and	_	_	O
60	_	_	B-PARAM
%	_	_	I-PARAM
chocolate	_	_	O
-	_	_	O
covered	_	_	O
almonds	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	B-CONST_DIR
on	_	_	I-CONST_DIR
hand	_	_	I-CONST_DIR
100	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
honey	_	_	O
-	_	_	O
roasted	_	_	O
almonds	_	_	O
and	_	_	O
150	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
chocolate	_	_	O
-	_	_	O
covered	_	_	O
almonds	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
kg	_	_	O
of	_	_	O
the	_	_	O
first	_	_	B-VAR
mix	_	_	I-VAR
is	_	_	O
$	_	_	O
12	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
kg	_	_	O
of	_	_	O
the	_	_	O
second	_	_	B-VAR
mix	_	_	I-VAR
is	_	_	O
$	_	_	O
15	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
kg	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
prepared	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
store	_	_	O
sells	_	_	O
two	_	_	O
tropical	_	_	O
fruit	_	_	O
bowls	_	_	O
.	_	_	O
The	_	_	O
small	_	_	B-VAR
bowl	_	_	I-VAR
contains	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
kiwi	_	_	O
,	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
mango	_	_	O
,	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
pineapple	_	_	O
.	_	_	O
The	_	_	O
large	_	_	B-VAR
bowl	_	_	I-VAR
contains	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
kiwi	_	_	O
,	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
mango	_	_	O
,	_	_	O
and	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
pineapple	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
100	_	_	B-LIMIT
units	_	_	O
of	_	_	O
kiwi	_	_	O
,	_	_	O
120	_	_	B-LIMIT
units	_	_	O
of	_	_	O
mango	_	_	O
,	_	_	O
and	_	_	O
150	_	_	B-LIMIT
units	_	_	O
of	_	_	O
pineapple	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
small	_	_	B-VAR
bowl	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
large	_	_	B-VAR
bowl	_	_	I-VAR
is	_	_	O
$	_	_	O
8	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
fast	_	_	O
-	_	_	O
food	_	_	O
restaurant	_	_	O
sells	_	_	O
wraps	_	_	B-VAR
and	_	_	O
bowls	_	_	B-VAR
.	_	_	O
Each	_	_	O
wrap	_	_	B-VAR
contains	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
rice	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
fish	_	_	O
.	_	_	O
Each	_	_	O
bowl	_	_	B-VAR
contains	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
rice	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
fish	_	_	O
.	_	_	O
The	_	_	O
restaurant	_	_	O
has	_	_	O
800	_	_	B-LIMIT
units	_	_	O
of	_	_	O
rice	_	_	O
available	_	_	B-CONST_DIR
and	_	_	O
700	_	_	B-LIMIT
units	_	_	O
of	_	_	O
fish	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
wrap	_	_	B-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
bowl	_	_	B-VAR
is	_	_	O
$	_	_	O
7	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
restaurant	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
man	_	_	O
knits	_	_	O
toques	_	_	B-VAR
and	_	_	O
scarfs	_	_	B-VAR
.	_	_	O
A	_	_	O
toque	_	_	B-VAR
requires	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
yarn	_	_	O
and	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
time	_	_	O
.	_	_	O
A	_	_	O
scarf	_	_	B-VAR
requires	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
yarn	_	_	O
and	_	_	O
40	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
time	_	_	O
.	_	_	O
The	_	_	O
man	_	_	O
has	_	_	O
200	_	_	B-LIMIT
units	_	_	O
of	_	_	O
yarn	_	_	O
available	_	_	B-CONST_DIR
and	_	_	O
1800	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
time	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
toque	_	_	B-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
scarf	_	_	B-VAR
is	_	_	O
$	_	_	O
7	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
knit	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
watch	_	_	O
company	_	_	O
makes	_	_	O
watches	_	_	O
by	_	_	O
hand	_	_	O
.	_	_	O
They	_	_	O
make	_	_	O
round	_	_	B-VAR
watches	_	_	I-VAR
and	_	_	O
square	_	_	B-VAR
watches	_	_	I-VAR
.	_	_	O
The	_	_	O
round	_	_	B-VAR
watches	_	_	I-VAR
are	_	_	O
made	_	_	O
by	_	_	O
team	_	_	O
A	_	_	O
and	_	_	O
they	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
5	_	_	B-LIMIT
a	_	_	O
day	_	_	O
.	_	_	O
The	_	_	O
square	_	_	B-VAR
watches	_	_	I-VAR
are	_	_	O
made	_	_	O
by	_	_	O
team	_	_	O
B	_	_	O
and	_	_	O
the	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
6	_	_	B-LIMIT
a	_	_	O
day	_	_	O
.	_	_	O
All	_	_	O
watches	_	_	O
have	_	_	O
to	_	_	O
be	_	_	O
quality	_	_	O
checked	_	_	O
by	_	_	O
a	_	_	O
senior	_	_	O
watchmaker	_	_	O
and	_	_	O
he	_	_	O
can	_	_	O
check	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
8	_	_	B-LIMIT
watches	_	_	O
total	_	_	O
a	_	_	O
day	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
round	_	_	B-VAR
watch	_	_	I-VAR
is	_	_	O
$	_	_	O
1000	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
square	_	_	B-VAR
watch	_	_	I-VAR
is	_	_	O
$	_	_	O
1250	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
watch	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
pie	_	_	O
shop	_	_	O
sells	_	_	O
regular	_	_	B-VAR
and	_	_	I-VAR
premium	_	_	B-VAR
pies	_	_	I-VAR
.	_	_	O
They	_	_	O
make	_	_	O
x1	_	_	O
regular	_	_	B-VAR
pies	_	_	I-VAR
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
8	_	_	B-PARAM
each	_	_	O
and	_	_	O
x2	_	_	O
premium	_	_	B-VAR
pies	_	_	I-VAR
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
10	_	_	B-PARAM
each	_	_	O
(	_	_	O
x1	_	_	O
and	_	_	O
x2	_	_	O
are	_	_	O
unknown	_	_	O
and	_	_	O
greater	_	_	O
than	_	_	O
or	_	_	O
equal	_	_	O
to	_	_	O
0	_	_	O
)	_	_	O
.	_	_	O
The	_	_	O
demand	_	_	O
for	_	_	O
regular	_	_	B-VAR
pies	_	_	I-VAR
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
50	_	_	B-LIMIT
and	_	_	O
the	_	_	O
demand	_	_	O
for	_	_	O
premium	_	_	B-VAR
pies	_	_	I-VAR
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
.	_	_	O
In	_	_	O
addition	_	_	O
the	_	_	O
shop	_	_	O
can	_	_	O
only	_	_	B-CONST_DIR
make	_	_	O
60	_	_	B-LIMIT
pies	_	_	O
total	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
hiker	_	_	O
eats	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
trail	_	_	O
mix	_	_	O
and	_	_	O
wants	_	_	O
to	_	_	O
make	_	_	O
sure	_	_	O
he	_	_	O
eats	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
units	_	_	O
of	_	_	O
almonds	_	_	O
and	_	_	O
15	_	_	B-LIMIT
units	_	_	O
of	_	_	O
chocolate	_	_	O
chips	_	_	O
.	_	_	O
Trail	_	_	B-VAR
mix	_	_	I-VAR
A	_	_	I-VAR
contains	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
almonds	_	_	O
and	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
chocolate	_	_	O
chips	_	_	O
per	_	_	O
bag	_	_	O
.	_	_	O
Trail	_	_	B-VAR
mix	_	_	I-VAR
B	_	_	I-VAR
contains	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
almonds	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
chocolate	_	_	O
chips	_	_	O
per	_	_	O
bag	_	_	O
.	_	_	O
If	_	_	O
trail	_	_	B-VAR
mix	_	_	I-VAR
A	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
5	_	_	B-PARAM
per	_	_	O
bag	_	_	O
and	_	_	O
trail	_	_	B-VAR
mix	_	_	I-VAR
B	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
8	_	_	B-PARAM
per	_	_	O
bag	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
bags	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
hiker	_	_	O
purchase	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
gardener	_	_	O
grows	_	_	O
beans	_	_	B-VAR
and	_	_	O
peas	_	_	B-VAR
in	_	_	B-CONST_DIR
their	_	_	O
100	_	_	B-LIMIT
acre	_	_	O
farm	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
beans	_	_	B-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
peas	_	_	B-VAR
is	_	_	O
$	_	_	O
250	_	_	B-PARAM
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
bug	_	_	O
repellant	_	_	O
must	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
grow	_	_	O
both	_	_	O
beans	_	_	B-VAR
and	_	_	O
peas	_	_	B-VAR
.	_	_	O
Per	_	_	O
acre	_	_	O
of	_	_	O
beans	_	_	B-VAR
,	_	_	O
12	_	_	B-PARAM
liters	_	_	O
of	_	_	O
bug	_	_	O
repellant	_	_	O
are	_	_	O
needed	_	_	O
.	_	_	O
Per	_	_	O
acre	_	_	O
of	_	_	O
peas	_	_	B-VAR
,	_	_	O
15	_	_	B-PARAM
liters	_	_	O
of	_	_	O
bug	_	_	O
repellant	_	_	O
are	_	_	O
needed	_	_	O
.	_	_	O
The	_	_	O
gardener	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
1350	_	_	B-LIMIT
liters	_	_	O
of	_	_	O
bug	_	_	O
repellant	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
gardener	_	_	O
grow	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
company	_	_	O
makes	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
phones	_	_	O
,	_	_	O
a	_	_	O
large	_	_	B-VAR
size	_	_	I-VAR
and	_	_	O
a	_	_	O
small	_	_	B-VAR
size	_	_	I-VAR
.	_	_	O
The	_	_	O
large	_	_	B-VAR
size	_	_	I-VAR
phone	_	_	I-VAR
take	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
manufacturing	_	_	O
belt	_	_	O
and	_	_	O
12	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
testing	_	_	O
.	_	_	O
The	_	_	O
small	_	_	B-VAR
size	_	_	I-VAR
phone	_	_	I-VAR
takes	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
manufacturing	_	_	O
belt	_	_	O
and	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
testing	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
1500	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
on	_	_	O
the	_	_	O
manufacturing	_	_	O
belt	_	_	O
and	_	_	O
1000	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
testing	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
large	_	_	B-VAR
phone	_	_	I-VAR
is	_	_	O
$	_	_	O
400	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
small	_	_	B-VAR
phone	_	_	I-VAR
is	_	_	O
$	_	_	O
300	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
sandwich	_	_	O
shop	_	_	O
specializes	_	_	O
in	_	_	O
cheese	_	_	O
sandwiches	_	_	O
and	_	_	O
they	_	_	O
make	_	_	O
two	_	_	O
types	_	_	O
.	_	_	O
Sandwich	_	_	B-VAR
A	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
cheddar	_	_	O
cheese	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
American	_	_	O
cheese	_	_	O
.	_	_	O
Sandwich	_	_	B-VAR
B	_	_	I-VAR
requires	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
cheddar	_	_	O
cheese	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
American	_	_	O
cheese	_	_	O
.	_	_	O
The	_	_	O
shop	_	_	O
has	_	_	O
500	_	_	B-LIMIT
units	_	_	O
and	_	_	O
400	_	_	B-LIMIT
units	_	_	O
of	_	_	O
cheddar	_	_	O
and	_	_	O
American	_	_	O
cheese	_	_	O
available	_	_	B-CONST_DIR
respectively	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
sandwich	_	_	B-VAR
A	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
sandwich	_	_	B-VAR
B	_	_	I-VAR
is	_	_	O
$	_	_	O
6	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
shop	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
dog	_	_	O
owner	_	_	O
mixes	_	_	O
two	_	_	O
brands	_	_	O
of	_	_	O
dog	_	_	O
food	_	_	O
to	_	_	O
ensure	_	_	O
his	_	_	O
puppy	_	_	O
gets	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
units	_	_	O
of	_	_	O
minerals	_	_	O
and	_	_	O
40	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamins	_	_	O
.	_	_	O
A	_	_	O
serving	_	_	O
of	_	_	O
dog	_	_	B-VAR
food	_	_	I-VAR
A	_	_	I-VAR
contains	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
minerals	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamins	_	_	O
.	_	_	O
A	_	_	O
serving	_	_	O
of	_	_	O
dog	_	_	B-VAR
food	_	_	I-VAR
B	_	_	I-VAR
contains	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
minerals	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamins	_	_	O
.	_	_	O
If	_	_	O
dog	_	_	B-VAR
food	_	_	I-VAR
A	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
3	_	_	B-PARAM
per	_	_	O
serving	_	_	O
and	_	_	O
dog	_	_	B-VAR
food	_	_	I-VAR
B	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
5	_	_	B-PARAM
per	_	_	O
serving	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
servings	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
owner	_	_	O
buy	_	_	O
and	_	_	O
feed	_	_	O
his	_	_	O
dog	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
small	_	_	O
cereal	_	_	O
company	_	_	O
makes	_	_	O
individual	_	_	B-VAR
and	_	_	O
family	_	_	B-VAR
size	_	_	O
cereal	_	_	O
boxes	_	_	O
.	_	_	O
To	_	_	O
make	_	_	O
an	_	_	O
individual	_	_	B-VAR
cereal	_	_	I-VAR
box	_	_	I-VAR
takes	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
cereal	_	_	O
and	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
fill	_	_	O
.	_	_	O
To	_	_	O
make	_	_	O
a	_	_	O
family	_	_	B-VAR
size	_	_	I-VAR
cereal	_	_	I-VAR
box	_	_	I-VAR
takes	_	_	O
60	_	_	B-PARAM
units	_	_	O
of	_	_	O
cereal	_	_	O
and	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
fill	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
2000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
cereal	_	_	O
available	_	_	B-CONST_DIR
and	_	_	O
750	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
filling	_	_	O
time	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
individual	_	_	B-VAR
cereal	_	_	I-VAR
box	_	_	I-VAR
is	_	_	O
$	_	_	O
4	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
family	_	_	B-VAR
size	_	_	I-VAR
cereal	_	_	I-VAR
box	_	_	I-VAR
is	_	_	O
$	_	_	O
8	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

You	_	_	O
have	_	_	B-CONST_DIR
$	_	_	O
300000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
four	_	_	O
different	_	_	O
tech	_	_	O
companies	_	_	O
who	_	_	O
specialize	_	_	O
in	_	_	O
specific	_	_	O
products	_	_	O
.	_	_	O
There	_	_	O
is	_	_	O
a	_	_	O
video	_	_	B-VAR
game	_	_	I-VAR
company	_	_	O
,	_	_	O
a	_	_	O
camera	_	_	B-VAR
company	_	_	I-VAR
,	_	_	O
a	_	_	O
cell	_	_	B-VAR
phone	_	_	I-VAR
company	_	_	I-VAR
,	_	_	O
and	_	_	O
a	_	_	O
laptop	_	_	B-VAR
company	_	_	I-VAR
.	_	_	O
The	_	_	O
return	_	_	B-OBJ_NAME
on	_	_	O
investment	_	_	O
for	_	_	O
each	_	_	O
is	_	_	O
as	_	_	O
follows	_	_	O
:	_	_	O
video	_	_	B-VAR
game	_	_	I-VAR
company	_	_	O
,	_	_	O
7	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
camera	_	_	B-VAR
company	_	_	I-VAR
,	_	_	O
3	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
cell	_	_	B-VAR
phone	_	_	I-VAR
company	_	_	I-VAR
,	_	_	O
9	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
laptop	_	_	B-VAR
company	_	_	I-VAR
7	_	_	B-PARAM
%	_	_	I-PARAM
.	_	_	O
You	_	_	O
have	_	_	O
self	_	_	O
imposed	_	_	O
some	_	_	O
restrictions	_	_	O
on	_	_	O
your	_	_	O
investment	_	_	O
.	_	_	O
For	_	_	O
instance	_	_	O
,	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
laptop	_	_	B-VAR
company	_	_	I-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
video	_	_	B-VAR
game	_	_	I-VAR
company	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
camera	_	_	B-VAR
company	_	_	I-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
cell	_	_	B-VAR
phone	_	_	I-VAR
company	_	_	I-VAR
.	_	_	O
Finally	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
15	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
your	_	_	O
total	_	_	O
investment	_	_	O
can	_	_	O
be	_	_	O
in	_	_	O
the	_	_	O
laptop	_	_	B-VAR
company	_	_	I-VAR
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
your	_	_	O
returns	_	_	B-OBJ_NAME
.	_	_	O

You	_	_	O
are	_	_	O
put	_	_	O
on	_	_	O
a	_	_	O
special	_	_	O
diet	_	_	O
where	_	_	O
you	_	_	O
can	_	_	O
drink	_	_	O
two	_	_	O
juices	_	_	O
.	_	_	O
Juice	_	_	B-VAR
A	_	_	I-VAR
contains	_	_	O
10	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
15	_	_	B-PARAM
grams	_	_	O
of	_	_	O
carbs	_	_	O
,	_	_	O
4	_	_	B-PARAM
grams	_	_	O
of	_	_	O
fat	_	_	O
,	_	_	O
and	_	_	O
300	_	_	B-PARAM
calories	_	_	B-OBJ_NAME
per	_	_	O
cup	_	_	O
.	_	_	O
Juice	_	_	B-VAR
B	_	_	I-VAR
contains	_	_	O
12	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
20	_	_	B-PARAM
grams	_	_	O
of	_	_	O
carbs	_	_	O
,	_	_	O
8	_	_	B-PARAM
grams	_	_	O
of	_	_	O
fat	_	_	O
,	_	_	O
and	_	_	O
350	_	_	B-PARAM
calories	_	_	B-OBJ_NAME
per	_	_	O
cup	_	_	O
.	_	_	O
You	_	_	O
must	_	_	O
consume	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
150	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
carbs	_	_	O
.	_	_	O
However	_	_	O
you	_	_	O
can	_	_	O
consume	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
50	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
cups	_	_	O
of	_	_	O
each	_	_	O
juice	_	_	O
should	_	_	O
you	_	_	O
drink	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
calories	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
tropical	_	_	O
farmer	_	_	O
has	_	_	B-CONST_DIR
100	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
to	_	_	O
grow	_	_	O
guavas	_	_	B-VAR
and	_	_	O
mangos	_	_	B-VAR
.	_	_	O
He	_	_	O
prefers	_	_	O
to	_	_	O
grow	_	_	O
more	_	_	O
mangos	_	_	B-VAR
than	_	_	O
guavas	_	_	B-VAR
,	_	_	O
but	_	_	O
because	_	_	O
they	_	_	O
require	_	_	O
so	_	_	O
much	_	_	O
more	_	_	O
work	_	_	O
,	_	_	O
he	_	_	O
can	_	_	O
grow	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
2	_	_	B-PARAM
times	_	_	O
the	_	_	O
amount	_	_	O
of	_	_	O
mangos	_	_	B-VAR
as	_	_	O
guavas	_	_	B-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
he	_	_	O
must	_	_	O
grow	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
guavas	_	_	B-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
40	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
mangos	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
guavas	_	_	B-VAR
is	_	_	O
$	_	_	O
300	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acres	_	_	O
of	_	_	O
mangos	_	_	B-VAR
is	_	_	O
$	_	_	O
500	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acre	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
grow	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
pharmacy	_	_	O
mixes	_	_	O
two	_	_	O
capsules	_	_	O
to	_	_	O
create	_	_	O
a	_	_	O
final	_	_	O
product	_	_	O
.	_	_	O
Capsule	_	_	B-VAR
A	_	_	I-VAR
contains	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
targeted	_	_	O
medicine	_	_	O
,	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
pain	_	_	O
reliever	_	_	O
,	_	_	O
and	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
filler	_	_	O
.	_	_	O
Capsule	_	_	B-VAR
B	_	_	I-VAR
contains	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
targeted	_	_	O
medicine	_	_	O
,	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
pain	_	_	O
reliever	_	_	O
,	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
filler	_	_	O
.	_	_	O
The	_	_	O
minimum	_	_	B-CONST_DIR
requirements	_	_	I-CONST_DIR
of	_	_	O
the	_	_	O
new	_	_	O
product	_	_	O
are	_	_	O
20	_	_	B-LIMIT
units	_	_	O
of	_	_	O
targeted	_	_	O
medicine	_	_	O
,	_	_	O
20	_	_	B-LIMIT
units	_	_	O
of	_	_	O
pain	_	_	O
reliever	_	_	O
,	_	_	O
and	_	_	O
15	_	_	B-LIMIT
units	_	_	O
of	_	_	O
filler	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
capsule	_	_	B-VAR
A	_	_	I-VAR
is	_	_	O
$	_	_	O
2	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
capsule	_	_	B-VAR
B	_	_	I-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
toy	_	_	O
shop	_	_	O
makes	_	_	O
wooden	_	_	O
dolls	_	_	B-VAR
and	_	_	O
soldiers	_	_	B-VAR
.	_	_	O
Each	_	_	O
doll	_	_	B-VAR
takes	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
crafting	_	_	O
and	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
sanding	_	_	O
.	_	_	O
Each	_	_	O
soldier	_	_	B-VAR
takes	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
crafting	_	_	O
and	_	_	O
8	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
sanding	_	_	O
.	_	_	O
The	_	_	O
shop	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
1000	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
crafting	_	_	O
and	_	_	O
800	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
sanding	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
doll	_	_	B-VAR
is	_	_	O
$	_	_	O
8	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
soldier	_	_	B-VAR
is	_	_	O
$	_	_	O
10	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
auto	_	_	O
plant	_	_	O
makes	_	_	O
cars	_	_	B-VAR
and	_	_	O
trucks	_	_	B-VAR
.	_	_	O
Each	_	_	O
car	_	_	B-VAR
takes	_	_	O
2	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
assembly	_	_	O
line	_	_	O
and	_	_	O
1	_	_	B-PARAM
hour	_	_	O
of	_	_	O
mechanic	_	_	O
time	_	_	O
.	_	_	O
Each	_	_	O
truck	_	_	B-VAR
takes	_	_	O
2.5	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
assembly	_	_	O
line	_	_	O
and	_	_	O
1.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
mechanic	_	_	O
time	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
800	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
assembly	_	_	O
line	_	_	O
time	_	_	O
available	_	_	B-CONST_DIR
and	_	_	O
600	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
mechanic	_	_	O
time	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
car	_	_	B-VAR
is	_	_	O
$	_	_	O
5000	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
truck	_	_	B-VAR
is	_	_	O
$	_	_	O
8000	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
plant	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

George	_	_	O
buys	_	_	O
sneakers	_	_	B-VAR
and	_	_	O
boots	_	_	B-VAR
for	_	_	O
resale	_	_	O
.	_	_	O
Each	_	_	O
sneaker	_	_	B-VAR
costs	_	_	O
him	_	_	O
$	_	_	O
150	_	_	B-PARAM
and	_	_	O
each	_	_	O
boot	_	_	B-VAR
costs	_	_	O
him	_	_	O
$	_	_	O
200	_	_	B-PARAM
.	_	_	O
He	_	_	O
knows	_	_	O
the	_	_	O
monthly	_	_	O
demand	_	_	O
for	_	_	O
these	_	_	O
shoes	_	_	O
,	_	_	O
both	_	_	O
sneakers	_	_	B-VAR
and	_	_	O
boots	_	_	B-VAR
,	_	_	O
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
50	_	_	B-LIMIT
.	_	_	O
Also	_	_	O
,	_	_	O
George	_	_	O
does	_	_	O
not	_	_	O
want	_	_	O
to	_	_	O
spend	_	_	O
more	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
$	_	_	O
8750	_	_	B-LIMIT
buying	_	_	O
these	_	_	O
shoes	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
sneaker	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
boot	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
80	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
buy	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
hardware	_	_	O
manufacturer	_	_	O
makes	_	_	O
CPUs	_	_	B-VAR
and	_	_	O
GPUs	_	_	B-VAR
.	_	_	O
Each	_	_	O
CPU	_	_	B-VAR
requires	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
wiring	_	_	O
while	_	_	O
each	_	_	O
GPU	_	_	B-VAR
requires	_	_	O
90	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
wiring	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
each	_	_	O
CPU	_	_	B-VAR
requires	_	_	O
50	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
soldering	_	_	O
and	_	_	O
each	_	_	O
GPU	_	_	B-VAR
requires	_	_	O
40	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
soldering	_	_	O
.	_	_	O
The	_	_	O
manufacturer	_	_	O
has	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
2000	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
wiring	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
2500	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
soldering	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
CPU	_	_	B-VAR
is	_	_	O
$	_	_	O
300	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
GPU	_	_	B-VAR
is	_	_	O
$	_	_	O
500	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
ferry	_	_	O
service	_	_	O
provides	_	_	O
vehicle	_	_	B-VAR
tickets	_	_	I-VAR
and	_	_	O
passenger	_	_	B-VAR
tickets	_	_	I-VAR
.	_	_	O
The	_	_	O
ferry	_	_	O
can	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
tickets	_	_	O
.	_	_	O
A	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
50	_	_	B-PARAM
is	_	_	O
made	_	_	O
per	_	_	O
vehicle	_	_	B-VAR
ticket	_	_	I-VAR
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
50	_	_	B-PARAM
is	_	_	O
made	_	_	O
per	_	_	O
passenger	_	_	B-VAR
ticket	_	_	I-VAR
.	_	_	O
The	_	_	O
ferry	_	_	O
reserved	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
10	_	_	B-LIMIT
tickets	_	_	O
for	_	_	O
vehicles	_	_	B-VAR
.	_	_	O
However	_	_	O
,	_	_	O
because	_	_	O
most	_	_	O
people	_	_	O
do	_	_	O
n't	_	_	O
have	_	_	O
cars	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-PARAM
times	_	_	O
as	_	_	O
may	_	_	O
people	_	_	O
buy	_	_	O
passenger	_	_	B-VAR
tickets	_	_	I-VAR
than	_	_	O
vehicle	_	_	B-VAR
tickets	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
be	_	_	O
sold	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
candy	_	_	O
shop	_	_	O
makes	_	_	O
a	_	_	O
mixture	_	_	O
of	_	_	O
candy	_	_	O
using	_	_	O
sour	_	_	B-VAR
drops	_	_	I-VAR
and	_	_	O
sour	_	_	B-VAR
belts	_	_	I-VAR
.	_	_	O
Each	_	_	O
sour	_	_	B-VAR
drop	_	_	I-VAR
has	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
sourness	_	_	O
and	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
flavoring	_	_	O
.	_	_	O
Each	_	_	O
sour	_	_	B-VAR
belt	_	_	I-VAR
has	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
sourness	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
flavoring	_	_	O
.	_	_	O
The	_	_	O
shop	_	_	O
want	_	_	O
to	_	_	O
make	_	_	O
sure	_	_	O
the	_	_	O
mixture	_	_	O
contains	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
units	_	_	O
of	_	_	O
sourness	_	_	O
and	_	_	O
40	_	_	B-LIMIT
units	_	_	O
of	_	_	O
flavoring	_	_	O
.	_	_	O
The	_	_	O
mixture	_	_	O
can	_	_	O
also	_	_	O
contain	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
5	_	_	B-LIMIT
sour	_	_	B-VAR
belts	_	_	I-VAR
.	_	_	O
If	_	_	O
it	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
0.50	_	_	B-PARAM
per	_	_	O
sour	_	_	B-VAR
drop	_	_	I-VAR
and	_	_	O
$	_	_	O
0.40	_	_	B-PARAM
per	_	_	O
sour	_	_	B-VAR
belt	_	_	I-VAR
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
of	_	_	O
the	_	_	O
mixture	_	_	O
?	_	_	O

A	_	_	O
factory	_	_	O
has	_	_	O
workers	_	_	O
who	_	_	O
knit	_	_	O
scarfs	_	_	B-VAR
and	_	_	O
toques	_	_	B-VAR
by	_	_	O
hand	_	_	O
.	_	_	O
The	_	_	O
factory	_	_	O
has	_	_	O
250000	_	_	B-LIMIT
knitting	_	_	O
minutes	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
A	_	_	O
scarf	_	_	B-VAR
takes	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
knit	_	_	O
and	_	_	O
a	_	_	O
toque	_	_	B-VAR
takes	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
knit	_	_	O
.	_	_	O
The	_	_	O
factory	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5000	_	_	B-LIMIT
scarfs	_	_	B-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3000	_	_	B-LIMIT
toques	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
scarf	_	_	B-VAR
is	_	_	O
$	_	_	O
20	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
toque	_	_	B-VAR
is	_	_	O
$	_	_	O
25	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
clothing	_	_	O
company	_	_	O
makes	_	_	O
blue	_	_	B-VAR
and	_	_	O
dark	_	_	B-VAR
blue	_	_	I-VAR
t	_	_	I-VAR
-	_	_	I-VAR
shirts	_	_	I-VAR
.	_	_	O
A	_	_	O
blue	_	_	B-VAR
t	_	_	I-VAR
-	_	_	I-VAR
shirt	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
unit	_	_	O
of	_	_	O
dye	_	_	O
,	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	O
,	_	_	O
and	_	_	O
30	_	_	B-PARAM
worker	_	_	O
minutes	_	_	O
.	_	_	O
A	_	_	O
dark	_	_	B-VAR
blue	_	_	I-VAR
t	_	_	I-VAR
-	_	_	I-VAR
shirt	_	_	I-VAR
requires	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
dye	_	_	O
,	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	O
,	_	_	O
and	_	_	O
25	_	_	B-PARAM
worker	_	_	O
minutes	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
only	_	_	O
has	_	_	O
1000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
dye	_	_	O
,	_	_	O
1200	_	_	B-LIMIT
units	_	_	O
of	_	_	O
water	_	_	O
,	_	_	O
and	_	_	O
8000	_	_	B-LIMIT
worker	_	_	O
minutes	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
blue	_	_	B-VAR
t	_	_	I-VAR
-	_	_	I-VAR
shirt	_	_	I-VAR
is	_	_	O
$	_	_	O
10	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
dark	_	_	B-VAR
blue	_	_	I-VAR
t	_	_	I-VAR
-	_	_	I-VAR
shirt	_	_	I-VAR
is	_	_	O
$	_	_	O
15	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
repairman	_	_	O
fixes	_	_	O
fridges	_	_	B-VAR
and	_	_	O
ovens	_	_	B-VAR
.	_	_	O
Each	_	_	O
fridge	_	_	B-VAR
takes	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
inspection	_	_	O
and	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
fixing	_	_	O
time	_	_	O
.	_	_	O
Each	_	_	O
oven	_	_	B-VAR
takes	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
inspection	_	_	O
and	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
fixing	_	_	O
time	_	_	O
.	_	_	O
The	_	_	O
repairman	_	_	O
has	_	_	O
1000	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
inspection	_	_	O
and	_	_	O
800	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
fixing	_	_	O
this	_	_	O
week	_	_	O
.	_	_	O
If	_	_	O
each	_	_	O
fridge	_	_	B-VAR
repaired	_	_	O
earns	_	_	B-OBJ_NAME
him	_	_	O
$	_	_	O
100	_	_	B-PARAM
and	_	_	O
each	_	_	O
oven	_	_	B-VAR
repaired	_	_	O
earns	_	_	B-OBJ_NAME
his	_	_	O
$	_	_	O
125	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
fix	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
earnings	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
factory	_	_	O
makes	_	_	O
backpacks	_	_	B-VAR
and	_	_	O
handbags	_	_	B-VAR
using	_	_	O
a	_	_	O
special	_	_	O
machine	_	_	O
.	_	_	O
This	_	_	O
machine	_	_	O
must	_	_	O
be	_	_	O
operated	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3000	_	_	B-LIMIT
minutes	_	_	O
per	_	_	O
week	_	_	O
.	_	_	O
Each	_	_	O
backpack	_	_	B-VAR
takes	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
machine	_	_	O
while	_	_	O
each	_	_	O
handbag	_	_	B-VAR
takes	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
machine	_	_	O
.	_	_	O
The	_	_	O
factory	_	_	O
must	_	_	O
make	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
180	_	_	B-LIMIT
items	_	_	O
total	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
for	_	_	O
producing	_	_	O
a	_	_	O
backpack	_	_	B-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
for	_	_	O
producing	_	_	O
a	_	_	O
handbag	_	_	B-VAR
is	_	_	O
$	_	_	O
8	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

You	_	_	O
are	_	_	O
buying	_	_	O
trucks	_	_	O
to	_	_	O
transport	_	_	O
goods	_	_	O
and	_	_	O
will	_	_	O
keep	_	_	O
them	_	_	O
in	_	_	O
your	_	_	O
parking	_	_	O
lot	_	_	O
.	_	_	O
A	_	_	O
small	_	_	B-VAR
truck	_	_	I-VAR
costs	_	_	O
$	_	_	O
5000	_	_	B-PARAM
,	_	_	O
takes	_	_	O
1	_	_	B-PARAM
parking	_	_	O
spot	_	_	O
,	_	_	O
and	_	_	O
can	_	_	O
carry	_	_	O
10	_	_	B-PARAM
boxes	_	_	B-OBJ_NAME
.	_	_	O
A	_	_	O
large	_	_	B-VAR
truck	_	_	I-VAR
costs	_	_	O
$	_	_	O
8000	_	_	B-PARAM
,	_	_	O
takes	_	_	O
2	_	_	B-PARAM
parking	_	_	O
spots	_	_	O
,	_	_	O
and	_	_	O
can	_	_	O
carry	_	_	O
15	_	_	B-PARAM
boxes	_	_	B-OBJ_NAME
.	_	_	O
You	_	_	O
have	_	_	O
a	_	_	O
$	_	_	O
100000	_	_	B-LIMIT
limit	_	_	B-CONST_DIR
and	_	_	O
have	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
15	_	_	B-LIMIT
parking	_	_	O
spots	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
truck	_	_	O
should	_	_	O
be	_	_	O
purchased	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
boxes	_	_	I-OBJ_NAME
you	_	_	O
can	_	_	O
carry	_	_	O
?	_	_	O

A	_	_	O
young	_	_	O
entrepreneur	_	_	O
has	_	_	O
$	_	_	O
500000	_	_	B-LIMIT
available	_	_	B-CONST_DIR
to	_	_	O
invest	_	_	O
in	_	_	O
a	_	_	O
12	_	_	O
-	_	_	O
month	_	_	O
commitment	_	_	O
.	_	_	O
He	_	_	O
can	_	_	O
either	_	_	O
invest	_	_	O
in	_	_	O
the	_	_	O
healthcare	_	_	B-VAR
industry	_	_	I-VAR
which	_	_	O
yields	_	_	O
a	_	_	O
4	_	_	B-PARAM
%	_	_	O
return	_	_	B-OBJ_NAME
or	_	_	O
in	_	_	O
the	_	_	O
energy	_	_	B-VAR
sector	_	_	I-VAR
which	_	_	O
yields	_	_	O
an	_	_	O
8	_	_	B-PARAM
%	_	_	O
return	_	_	B-OBJ_NAME
.	_	_	O
His	_	_	O
father	_	_	O
has	_	_	O
advised	_	_	O
him	_	_	O
that	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
60	_	_	B-LIMIT
%	_	_	O
of	_	_	O
the	_	_	O
investment	_	_	O
be	_	_	O
placed	_	_	O
in	_	_	O
the	_	_	O
healthcare	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
Due	_	_	O
to	_	_	O
recent	_	_	O
issues	_	_	O
in	_	_	O
the	_	_	O
energy	_	_	O
sector	_	_	O
,	_	_	O
he	_	_	O
has	_	_	O
decided	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
35	_	_	B-LIMIT
%	_	_	O
of	_	_	O
his	_	_	O
investment	_	_	O
be	_	_	O
placed	_	_	O
in	_	_	O
the	_	_	O
energy	_	_	B-VAR
sector	_	_	I-VAR
.	_	_	O
How	_	_	O
much	_	_	O
should	_	_	O
he	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
area	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
return	_	_	B-OBJ_NAME
on	_	_	O
investments	_	_	O
?	_	_	O

The	_	_	O
mayor	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
up	_	_	O
to	_	_	O
$	_	_	O
3500	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
city	_	_	O
infrastructure	_	_	O
.	_	_	O
He	_	_	O
can	_	_	O
invest	_	_	O
his	_	_	O
money	_	_	O
on	_	_	O
roads	_	_	B-VAR
and	_	_	O
housing	_	_	B-VAR
.	_	_	O
Each	_	_	O
dollar	_	_	O
invested	_	_	O
in	_	_	O
housing	_	_	B-VAR
yields	_	_	O
a	_	_	O
$	_	_	O
0.95	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
.	_	_	O
Each	_	_	O
dollar	_	_	O
invested	_	_	O
on	_	_	O
roads	_	_	B-VAR
yields	_	_	O
a	_	_	O
$	_	_	O
0.32	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
.	_	_	O
No	_	_	B-CONST_DIR
less	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
$	_	_	O
750	_	_	B-LIMIT
must	_	_	O
be	_	_	O
in	_	_	O
housing	_	_	B-VAR
and	_	_	O
no	_	_	B-CONST_DIR
less	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
24	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
all	_	_	O
money	_	_	O
invested	_	_	O
must	_	_	O
be	_	_	O
in	_	_	O
roads	_	_	B-VAR
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
that	_	_	O
can	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
total	_	_	O
profit	_	_	B-OBJ_NAME
earned	_	_	O
from	_	_	O
his	_	_	O
investment	_	_	O
.	_	_	O

Each	_	_	O
month	_	_	O
,	_	_	O
a	_	_	O
video	_	_	O
-	_	_	O
game	_	_	O
store	_	_	O
owner	_	_	O
can	_	_	O
spend	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
30000	_	_	B-LIMIT
on	_	_	O
consoles	_	_	B-VAR
and	_	_	O
discs	_	_	B-VAR
.	_	_	O
A	_	_	O
console	_	_	B-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
owner	_	_	O
$	_	_	O
300	_	_	B-PARAM
and	_	_	O
a	_	_	O
disc	_	_	B-VAR
costs	_	_	O
$	_	_	O
30	_	_	B-PARAM
.	_	_	O
Each	_	_	O
console	_	_	B-VAR
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
200	_	_	B-PARAM
while	_	_	O
each	_	_	O
disc	_	_	B-VAR
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
30	_	_	B-PARAM
.	_	_	O
The	_	_	O
store	_	_	O
owner	_	_	O
estimates	_	_	O
that	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
20	_	_	B-LIMIT
but	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
50	_	_	B-LIMIT
consoles	_	_	B-VAR
are	_	_	O
sold	_	_	O
each	_	_	O
month	_	_	O
.	_	_	O
He	_	_	O
also	_	_	O
estimates	_	_	O
that	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
discs	_	_	B-VAR
sold	_	_	O
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
five	_	_	B-PARAM
times	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
consoles	_	_	B-VAR
sold	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
,	_	_	O
consoles	_	_	B-VAR
and	_	_	O
discs	_	_	B-VAR
,	_	_	O
should	_	_	O
be	_	_	O
sold	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

There	_	_	O
is	_	_	O
only	_	_	B-CONST_DIR
2000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
lettuce	_	_	O
that	_	_	O
is	_	_	O
needed	_	_	O
to	_	_	O
make	_	_	O
both	_	_	O
the	_	_	O
caesar	_	_	B-VAR
and	_	_	O
house	_	_	B-VAR
salad	_	_	I-VAR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
caesar	_	_	B-VAR
salad	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
house	_	_	B-VAR
salad	_	_	I-VAR
is	_	_	O
$	_	_	O
8	_	_	B-PARAM
.	_	_	O
The	_	_	O
caesar	_	_	B-VAR
salad	_	_	I-VAR
contains	_	_	O
20	_	_	B-PARAM
grams	_	_	O
of	_	_	O
lettuce	_	_	O
and	_	_	O
the	_	_	O
house	_	_	B-VAR
salad	_	_	I-VAR
contains	_	_	O
30	_	_	B-PARAM
grams	_	_	O
of	_	_	O
lettuce	_	_	O
.	_	_	O
The	_	_	O
house	_	_	B-VAR
salad	_	_	I-VAR
is	_	_	O
much	_	_	O
more	_	_	O
popular	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	O
the	_	_	O
amount	_	_	O
of	_	_	O
house	_	_	B-VAR
salads	_	_	I-VAR
needs	_	_	O
to	_	_	O
be	_	_	O
made	_	_	O
than	_	_	O
the	_	_	O
caesar	_	_	B-VAR
salads	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
8	_	_	B-LIMIT
caesar	_	_	B-VAR
salads	_	_	I-VAR
needs	_	_	O
to	_	_	O
be	_	_	O
made	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
salad	_	_	O
should	_	_	O
me	_	_	O
made	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
company	_	_	O
is	_	_	O
deciding	_	_	O
how	_	_	O
to	_	_	O
run	_	_	O
its	_	_	O
tv	_	_	O
commercials	_	_	O
.	_	_	O
They	_	_	O
can	_	_	O
be	_	_	O
run	_	_	O
during	_	_	O
movies	_	_	B-VAR
,	_	_	O
sports	_	_	B-VAR
games	_	_	I-VAR
,	_	_	O
or	_	_	O
comedy	_	_	B-VAR
shows	_	_	I-VAR
.	_	_	O
The	_	_	O
cost	_	_	O
for	_	_	O
a	_	_	O
commercial	_	_	O
as	_	_	O
well	_	_	O
as	_	_	O
the	_	_	O
expected	_	_	O
audience	_	_	O
reach	_	_	O
is	_	_	O
given	_	_	O
.	_	_	O
During	_	_	O
movies	_	_	B-VAR
,	_	_	O
a	_	_	O
commercial	_	_	O
costs	_	_	O
$	_	_	O
1000	_	_	B-PARAM
and	_	_	O
attracts	_	_	O
25000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
During	_	_	O
sports	_	_	B-VAR
games	_	_	I-VAR
,	_	_	O
a	_	_	O
commercial	_	_	O
costs	_	_	O
$	_	_	O
5000	_	_	B-PARAM
and	_	_	O
attracts	_	_	O
100000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
During	_	_	O
comedy	_	_	B-VAR
shows	_	_	I-VAR
,	_	_	O
a	_	_	O
commercial	_	_	O
costs	_	_	O
$	_	_	O
2000	_	_	B-PARAM
and	_	_	O
attracts	_	_	O
45000	_	_	B-PARAM
peoples	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
sports	_	_	O
broadcaster	_	_	O
limits	_	_	B-CONST_DIR
the	_	_	I-CONST_DIR
number	_	_	I-CONST_DIR
of	_	_	O
commercials	_	_	O
during	_	_	O
sports	_	_	B-VAR
games	_	_	I-VAR
from	_	_	O
a	_	_	O
single	_	_	O
company	_	_	O
to	_	_	O
five	_	_	B-LIMIT
.	_	_	O
In	_	_	O
order	_	_	O
to	_	_	O
attract	_	_	O
a	_	_	O
wide	_	_	O
range	_	_	O
of	_	_	O
people	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
a	_	_	O
third	_	_	B-LIMIT
of	_	_	O
all	_	_	O
commercials	_	_	O
should	_	_	O
occur	_	_	O
during	_	_	O
comedy	_	_	B-VAR
shows	_	_	I-VAR
and	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
15	_	_	B-LIMIT
%	_	_	I-LIMIT
should	_	_	O
occur	_	_	O
during	_	_	O
movies	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
weekly	_	_	O
budget	_	_	B-CONST_DIR
is	_	_	O
$	_	_	O
50000	_	_	B-LIMIT
,	_	_	O
how	_	_	O
many	_	_	O
commercials	_	_	O
should	_	_	O
be	_	_	O
run	_	_	O
in	_	_	O
each	_	_	O
of	_	_	O
the	_	_	O
three	_	_	O
possible	_	_	O
choices	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
audience	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
cruise	_	_	O
ship	_	_	O
can	_	_	O
carry	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
500	_	_	B-LIMIT
passengers	_	_	O
.	_	_	O
They	_	_	O
offer	_	_	O
luxury	_	_	B-VAR
tickets	_	_	I-VAR
as	_	_	O
well	_	_	O
as	_	_	O
regular	_	_	B-VAR
tickets	_	_	I-VAR
.	_	_	O
The	_	_	O
cruise	_	_	O
ship	_	_	O
reserves	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
luxury	_	_	B-VAR
tickets	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
2	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
passengers	_	_	O
prefer	_	_	O
to	_	_	O
buy	_	_	O
regular	_	_	B-VAR
tickets	_	_	I-VAR
than	_	_	O
the	_	_	O
luxury	_	_	B-VAR
tickets	_	_	I-VAR
.	_	_	O
A	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
500	_	_	B-PARAM
is	_	_	O
made	_	_	O
per	_	_	O
luxury	_	_	B-VAR
ticket	_	_	I-VAR
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
300	_	_	B-PARAM
is	_	_	O
made	_	_	O
per	_	_	O
regular	_	_	B-VAR
ticket	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
ticket	_	_	O
should	_	_	O
be	_	_	O
sold	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O
What	_	_	O
is	_	_	O
that	_	_	O
profit	_	_	O
?	_	_	O

A	_	_	O
hedge	_	_	O
fund	_	_	O
is	_	_	O
attempting	_	_	O
to	_	_	O
determine	_	_	O
where	_	_	O
its	_	_	O
assets	_	_	O
should	_	_	O
be	_	_	O
invested	_	_	O
during	_	_	O
the	_	_	O
current	_	_	O
year	_	_	O
.	_	_	O
At	_	_	O
present	_	_	O
,	_	_	O
$	_	_	O
3,200,000	_	_	B-LIMIT
is	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
investment	_	_	O
in	_	_	O
stocks	_	_	B-VAR
,	_	_	O
options	_	_	B-VAR
,	_	_	O
security	_	_	B-VAR
swaps	_	_	I-VAR
,	_	_	O
and	_	_	O
futures	_	_	B-VAR
.	_	_	O
The	_	_	O
annual	_	_	O
rate	_	_	O
of	_	_	O
return	_	_	B-OBJ_NAME
on	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
investment	_	_	O
is	_	_	O
known	_	_	O
to	_	_	O
be	_	_	O
:	_	_	O
stocks	_	_	B-VAR
,	_	_	O
11	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
options	_	_	B-VAR
,	_	_	O
30	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
security	_	_	B-VAR
swaps	_	_	I-VAR
,	_	_	O
5	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
futures	_	_	B-VAR
,	_	_	O
15	_	_	B-PARAM
%	_	_	I-PARAM
.	_	_	O
To	_	_	O
ensure	_	_	O
that	_	_	O
the	_	_	O
hedge	_	_	O
fund	_	_	O
’s	_	_	O
portfolio	_	_	O
is	_	_	O
not	_	_	O
too	_	_	O
risky	_	_	O
,	_	_	O
the	_	_	O
hedge	_	_	O
fund	_	_	O
’s	_	_	O
investment	_	_	O
manager	_	_	O
has	_	_	O
placed	_	_	O
the	_	_	O
following	_	_	O
three	_	_	O
restrictions	_	_	O
on	_	_	O
the	_	_	O
hedge	_	_	O
fund	_	_	O
’s	_	_	O
portfolio	_	_	O
:	_	_	O
a	_	_	O
The	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
futures	_	_	B-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
stocks	_	_	B-VAR
.	_	_	O
b	_	_	O
At	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
35	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
total	_	_	O
amount	_	_	O
invested	_	_	O
may	_	_	O
be	_	_	O
in	_	_	O
futures	_	_	B-VAR
.	_	_	O
c	_	_	O
The	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
options	_	_	B-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
security	_	_	B-VAR
swaps	_	_	I-VAR
.	_	_	O
The	_	_	O
hedge	_	_	O
fund	_	_	O
’s	_	_	O
objective	_	_	O
is	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
annual	_	_	O
return	_	_	B-OBJ_NAME
on	_	_	O
its	_	_	O
investment	_	_	O
portfolio	_	_	O
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
that	_	_	O
will	_	_	O
enable	_	_	O
the	_	_	O
hedge	_	_	O
fund	_	_	O
to	_	_	O
meet	_	_	O
this	_	_	O
goal	_	_	O
.	_	_	O

A	_	_	O
farmer	_	_	O
has	_	_	O
30	_	_	B-LIMIT
acres	_	_	O
available	_	_	B-CONST_DIR
to	_	_	O
grow	_	_	O
carrots	_	_	B-VAR
and	_	_	O
beets	_	_	B-VAR
.	_	_	O
He	_	_	O
must	_	_	O
grow	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
3	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
carrots	_	_	B-VAR
and	_	_	O
5	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
beets	_	_	B-VAR
.	_	_	O
Beets	_	_	B-VAR
sell	_	_	B-OBJ_NAME
better	_	_	O
so	_	_	O
he	_	_	O
prefers	_	_	O
to	_	_	O
plant	_	_	O
more	_	_	O
beets	_	_	B-VAR
than	_	_	O
carrots	_	_	B-VAR
.	_	_	O
However	_	_	O
,	_	_	O
due	_	_	O
to	_	_	O
labor	_	_	O
constraints	_	_	O
,	_	_	O
he	_	_	O
can	_	_	O
only	_	_	O
plant	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
2	_	_	B-PARAM
times	_	_	O
the	_	_	O
quantity	_	_	O
of	_	_	O
beets	_	_	B-VAR
as	_	_	O
carrots	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
carrots	_	_	B-VAR
is	_	_	O
$	_	_	O
500	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
beets	_	_	B-VAR
is	_	_	O
$	_	_	O
400	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
farmer	_	_	O
plant	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
cruise	_	_	O
ship	_	_	O
has	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
800	_	_	B-LIMIT
rooms	_	_	O
.	_	_	O
A	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
200	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
single	_	_	B-VAR
room	_	_	I-VAR
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
1200	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
couple	_	_	B-VAR
's	_	_	I-VAR
room	_	_	I-VAR
.	_	_	O
The	_	_	O
cruise	_	_	O
ship	_	_	O
reserves	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
125	_	_	B-LIMIT
rooms	_	_	O
for	_	_	O
single	_	_	B-VAR
rooms	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
twice	_	_	B-PARAM
as	_	_	O
many	_	_	O
passengers	_	_	O
prefer	_	_	O
to	_	_	O
travel	_	_	O
as	_	_	O
a	_	_	O
couple	_	_	O
and	_	_	O
stay	_	_	O
in	_	_	O
a	_	_	O
couple	_	_	B-VAR
's	_	_	I-VAR
room	_	_	I-VAR
than	_	_	O
stay	_	_	O
in	_	_	O
a	_	_	O
single	_	_	B-VAR
's	_	_	I-VAR
room	_	_	I-VAR
.	_	_	O
Determine	_	_	O
how	_	_	O
many	_	_	O
rooms	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
must	_	_	O
be	_	_	O
sold	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
profit	_	_	B-OBJ_NAME
for	_	_	O
the	_	_	O
cruise	_	_	O
ship	_	_	O
.	_	_	O
What	_	_	O
is	_	_	O
the	_	_	O
maximum	_	_	O
profit	_	_	O
?	_	_	O

A	_	_	O
food	_	_	O
truck	_	_	O
sells	_	_	O
tacos	_	_	B-VAR
and	_	_	O
burritos	_	_	B-VAR
.	_	_	O
To	_	_	O
stay	_	_	O
in	_	_	O
business	_	_	O
,	_	_	O
they	_	_	O
must	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
tacos	_	_	B-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
burritos	_	_	B-VAR
.	_	_	O
However	_	_	O
,	_	_	O
they	_	_	O
only	_	_	B-CONST_DIR
have	_	_	O
enough	_	_	O
supplies	_	_	O
to	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
80	_	_	B-LIMIT
tacos	_	_	B-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
50	_	_	B-LIMIT
burritos	_	_	B-VAR
.	_	_	O
Given	_	_	O
their	_	_	O
tight	_	_	O
schedule	_	_	O
,	_	_	O
they	_	_	O
can	_	_	O
also	_	_	O
cook	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
items	_	_	O
total	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
taco	_	_	B-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
burrito	_	_	B-VAR
is	_	_	O
$	_	_	O
6	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
item	_	_	O
should	_	_	O
they	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

You	_	_	O
are	_	_	O
playing	_	_	O
a	_	_	O
game	_	_	O
where	_	_	O
a	_	_	O
short	_	_	B-VAR
shot	_	_	I-VAR
is	_	_	O
worth	_	_	O
2	_	_	B-PARAM
points	_	_	B-OBJ_NAME
and	_	_	O
a	_	_	O
long	_	_	B-VAR
shot	_	_	I-VAR
is	_	_	O
worth	_	_	O
5	_	_	B-PARAM
points	_	_	B-OBJ_NAME
.	_	_	O
In	_	_	O
total	_	_	O
,	_	_	O
you	_	_	O
can	_	_	O
take	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
14	_	_	B-LIMIT
shots	_	_	O
.	_	_	O
You	_	_	O
must	_	_	O
take	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
short	_	_	B-VAR
shots	_	_	I-VAR
and	_	_	O
2	_	_	B-LIMIT
long	_	_	B-VAR
shots	_	_	I-VAR
,	_	_	O
but	_	_	O
time	_	_	O
restricts	_	_	O
taking	_	_	O
more	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
8	_	_	B-LIMIT
of	_	_	O
either	_	_	O
type	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
shot	_	_	O
must	_	_	O
you	_	_	O
take	_	_	O
,	_	_	O
assuming	_	_	O
all	_	_	O
your	_	_	O
shots	_	_	O
get	_	_	O
points	_	_	O
,	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
your	_	_	O
score	_	_	B-OBJ_NAME
?	_	_	O
What	_	_	O
is	_	_	O
your	_	_	O
maximum	_	_	O
score	_	_	O
?	_	_	O

A	_	_	O
hot	_	_	O
dog	_	_	O
store	_	_	O
sells	_	_	O
two	_	_	O
products	_	_	O
:	_	_	O
its	_	_	O
regular	_	_	B-VAR
hot	_	_	I-VAR
-	_	_	I-VAR
dog	_	_	I-VAR
,	_	_	O
and	_	_	O
a	_	_	O
premium	_	_	B-VAR
hot	_	_	I-VAR
-	_	_	I-VAR
dog	_	_	I-VAR
with	_	_	O
more	_	_	O
toppings	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
makes	_	_	O
x1	_	_	O
regular	_	_	B-VAR
hot	_	_	I-VAR
-	_	_	I-VAR
dogs	_	_	I-VAR
a	_	_	O
day	_	_	O
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
3	_	_	B-PARAM
each	_	_	O
and	_	_	O
x2	_	_	O
premium	_	_	B-VAR
hot	_	_	I-VAR
-	_	_	I-VAR
dogs	_	_	I-VAR
a	_	_	O
day	_	_	O
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
5	_	_	B-PARAM
each	_	_	O
.	_	_	O
(	_	_	O
x1	_	_	O
and	_	_	O
x2	_	_	O
are	_	_	O
unknowns	_	_	O
and	_	_	O
they	_	_	O
both	_	_	O
must	_	_	O
be	_	_	O
greater	_	_	O
than	_	_	O
or	_	_	O
equal	_	_	O
to	_	_	O
0	_	_	O
)	_	_	O
.	_	_	O
Currently	_	_	O
,	_	_	O
the	_	_	O
demand	_	_	O
is	_	_	O
limited	_	_	O
to	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
regular	_	_	B-VAR
hot	_	_	I-VAR
-	_	_	I-VAR
dogs	_	_	I-VAR
per	_	_	O
day	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
250	_	_	B-LIMIT
premium	_	_	B-VAR
hot	_	_	I-VAR
-	_	_	I-VAR
dogs	_	_	I-VAR
per	_	_	O
day	_	_	O
.	_	_	O
Also	_	_	O
,	_	_	O
the	_	_	O
store	_	_	O
can	_	_	O
make	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
300	_	_	B-LIMIT
hot	_	_	O
-	_	_	O
dogs	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
hot	_	_	O
-	_	_	O
dog	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

You	_	_	O
have	_	_	O
$	_	_	O
100000	_	_	B-LIMIT
available	_	_	B-CONST_DIR
to	_	_	O
invest	_	_	O
in	_	_	O
either	_	_	O
the	_	_	O
vaccine	_	_	B-VAR
industry	_	_	I-VAR
or	_	_	O
the	_	_	O
meat	_	_	B-VAR
-	_	_	I-VAR
replacement	_	_	I-VAR
industry	_	_	I-VAR
.	_	_	O
Money	_	_	O
placed	_	_	O
in	_	_	O
the	_	_	O
vaccine	_	_	B-VAR
industry	_	_	I-VAR
yields	_	_	O
a	_	_	O
return	_	_	B-OBJ_NAME
of	_	_	O
5	_	_	B-PARAM
%	_	_	I-PARAM
while	_	_	O
money	_	_	O
placed	_	_	O
in	_	_	O
the	_	_	O
meat	_	_	B-VAR
-	_	_	I-VAR
replacement	_	_	I-VAR
industry	_	_	I-VAR
yields	_	_	O
a	_	_	O
return	_	_	B-OBJ_NAME
of	_	_	O
7	_	_	B-PARAM
%	_	_	I-PARAM
.	_	_	O
Due	_	_	O
to	_	_	O
your	_	_	O
strong	_	_	O
belief	_	_	O
in	_	_	O
the	_	_	O
meat	_	_	B-VAR
-	_	_	I-VAR
replacement	_	_	I-VAR
industry	_	_	I-VAR
,	_	_	O
you	_	_	O
decide	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
60	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
your	_	_	O
investment	_	_	O
be	_	_	O
placed	_	_	O
in	_	_	O
the	_	_	O
meat	_	_	B-VAR
-	_	_	I-VAR
replacement	_	_	I-VAR
industry	_	_	I-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
your	_	_	O
investment	_	_	O
can	_	_	O
be	_	_	O
in	_	_	O
the	_	_	O
vaccine	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
How	_	_	O
much	_	_	O
should	_	_	O
you	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
your	_	_	O
return	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
toy	_	_	O
company	_	_	O
makes	_	_	O
stuffed	_	_	B-VAR
beavers	_	_	I-VAR
and	_	_	O
stuffed	_	_	B-VAR
bears	_	_	I-VAR
.	_	_	O
Each	_	_	O
beaver	_	_	B-VAR
takes	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
make	_	_	O
and	_	_	O
each	_	_	O
bear	_	_	B-VAR
takes	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
make	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
2000	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
to	_	_	O
make	_	_	O
both	_	_	O
stuffer	_	_	O
animals	_	_	O
.	_	_	O
Due	_	_	O
to	_	_	O
the	_	_	O
popularity	_	_	O
of	_	_	O
beavers	_	_	B-VAR
,	_	_	O
the	_	_	O
company	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
beavers	_	_	B-VAR
as	_	_	O
bears	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
beaver	_	_	B-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
bear	_	_	B-VAR
is	_	_	O
$	_	_	O
7	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
dentist	_	_	O
can	_	_	O
invest	_	_	O
up	_	_	B-CONST_DIR
to	_	_	I-CONST_DIR
$	_	_	O
5000	_	_	B-LIMIT
in	_	_	O
two	_	_	O
toothpaste	_	_	O
companies	_	_	O
.	_	_	O
Each	_	_	O
dollar	_	_	O
invested	_	_	O
in	_	_	O
toothpaste	_	_	O
company	_	_	B-VAR
A	_	_	I-VAR
yields	_	_	O
a	_	_	O
$	_	_	O
0.12	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
.	_	_	O
Each	_	_	O
dollar	_	_	O
invested	_	_	O
in	_	_	O
toothpaste	_	_	O
company	_	_	B-VAR
B	_	_	I-VAR
yields	_	_	O
a	_	_	O
$	_	_	O
0.14	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
.	_	_	O
He	_	_	O
wants	_	_	O
to	_	_	O
invest	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
40	_	_	B-LIMIT
%	_	_	I-LIMIT
in	_	_	O
toothpaste	_	_	O
company	_	_	B-VAR
A	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
$	_	_	O
1000	_	_	B-LIMIT
in	_	_	O
toothpaste	_	_	O
company	_	_	B-VAR
B.	_	_	I-VAR
How	_	_	O
much	_	_	O
money	_	_	O
should	_	_	O
he	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

There	_	_	O
is	_	_	O
only	_	_	O
2000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
coffee	_	_	O
available	_	_	B-CONST_DIR
to	_	_	O
make	_	_	O
small	_	_	B-VAR
and	_	_	O
large	_	_	B-VAR
coffee	_	_	I-VAR
pods	_	_	I-VAR
.	_	_	O
Each	_	_	O
small	_	_	B-VAR
coffee	_	_	I-VAR
pod	_	_	I-VAR
requires	_	_	O
15	_	_	B-PARAM
grams	_	_	O
of	_	_	O
coffee	_	_	O
while	_	_	O
each	_	_	O
large	_	_	B-VAR
coffee	_	_	I-VAR
pod	_	_	I-VAR
requires	_	_	O
20	_	_	B-PARAM
grams	_	_	O
of	_	_	O
coffee	_	_	O
.	_	_	O
Due	_	_	O
to	_	_	O
the	_	_	O
high	_	_	O
caffeine	_	_	O
content	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
4	_	_	B-PARAM
times	_	_	O
the	_	_	O
amount	_	_	O
of	_	_	O
small	_	_	B-VAR
coffee	_	_	I-VAR
pods	_	_	I-VAR
are	_	_	O
needed	_	_	O
than	_	_	O
large	_	_	B-VAR
coffee	_	_	I-VAR
pods	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
large	_	_	B-VAR
coffee	_	_	I-VAR
pods	_	_	I-VAR
need	_	_	O
to	_	_	O
be	_	_	O
made	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
small	_	_	B-VAR
coffee	_	_	I-VAR
pod	_	_	I-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
large	_	_	B-VAR
coffee	_	_	I-VAR
pod	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
sports	_	_	O
warehouse	_	_	O
stocks	_	_	O
hockey	_	_	B-VAR
nets	_	_	I-VAR
and	_	_	O
basketball	_	_	B-VAR
hoops	_	_	I-VAR
.	_	_	O
Each	_	_	O
hockey	_	_	B-VAR
net	_	_	I-VAR
takes	_	_	O
5	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
of	_	_	O
space	_	_	O
while	_	_	O
each	_	_	O
basketball	_	_	B-VAR
hoop	_	_	I-VAR
takes	_	_	O
3	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
of	_	_	O
space	_	_	O
.	_	_	O
The	_	_	O
warehouse	_	_	O
has	_	_	O
300	_	_	B-LIMIT
sq	_	_	O
ft	_	_	O
of	_	_	O
space	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
The	_	_	O
warehouse	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
10000	_	_	B-LIMIT
with	_	_	O
each	_	_	O
hockey	_	_	B-VAR
net	_	_	I-VAR
costing	_	_	O
$	_	_	O
100	_	_	B-PARAM
and	_	_	O
each	_	_	O
basketball	_	_	B-VAR
hoop	_	_	I-VAR
costing	_	_	O
$	_	_	O
150	_	_	B-PARAM
.	_	_	O
With	_	_	O
hockey	_	_	O
being	_	_	O
much	_	_	O
more	_	_	O
popular	_	_	O
in	_	_	O
the	_	_	O
area	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
65	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
all	_	_	O
items	_	_	O
in	_	_	O
stock	_	_	O
must	_	_	O
be	_	_	O
hockey	_	_	B-VAR
nets	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
hockey	_	_	B-VAR
net	_	_	I-VAR
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
basketball	_	_	B-VAR
hoop	_	_	I-VAR
is	_	_	O
$	_	_	O
75	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
bought	_	_	O
and	_	_	O
sold	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
camera	_	_	O
store	_	_	O
can	_	_	O
spend	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
10000	_	_	B-PARAM
on	_	_	O
camera	_	_	O
equipment	_	_	O
.	_	_	O
Each	_	_	O
lens	_	_	B-VAR
costs	_	_	O
$	_	_	O
400	_	_	B-PARAM
and	_	_	O
each	_	_	O
tripod	_	_	B-VAR
costs	_	_	O
$	_	_	O
300	_	_	B-PARAM
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
lens	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
tripod	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
150	_	_	B-PARAM
.	_	_	O
The	_	_	O
store	_	_	O
owner	_	_	O
estimates	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
lenses	_	_	B-VAR
but	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
25	_	_	B-LIMIT
are	_	_	O
sold	_	_	O
each	_	_	O
month	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
tripods	_	_	B-VAR
sold	_	_	O
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
a	_	_	O
third	_	_	B-PARAM
of	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
lenses	_	_	B-VAR
sold	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
store	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
company	_	_	O
decides	_	_	O
to	_	_	O
promote	_	_	O
their	_	_	O
product	_	_	O
by	_	_	O
buying	_	_	O
ad	_	_	O
space	_	_	O
on	_	_	O
taxis	_	_	B-VAR
,	_	_	O
buses	_	_	B-VAR
,	_	_	O
and	_	_	O
privately	_	_	B-VAR
owned	_	_	I-VAR
cars	_	_	I-VAR
.	_	_	O
The	_	_	O
cost	_	_	O
of	_	_	O
an	_	_	O
ad	_	_	O
as	_	_	O
well	_	_	O
as	_	_	O
the	_	_	O
expected	_	_	O
viewership	_	_	O
is	_	_	O
given	_	_	O
as	_	_	O
follows	_	_	O
.	_	_	O
An	_	_	O
ad	_	_	O
on	_	_	O
a	_	_	O
taxi	_	_	B-VAR
costs	_	_	O
$	_	_	O
500	_	_	B-PARAM
and	_	_	O
reaches	_	_	O
5000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
An	_	_	O
ad	_	_	O
on	_	_	O
a	_	_	O
bus	_	_	B-VAR
costs	_	_	O
$	_	_	O
1000	_	_	B-PARAM
and	_	_	O
reaches	_	_	O
12000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
Finally	_	_	O
an	_	_	O
ad	_	_	O
on	_	_	O
a	_	_	O
privately	_	_	B-VAR
owned	_	_	I-VAR
car	_	_	I-VAR
cost	_	_	O
$	_	_	O
300	_	_	B-PARAM
and	_	_	O
reaches	_	_	O
2000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
bus	_	_	B-VAR
company	_	_	O
limits	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
ads	_	_	O
from	_	_	O
a	_	_	O
single	_	_	O
company	_	_	O
to	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
8	_	_	B-LIMIT
.	_	_	O
In	_	_	O
addition	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
ads	_	_	O
should	_	_	O
be	_	_	O
on	_	_	O
taxis	_	_	B-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
ads	_	_	O
should	_	_	O
be	_	_	O
on	_	_	O
privately	_	_	O
owned	_	_	O
cars	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
company	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
20000	_	_	B-LIMIT
,	_	_	O
how	_	_	O
many	_	_	O
ads	_	_	O
should	_	_	O
be	_	_	O
bought	_	_	O
for	_	_	O
each	_	_	O
option	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
viewership	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
businessman	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
50000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
two	_	_	O
farms	_	_	O
,	_	_	O
Bob	_	_	B-VAR
's	_	_	I-VAR
farm	_	_	I-VAR
and	_	_	O
Joe	_	_	B-VAR
's	_	_	I-VAR
farm	_	_	I-VAR
.	_	_	O
Because	_	_	O
Bob	_	_	O
has	_	_	O
more	_	_	O
experience	_	_	O
,	_	_	O
he	_	_	O
has	_	_	O
decided	_	_	O
to	_	_	O
invest	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	O
as	_	_	O
much	_	_	O
money	_	_	O
in	_	_	O
Bob	_	_	B-VAR
's	_	_	I-VAR
farm	_	_	I-VAR
than	_	_	O
in	_	_	O
Joe	_	_	B-VAR
's	_	_	I-VAR
farm	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
Bob	_	_	B-VAR
's	_	_	I-VAR
farm	_	_	I-VAR
can	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
40000	_	_	B-LIMIT
.	_	_	O
If	_	_	O
investments	_	_	O
in	_	_	O
Bob	_	_	B-VAR
's	_	_	I-VAR
farm	_	_	I-VAR
earn	_	_	B-OBJ_NAME
8	_	_	B-PARAM
%	_	_	I-PARAM
and	_	_	O
investments	_	_	O
in	_	_	O
Joe	_	_	B-VAR
's	_	_	I-VAR
farm	_	_	I-VAR
earn	_	_	B-OBJ_NAME
6	_	_	B-PARAM
%	_	_	I-PARAM
,	_	_	O
how	_	_	O
much	_	_	O
money	_	_	O
should	_	_	O
he	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
earnings	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
bus	_	_	O
has	_	_	B-CONST_DIR
150	_	_	B-LIMIT
seats	_	_	O
.	_	_	O
A	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
30	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
cushioned	_	_	B-VAR
seat	_	_	I-VAR
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
10	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
regular	_	_	B-VAR
seat	_	_	I-VAR
.	_	_	O
The	_	_	O
bus	_	_	O
reserves	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
seats	_	_	O
to	_	_	O
be	_	_	O
cushioned	_	_	B-VAR
but	_	_	O
because	_	_	O
the	_	_	O
journey	_	_	O
is	_	_	O
short	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
2	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
people	_	_	O
prefer	_	_	O
to	_	_	O
save	_	_	O
money	_	_	O
and	_	_	O
travel	_	_	O
by	_	_	O
regular	_	_	B-VAR
seats	_	_	I-VAR
than	_	_	O
cushioned	_	_	B-VAR
seats	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
seat	_	_	O
type	_	_	O
should	_	_	O
be	_	_	O
sold	_	_	O
to	_	_	O
passengers	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
gift	_	_	O
store	_	_	O
has	_	_	O
to	_	_	O
send	_	_	O
out	_	_	O
their	_	_	O
gifts	_	_	O
.	_	_	O
They	_	_	O
can	_	_	O
send	_	_	O
the	_	_	O
gifts	_	_	O
using	_	_	O
the	_	_	O
postal	_	_	B-VAR
service	_	_	I-VAR
which	_	_	O
can	_	_	O
take	_	_	O
100	_	_	B-PARAM
gifts	_	_	B-OBJ_NAME
per	_	_	O
pickup	_	_	O
or	_	_	O
by	_	_	O
hiring	_	_	O
vans	_	_	B-VAR
which	_	_	O
can	_	_	O
take	_	_	O
80	_	_	B-PARAM
gifts	_	_	B-OBJ_NAME
each	_	_	O
.	_	_	O
The	_	_	O
cost	_	_	O
per	_	_	O
pickup	_	_	O
from	_	_	O
the	_	_	O
postal	_	_	B-VAR
office	_	_	I-VAR
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	O
per	_	_	O
van	_	_	B-VAR
is	_	_	O
$	_	_	O
40	_	_	B-PARAM
.	_	_	O
In	_	_	O
addition	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
vans	_	_	B-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
postal	_	_	B-VAR
service	_	_	I-VAR
pickups	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
store	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
1000	_	_	B-LIMIT
,	_	_	O
how	_	_	O
should	_	_	O
they	_	_	O
spend	_	_	O
their	_	_	O
money	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
gifts	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
sent	_	_	O
?	_	_	O

An	_	_	O
engineering	_	_	O
company	_	_	O
has	_	_	O
new	_	_	B-VAR
grad	_	_	I-VAR
engineers	_	_	I-VAR
earning	_	_	B-OBJ_NAME
$	_	_	O
1000	_	_	B-PARAM
a	_	_	O
week	_	_	O
and	_	_	O
senior	_	_	B-VAR
engineers	_	_	I-VAR
earning	_	_	B-OBJ_NAME
$	_	_	O
3000	_	_	B-PARAM
a	_	_	O
week	_	_	O
.	_	_	O
The	_	_	O
weekly	_	_	O
wage	_	_	O
bill	_	_	O
must	_	_	O
be	_	_	O
kept	_	_	O
below	_	_	B-CONST_DIR
$	_	_	O
100000	_	_	B-LIMIT
.	_	_	O
The	_	_	O
projects	_	_	O
require	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
50	_	_	B-LIMIT
engineers	_	_	O
of	_	_	O
whom	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
must	_	_	O
be	_	_	O
senior	_	_	B-VAR
engineers	_	_	I-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
senior	_	_	B-VAR
engineers	_	_	I-VAR
should	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
a	_	_	O
third	_	_	B-PARAM
the	_	_	O
number	_	_	O
of	_	_	O
new	_	_	B-VAR
grad	_	_	I-VAR
engineers	_	_	I-VAR
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	B-OBJ_NAME
wage	_	_	I-OBJ_NAME
bill	_	_	I-OBJ_NAME
.	_	_	O

A	_	_	O
man	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
1000000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
four	_	_	O
industries	_	_	O
.	_	_	O
He	_	_	O
can	_	_	O
invest	_	_	O
in	_	_	O
the	_	_	O
biotech	_	_	B-VAR
industry	_	_	I-VAR
,	_	_	O
food	_	_	B-VAR
industry	_	_	I-VAR
,	_	_	O
finance	_	_	B-VAR
industry	_	_	I-VAR
,	_	_	O
and	_	_	O
health	_	_	B-VAR
care	_	_	I-VAR
industry	_	_	O
.	_	_	O
The	_	_	O
return	_	_	B-OBJ_NAME
on	_	_	O
investment	_	_	O
for	_	_	O
each	_	_	O
of	_	_	O
the	_	_	O
industries	_	_	O
is	_	_	O
as	_	_	O
follows	_	_	O
:	_	_	O
biotech	_	_	B-VAR
,	_	_	O
4	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
food	_	_	B-VAR
,	_	_	O
6	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
finance	_	_	B-VAR
,	_	_	O
8	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
and	_	_	O
health	_	_	B-VAR
care	_	_	I-VAR
10	_	_	B-PARAM
%	_	_	I-PARAM
.	_	_	O
To	_	_	O
be	_	_	O
safe	_	_	O
,	_	_	O
he	_	_	O
wants	_	_	O
to	_	_	O
make	_	_	O
sure	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
health	_	_	B-VAR
care	_	_	I-VAR
industry	_	_	O
does	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
biotech	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
Also	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
food	_	_	B-VAR
industry	_	_	I-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
finance	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
Lastly	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
investment	_	_	O
can	_	_	O
be	_	_	O
in	_	_	O
the	_	_	O
health	_	_	B-VAR
care	_	_	I-VAR
industry	_	_	O
.	_	_	O
How	_	_	O
much	_	_	O
should	_	_	O
he	_	_	O
invested	_	_	O
in	_	_	O
each	_	_	O
industry	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
returns	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
farmer	_	_	O
has	_	_	B-CONST_DIR
50	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
to	_	_	O
grow	_	_	O
oats	_	_	B-VAR
and	_	_	O
flaxseed	_	_	B-VAR
.	_	_	I-VAR
He	_	_	O
must	_	_	O
grow	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
oats	_	_	B-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
8	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
flaxseed	_	_	B-VAR
.	_	_	I-VAR
Although	_	_	O
oats	_	_	B-VAR
are	_	_	O
easier	_	_	O
to	_	_	O
grow	_	_	O
,	_	_	O
he	_	_	O
can	_	_	O
only	_	_	O
grow	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
2	_	_	B-PARAM
times	_	_	O
the	_	_	O
amount	_	_	O
of	_	_	O
oats	_	_	B-VAR
as	_	_	O
flaxseed	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
oats	_	_	B-VAR
is	_	_	O
$	_	_	O
500	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
flaxseed	_	_	B-VAR
is	_	_	O
$	_	_	O
400	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
grow	_	_	O
to	_	_	O
make	_	_	O
maximum	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

In	_	_	O
a	_	_	O
cold	_	_	O
region	_	_	O
,	_	_	O
a	_	_	O
train	_	_	O
service	_	_	O
offers	_	_	O
heated	_	_	B-VAR
seats	_	_	I-VAR
and	_	_	O
regular	_	_	B-VAR
seats	_	_	I-VAR
.	_	_	O
The	_	_	O
train	_	_	O
has	_	_	O
100	_	_	B-LIMIT
seats	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
The	_	_	O
trains	_	_	O
reserves	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
15	_	_	B-LIMIT
seats	_	_	O
to	_	_	O
be	_	_	O
heated	_	_	B-VAR
.	_	_	O
However	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
people	_	_	O
prefer	_	_	O
regular	_	_	B-VAR
seats	_	_	I-VAR
to	_	_	O
heated	_	_	B-VAR
seats	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
heated	_	_	B-VAR
seat	_	_	I-VAR
is	_	_	O
$	_	_	O
20	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
regular	_	_	B-VAR
seat	_	_	I-VAR
is	_	_	O
$	_	_	O
15	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
seat	_	_	O
type	_	_	O
should	_	_	O
be	_	_	O
sold	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
stationary	_	_	O
company	_	_	O
sells	_	_	O
one	_	_	B-VAR
-	_	_	I-VAR
inch	_	_	I-VAR
and	_	_	O
two	_	_	B-VAR
-	_	_	I-VAR
inch	_	_	I-VAR
binders	_	_	O
.	_	_	O
To	_	_	O
meet	_	_	O
demand	_	_	O
,	_	_	O
the	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
60	_	_	B-LIMIT
one	_	_	B-VAR
-	_	_	I-VAR
inch	_	_	I-VAR
binders	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
70	_	_	B-LIMIT
two	_	_	B-VAR
-	_	_	I-VAR
inch	_	_	I-VAR
binders	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
they	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
150	_	_	B-LIMIT
one	_	_	B-VAR
-	_	_	I-VAR
inch	_	_	I-VAR
binders	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
160	_	_	B-LIMIT
two	_	_	B-VAR
-	_	_	I-VAR
inch	_	_	I-VAR
binders	_	_	I-VAR
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
a	_	_	O
contract	_	_	O
with	_	_	O
a	_	_	O
school	_	_	O
to	_	_	O
send	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
200	_	_	B-LIMIT
binders	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
one	_	_	B-VAR
-	_	_	I-VAR
inch	_	_	I-VAR
binder	_	_	I-VAR
is	_	_	O
$	_	_	O
1	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
two	_	_	B-VAR
-	_	_	I-VAR
inch	_	_	I-VAR
binder	_	_	I-VAR
is	_	_	O
$	_	_	O
2	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
ice	_	_	O
cream	_	_	O
bar	_	_	O
sells	_	_	O
chocolate	_	_	B-VAR
and	_	_	O
vanilla	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
cones	_	_	O
.	_	_	O
They	_	_	O
must	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
chocolate	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
cones	_	_	I-VAR
but	_	_	O
can	_	_	O
not	_	_	O
sell	_	_	O
more	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
50	_	_	B-LIMIT
.	_	_	O
They	_	_	O
must	_	_	O
also	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
vanilla	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
cones	_	_	I-VAR
but	_	_	O
can	_	_	O
not	_	_	O
sell	_	_	O
more	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
60	_	_	B-LIMIT
.	_	_	O
In	_	_	O
total	_	_	O
,	_	_	O
they	_	_	O
only	_	_	B-CONST_DIR
have	_	_	O
enough	_	_	O
cones	_	_	O
to	_	_	O
sell	_	_	O
70	_	_	B-LIMIT
items	_	_	O
total	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
chocolate	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
cone	_	_	I-VAR
is	_	_	O
$	_	_	O
2	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
vanilla	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
cone	_	_	I-VAR
is	_	_	O
$	_	_	O
1.50	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

In	_	_	O
a	_	_	O
video	_	_	O
game	_	_	O
,	_	_	O
you	_	_	O
can	_	_	O
solve	_	_	O
easy	_	_	B-VAR
puzzles	_	_	I-VAR
worth	_	_	O
5	_	_	B-PARAM
points	_	_	B-OBJ_NAME
or	_	_	O
hard	_	_	B-VAR
puzzles	_	_	I-VAR
worth	_	_	O
8	_	_	B-PARAM
points	_	_	B-OBJ_NAME
.	_	_	O
You	_	_	O
have	_	_	O
to	_	_	O
solve	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-LIMIT
easy	_	_	B-VAR
puzzles	_	_	I-VAR
and	_	_	O
1	_	_	B-LIMIT
hard	_	_	B-VAR
puzzle	_	_	I-VAR
.	_	_	O
Due	_	_	O
to	_	_	O
time	_	_	O
restrictions	_	_	O
,	_	_	O
you	_	_	O
can	_	_	O
solve	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
10	_	_	B-LIMIT
easy	_	_	B-VAR
puzzles	_	_	I-VAR
and	_	_	O
5	_	_	B-LIMIT
hard	_	_	B-VAR
puzzles	_	_	I-VAR
.	_	_	O
In	_	_	O
total	_	_	O
,	_	_	O
you	_	_	O
can	_	_	O
only	_	_	O
solve	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
10	_	_	B-LIMIT
puzzles	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
puzzle	_	_	O
type	_	_	O
should	_	_	O
you	_	_	O
solve	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
your	_	_	O
points	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
office	_	_	O
chair	_	_	O
company	_	_	O
makes	_	_	O
leather	_	_	B-VAR
and	_	_	O
mesh	_	_	B-VAR
chairs	_	_	I-VAR
.	_	_	O
Two	_	_	O
different	_	_	O
teams	_	_	O
make	_	_	O
the	_	_	O
chairs	_	_	O
.	_	_	O
Team	_	_	O
A	_	_	O
who	_	_	O
make	_	_	O
the	_	_	O
leather	_	_	B-VAR
chairs	_	_	I-VAR
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
20	_	_	B-LIMIT
a	_	_	O
day	_	_	O
.	_	_	O
Team	_	_	O
B	_	_	O
who	_	_	O
make	_	_	O
the	_	_	O
mesh	_	_	B-VAR
chairs	_	_	I-VAR
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
a	_	_	O
day	_	_	O
.	_	_	O
Both	_	_	O
chairs	_	_	O
have	_	_	O
to	_	_	O
be	_	_	O
quality	_	_	O
checked	_	_	O
by	_	_	O
another	_	_	O
team	_	_	O
,	_	_	O
and	_	_	O
this	_	_	O
team	_	_	O
can	_	_	O
quality	_	_	O
check	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
chairs	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
leather	_	_	B-VAR
chair	_	_	I-VAR
is	_	_	O
$	_	_	O
150	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
mesh	_	_	B-VAR
chair	_	_	I-VAR
is	_	_	O
$	_	_	O
100	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
hot	_	_	O
dog	_	_	O
stand	_	_	O
sells	_	_	O
regular	_	_	B-VAR
hot	_	_	I-VAR
dogs	_	_	I-VAR
and	_	_	O
premium	_	_	B-VAR
hot	_	_	I-VAR
dogs	_	_	I-VAR
with	_	_	O
extra	_	_	O
toppings	_	_	O
.	_	_	O
The	_	_	O
stand	_	_	O
makes	_	_	O
x1	_	_	O
regular	_	_	B-VAR
hot	_	_	I-VAR
dogs	_	_	I-VAR
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
3	_	_	B-PARAM
each	_	_	O
and	_	_	O
x2	_	_	O
premium	_	_	B-VAR
hot	_	_	I-VAR
dogs	_	_	I-VAR
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
5	_	_	B-PARAM
each	_	_	O
(	_	_	O
x1	_	_	O
and	_	_	O
x2	_	_	O
are	_	_	O
unknown	_	_	O
variables	_	_	O
both	_	_	O
greater	_	_	O
than	_	_	O
or	_	_	O
equal	_	_	O
to	_	_	O
0	_	_	O
)	_	_	O
.	_	_	O
There	_	_	O
is	_	_	O
a	_	_	O
demand	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
80	_	_	B-LIMIT
regular	_	_	B-VAR
hot	_	_	I-VAR
dogs	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
70	_	_	B-LIMIT
premium	_	_	B-VAR
hot	_	_	I-VAR
dogs	_	_	I-VAR
.	_	_	O
The	_	_	O
stand	_	_	O
only	_	_	O
has	_	_	O
enough	_	_	O
supplies	_	_	O
to	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
120	_	_	B-LIMIT
hot	_	_	O
-	_	_	O
dogs	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
hot	_	_	O
-	_	_	O
dog	_	_	O
should	_	_	O
the	_	_	O
stand	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
woman	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
300000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
two	_	_	O
health	_	_	O
food	_	_	O
industries	_	_	O
.	_	_	O
She	_	_	O
decides	_	_	O
to	_	_	O
invest	_	_	O
in	_	_	O
the	_	_	O
avocado	_	_	B-VAR
industry	_	_	I-VAR
and	_	_	O
kale	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
Money	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
avocado	_	_	B-VAR
industry	_	_	I-VAR
yields	_	_	O
a	_	_	O
return	_	_	B-OBJ_NAME
of	_	_	O
5	_	_	B-PARAM
%	_	_	I-PARAM
while	_	_	O
money	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
kale	_	_	B-VAR
industry	_	_	I-VAR
yields	_	_	O
a	_	_	O
return	_	_	B-OBJ_NAME
of	_	_	O
8	_	_	B-PARAM
%	_	_	I-PARAM
.	_	_	O
She	_	_	O
has	_	_	O
been	_	_	O
advised	_	_	O
to	_	_	O
invest	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
money	_	_	O
in	_	_	O
the	_	_	O
avocado	_	_	B-VAR
industry	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
60	_	_	B-LIMIT
%	_	_	I-LIMIT
in	_	_	O
the	_	_	O
kale	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
How	_	_	O
much	_	_	O
should	_	_	O
she	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
her	_	_	O
return	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
toy	_	_	O
store	_	_	O
sells	_	_	O
hand	_	_	O
made	_	_	O
wooden	_	_	O
trains	_	_	B-VAR
and	_	_	O
planes	_	_	B-VAR
.	_	_	O
Each	_	_	O
train	_	_	B-VAR
takes	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
woodworker	_	_	O
time	_	_	O
and	_	_	O
each	_	_	O
plane	_	_	B-VAR
takes	_	_	O
40	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
woodworker	_	_	O
time	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
4000	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
woodworker	_	_	O
time	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
Since	_	_	O
planes	_	_	B-VAR
are	_	_	O
most	_	_	O
popular	_	_	O
,	_	_	O
the	_	_	O
store	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
thrice	_	_	B-PARAM
the	_	_	O
number	_	_	O
of	_	_	O
planes	_	_	B-VAR
as	_	_	O
trains	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
train	_	_	B-VAR
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
plane	_	_	B-VAR
is	_	_	O
$	_	_	O
60	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
woman	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
5000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
her	_	_	O
sisters	_	_	O
'	_	_	O
companies	_	_	O
.	_	_	O
She	_	_	O
can	_	_	O
invest	_	_	O
in	_	_	O
her	_	_	O
younger	_	_	B-VAR
sister	_	_	I-VAR
's	_	_	O
company	_	_	O
and	_	_	O
her	_	_	O
elder	_	_	B-VAR
sister	_	_	I-VAR
's	_	_	O
company	_	_	O
.	_	_	O
Each	_	_	O
dollar	_	_	O
invested	_	_	O
in	_	_	O
her	_	_	O
younger	_	_	B-VAR
sister	_	_	I-VAR
's	_	_	O
company	_	_	O
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
0.05	_	_	B-PARAM
while	_	_	O
each	_	_	O
dollar	_	_	O
invested	_	_	O
in	_	_	O
her	_	_	O
elder	_	_	B-VAR
sister	_	_	I-VAR
's	_	_	O
company	_	_	O
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
0.08	_	_	B-PARAM
.	_	_	O
She	_	_	O
wants	_	_	O
to	_	_	O
invest	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
40	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
her	_	_	O
investment	_	_	O
into	_	_	O
her	_	_	O
younger	_	_	B-VAR
sister	_	_	I-VAR
's	_	_	O
company	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
$	_	_	O
2000	_	_	B-LIMIT
in	_	_	O
her	_	_	O
elder	_	_	B-VAR
sister	_	_	I-VAR
's	_	_	O
company	_	_	O
.	_	_	O
How	_	_	O
much	_	_	O
money	_	_	O
should	_	_	O
she	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
her	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
jeweler	_	_	O
has	_	_	B-CONST_DIR
1000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
gold	_	_	O
to	_	_	O
make	_	_	O
rings	_	_	B-VAR
and	_	_	O
necklaces	_	_	B-VAR
.	_	_	O
Each	_	_	O
ring	_	_	B-VAR
needs	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
gold	_	_	O
and	_	_	O
each	_	_	O
necklace	_	_	B-VAR
needs	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
gold	_	_	O
.	_	_	O
Due	_	_	O
to	_	_	O
popularity	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
rings	_	_	B-VAR
are	_	_	O
needed	_	_	O
than	_	_	O
necklaces	_	_	B-VAR
and	_	_	O
there	_	_	O
needs	_	_	O
to	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
necklaces	_	_	B-VAR
made	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
ring	_	_	B-VAR
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
necklace	_	_	B-VAR
is	_	_	O
$	_	_	O
75	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
instrument	_	_	O
store	_	_	O
sells	_	_	O
pianos	_	_	B-VAR
and	_	_	O
guitars	_	_	B-VAR
.	_	_	O
A	_	_	O
piano	_	_	B-VAR
takes	_	_	O
8	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
of	_	_	O
space	_	_	O
while	_	_	O
a	_	_	O
guitar	_	_	B-VAR
takes	_	_	O
3	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
of	_	_	O
space	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
100	_	_	B-LIMIT
sq	_	_	O
ft	_	_	O
of	_	_	O
space	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
A	_	_	O
piano	_	_	B-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
500	_	_	B-PARAM
and	_	_	O
a	_	_	O
guitar	_	_	B-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
300	_	_	B-PARAM
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
8000	_	_	B-LIMIT
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
items	_	_	O
in	_	_	O
stock	_	_	O
must	_	_	O
be	_	_	O
guitars	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
piano	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
300	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
guitar	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
store	_	_	O
stock	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
winter	_	_	O
sports	_	_	O
store	_	_	O
sells	_	_	O
skis	_	_	B-VAR
and	_	_	O
snowboards	_	_	B-VAR
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
20000	_	_	B-LIMIT
.	_	_	O
Each	_	_	O
pair	_	_	O
of	_	_	O
skis	_	_	B-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
500	_	_	B-PARAM
and	_	_	O
each	_	_	O
snowboard	_	_	B-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
400	_	_	B-PARAM
.	_	_	O
Each	_	_	O
pair	_	_	O
of	_	_	O
skis	_	_	B-VAR
is	_	_	O
then	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
200	_	_	B-PARAM
while	_	_	O
each	_	_	O
snowboard	_	_	B-VAR
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
175	_	_	B-PARAM
.	_	_	O
The	_	_	O
owner	_	_	O
estimates	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
but	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
pairs	_	_	O
of	_	_	O
skis	_	_	B-VAR
will	_	_	O
be	_	_	O
sold	_	_	O
.	_	_	O
The	_	_	O
number	_	_	O
of	_	_	O
snowboards	_	_	B-VAR
sold	_	_	O
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
a	_	_	O
half	_	_	B-PARAM
the	_	_	O
number	_	_	O
of	_	_	O
skis	_	_	B-VAR
sold	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
pairs	_	_	O
of	_	_	O
skis	_	_	B-VAR
and	_	_	O
snowboards	_	_	B-VAR
should	_	_	O
the	_	_	O
store	_	_	O
buy	_	_	O
and	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
company	_	_	O
is	_	_	O
looking	_	_	O
too	_	_	O
purchase	_	_	O
ads	_	_	O
in	_	_	O
three	_	_	O
locations	_	_	O
:	_	_	O
airports	_	_	B-VAR
,	_	_	O
malls	_	_	B-VAR
,	_	_	O
and	_	_	O
movie	_	_	B-VAR
theatres	_	_	I-VAR
.	_	_	O
The	_	_	O
cost	_	_	O
of	_	_	O
placing	_	_	O
an	_	_	O
ad	_	_	O
at	_	_	O
each	_	_	O
location	_	_	O
and	_	_	O
the	_	_	O
expected	_	_	O
viewership	_	_	O
is	_	_	O
given	_	_	O
as	_	_	O
follows	_	_	O
.	_	_	O
Each	_	_	O
ad	_	_	O
placed	_	_	O
in	_	_	O
an	_	_	O
airport	_	_	B-VAR
costs	_	_	O
$	_	_	O
10000	_	_	B-PARAM
and	_	_	O
reaches	_	_	O
100000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
Each	_	_	O
ad	_	_	O
places	_	_	O
in	_	_	O
a	_	_	O
mall	_	_	B-VAR
costs	_	_	O
$	_	_	O
3000	_	_	B-PARAM
and	_	_	O
reaches	_	_	O
40000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
Finally	_	_	O
each	_	_	O
ad	_	_	O
places	_	_	O
in	_	_	O
a	_	_	O
movie	_	_	B-VAR
theatre	_	_	I-VAR
costs	_	_	O
$	_	_	O
2000	_	_	B-PARAM
and	_	_	O
reaches	_	_	O
10000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
airport	_	_	B-VAR
authority	_	_	O
limits	_	_	B-CONST_DIR
the	_	_	I-CONST_DIR
number	_	_	I-CONST_DIR
of	_	_	O
ads	_	_	O
from	_	_	O
a	_	_	O
single	_	_	O
company	_	_	O
to	_	_	O
5	_	_	B-LIMIT
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
half	_	_	B-LIMIT
the	_	_	O
number	_	_	O
of	_	_	O
ads	_	_	O
should	_	_	O
be	_	_	O
at	_	_	O
movie	_	_	B-VAR
theatres	_	_	I-VAR
,	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
ads	_	_	O
should	_	_	O
be	_	_	O
at	_	_	O
malls	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
company	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
100000	_	_	B-LIMIT
,	_	_	O
how	_	_	O
many	_	_	O
ads	_	_	O
should	_	_	O
they	_	_	O
place	_	_	O
in	_	_	O
each	_	_	O
location	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
viewership	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
movie	_	_	O
producer	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
500000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
two	_	_	O
movies	_	_	O
,	_	_	O
an	_	_	O
action	_	_	B-VAR
movie	_	_	I-VAR
and	_	_	O
an	_	_	O
animation	_	_	B-VAR
.	_	_	O
She	_	_	O
has	_	_	O
decided	_	_	O
to	_	_	O
invest	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	O
as	_	_	O
much	_	_	O
money	_	_	O
in	_	_	O
the	_	_	O
animation	_	_	B-VAR
movie	_	_	I-VAR
than	_	_	O
in	_	_	O
the	_	_	O
action	_	_	B-VAR
movie	_	_	I-VAR
.	_	_	O
However	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
animation	_	_	B-VAR
movie	_	_	I-VAR
can	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
400000	_	_	B-LIMIT
.	_	_	O
If	_	_	O
the	_	_	O
money	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
action	_	_	B-VAR
movie	_	_	I-VAR
earns	_	_	B-OBJ_NAME
9	_	_	B-PARAM
%	_	_	I-PARAM
and	_	_	O
the	_	_	O
money	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
animation	_	_	B-VAR
movie	_	_	I-VAR
earns	_	_	B-OBJ_NAME
6	_	_	B-PARAM
%	_	_	I-PARAM
.	_	_	O
How	_	_	O
much	_	_	O
money	_	_	O
should	_	_	O
she	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
her	_	_	O
earnings	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
amusement	_	_	O
park	_	_	O
sells	_	_	O
regular	_	_	B-VAR
tickets	_	_	I-VAR
and	_	_	O
premium	_	_	B-VAR
tickets	_	_	I-VAR
,	_	_	O
which	_	_	O
allow	_	_	O
you	_	_	O
to	_	_	O
skip	_	_	O
lines	_	_	O
.	_	_	O
The	_	_	O
amusement	_	_	O
park	_	_	O
can	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
1000	_	_	B-LIMIT
tickets	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
regular	_	_	B-VAR
ticket	_	_	I-VAR
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
premium	_	_	B-VAR
ticket	_	_	I-VAR
is	_	_	O
$	_	_	O
100	_	_	B-PARAM
.	_	_	O
The	_	_	O
park	_	_	O
reserves	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
tickets	_	_	O
to	_	_	O
be	_	_	O
premium	_	_	B-VAR
but	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
people	_	_	O
prefer	_	_	O
to	_	_	O
buy	_	_	O
regular	_	_	B-VAR
tickets	_	_	I-VAR
than	_	_	O
premium	_	_	B-VAR
tickets	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
tickets	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
the	_	_	O
amusement	_	_	O
park	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
farm	_	_	O
has	_	_	O
to	_	_	O
transport	_	_	O
their	_	_	O
chickens	_	_	O
.	_	_	O
They	_	_	O
can	_	_	O
either	_	_	O
be	_	_	O
transported	_	_	O
by	_	_	O
train	_	_	B-VAR
or	_	_	O
by	_	_	O
truck	_	_	B-VAR
.	_	_	O
Each	_	_	O
train	_	_	B-VAR
trip	_	_	I-VAR
can	_	_	O
take	_	_	O
500	_	_	B-PARAM
chicken	_	_	B-OBJ_NAME
while	_	_	O
each	_	_	O
truck	_	_	B-VAR
trip	_	_	I-VAR
can	_	_	O
take	_	_	O
300	_	_	B-PARAM
chicken	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
cost	_	_	O
per	_	_	O
train	_	_	B-VAR
trip	_	_	I-VAR
is	_	_	O
$	_	_	O
100	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	O
per	_	_	O
truck	_	_	B-VAR
trip	_	_	I-VAR
is	_	_	O
$	_	_	O
80	_	_	B-PARAM
.	_	_	O
The	_	_	O
farm	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
2000	_	_	B-LIMIT
and	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
train	_	_	B-VAR
trips	_	_	I-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
truck	_	_	B-VAR
trips	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
trip	_	_	O
should	_	_	O
be	_	_	O
taken	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
chickens	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
transported	_	_	O
?	_	_	O

A	_	_	O
summer	_	_	O
painting	_	_	O
company	_	_	O
employs	_	_	O
students	_	_	B-VAR
earning	_	_	B-OBJ_NAME
$	_	_	O
200	_	_	B-PARAM
a	_	_	O
week	_	_	O
and	_	_	O
full	_	_	B-VAR
-	_	_	I-VAR
time	_	_	I-VAR
employees	_	_	I-VAR
earning	_	_	B-OBJ_NAME
$	_	_	O
500	_	_	B-PARAM
a	_	_	O
week	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
needs	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
painters	_	_	O
of	_	_	O
whom	_	_	O
at	_	_	B-CONST_DIR
30	_	_	B-LIMIT
must	_	_	O
be	_	_	O
full	_	_	B-VAR
-	_	_	I-VAR
time	_	_	I-VAR
employees	_	_	I-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
to	_	_	O
make	_	_	O
sure	_	_	O
there	_	_	O
is	_	_	O
enough	_	_	O
experience	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
full	_	_	B-VAR
-	_	_	I-VAR
time	_	_	I-VAR
employees	_	_	I-VAR
should	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
half	_	_	B-PARAM
the	_	_	O
number	_	_	O
of	_	_	O
students	_	_	B-VAR
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	B-OBJ_NAME
wage	_	_	I-OBJ_NAME
bill	_	_	I-OBJ_NAME
.	_	_	O

A	_	_	O
fruit	_	_	O
investor	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
300000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
four	_	_	O
industries	_	_	O
:	_	_	O
the	_	_	O
apple	_	_	B-VAR
industry	_	_	I-VAR
,	_	_	O
the	_	_	O
orange	_	_	B-VAR
industry	_	_	I-VAR
,	_	_	O
the	_	_	O
pear	_	_	B-VAR
industry	_	_	I-VAR
,	_	_	O
and	_	_	O
the	_	_	O
banana	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
The	_	_	O
rate	_	_	O
of	_	_	O
return	_	_	B-OBJ_NAME
for	_	_	O
each	_	_	O
investment	_	_	O
is	_	_	O
as	_	_	O
follows	_	_	O
:	_	_	O
apple	_	_	B-VAR
industry	_	_	I-VAR
,	_	_	O
5	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
orange	_	_	B-VAR
industry	_	_	I-VAR
,	_	_	O
6	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
pear	_	_	B-VAR
industry	_	_	I-VAR
,	_	_	O
3	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
and	_	_	O
banana	_	_	B-VAR
industry	_	_	I-VAR
,	_	_	O
8	_	_	B-PARAM
%	_	_	I-PARAM
.	_	_	O
Here	_	_	O
are	_	_	O
some	_	_	O
restrictions	_	_	O
on	_	_	O
the	_	_	O
investments	_	_	O
.	_	_	O
The	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
banana	_	_	B-VAR
industry	_	_	I-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
apple	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
The	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
orange	_	_	B-VAR
industry	_	_	I-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
pear	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
Finally	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
total	_	_	O
amount	_	_	O
can	_	_	O
be	_	_	O
in	_	_	O
the	_	_	O
banana	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
How	_	_	O
much	_	_	O
should	_	_	O
the	_	_	O
fruit	_	_	O
investor	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
industry	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
return	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
man	_	_	O
has	_	_	B-CONST_DIR
300	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
on	_	_	O
which	_	_	O
he	_	_	O
grows	_	_	O
oak	_	_	B-VAR
and	_	_	O
elm	_	_	B-VAR
trees	_	_	I-VAR
.	_	_	O
He	_	_	O
must	_	_	O
grow	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
oak	_	_	B-VAR
trees	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
70	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
elm	_	_	B-VAR
trees	_	_	I-VAR
.	_	_	O
He	_	_	O
prefers	_	_	O
to	_	_	O
grow	_	_	O
elm	_	_	B-VAR
trees	_	_	I-VAR
but	_	_	O
can	_	_	O
grow	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
2	_	_	B-PARAM
times	_	_	O
the	_	_	O
amount	_	_	O
of	_	_	O
elm	_	_	B-VAR
trees	_	_	I-VAR
as	_	_	O
oak	_	_	B-VAR
trees	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
oak	_	_	B-VAR
trees	_	_	I-VAR
is	_	_	O
$	_	_	O
1000	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
elm	_	_	B-VAR
trees	_	_	I-VAR
is	_	_	O
$	_	_	O
1200	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
grow	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
museum	_	_	O
can	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
300	_	_	B-LIMIT
tickets	_	_	O
.	_	_	O
They	_	_	O
offer	_	_	O
guided	_	_	B-VAR
tickets	_	_	I-VAR
as	_	_	O
well	_	_	O
as	_	_	O
regular	_	_	B-VAR
tickets	_	_	I-VAR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
guided	_	_	B-VAR
ticket	_	_	I-VAR
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
regular	_	_	B-VAR
ticket	_	_	I-VAR
is	_	_	O
$	_	_	O
20	_	_	B-PARAM
.	_	_	O
The	_	_	O
museum	_	_	O
reserves	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
tickets	_	_	O
to	_	_	O
be	_	_	O
guided	_	_	B-VAR
,	_	_	O
but	_	_	O
since	_	_	O
most	_	_	O
people	_	_	O
like	_	_	O
to	_	_	O
go	_	_	O
at	_	_	O
their	_	_	O
own	_	_	O
pace	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
people	_	_	O
prefer	_	_	O
to	_	_	O
buy	_	_	O
regular	_	_	B-VAR
tickets	_	_	I-VAR
than	_	_	O
guided	_	_	B-VAR
tickets	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
tickets	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
be	_	_	O
sold	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
watch	_	_	O
company	_	_	O
makes	_	_	O
digital	_	_	B-VAR
watches	_	_	I-VAR
and	_	_	O
analog	_	_	B-VAR
watches	_	_	I-VAR
.	_	_	O
There	_	_	O
is	_	_	O
a	_	_	O
demand	_	_	O
of	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
150	_	_	B-LIMIT
digital	_	_	B-VAR
watches	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
120	_	_	B-LIMIT
analog	_	_	B-VAR
watches	_	_	I-VAR
per	_	_	O
day	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
the	_	_	O
company	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
200	_	_	B-LIMIT
digital	_	_	B-VAR
watches	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
180	_	_	B-LIMIT
analog	_	_	B-VAR
watches	_	_	I-VAR
per	_	_	O
day	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
they	_	_	O
have	_	_	O
a	_	_	O
contract	_	_	O
to	_	_	O
ship	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
300	_	_	B-LIMIT
watches	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
digital	_	_	B-VAR
watch	_	_	I-VAR
is	_	_	O
$	_	_	O
15	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
analog	_	_	B-VAR
watch	_	_	I-VAR
is	_	_	O
$	_	_	O
10	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
taco	_	_	O
stand	_	_	O
sells	_	_	O
fish	_	_	B-VAR
and	_	_	O
chicken	_	_	B-VAR
tacos	_	_	I-VAR
.	_	_	O
In	_	_	O
a	_	_	O
day	_	_	O
,	_	_	O
they	_	_	O
must	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
fish	_	_	B-VAR
tacos	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
40	_	_	B-LIMIT
chicken	_	_	B-VAR
tacos	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
they	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
50	_	_	B-LIMIT
fish	_	_	B-VAR
tacos	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
60	_	_	B-LIMIT
chicken	_	_	B-VAR
tacos	_	_	I-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
they	_	_	O
only	_	_	B-CONST_DIR
have	_	_	O
enough	_	_	O
taco	_	_	O
shells	_	_	O
to	_	_	O
make	_	_	O
80	_	_	B-LIMIT
tacos	_	_	O
total	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
fish	_	_	B-VAR
taco	_	_	I-VAR
is	_	_	O
$	_	_	O
6	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
chicken	_	_	B-VAR
taco	_	_	I-VAR
is	_	_	O
$	_	_	O
4	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

You	_	_	O
are	_	_	O
playing	_	_	O
a	_	_	O
game	_	_	O
where	_	_	O
you	_	_	O
can	_	_	O
hit	_	_	O
slow	_	_	B-VAR
balls	_	_	I-VAR
or	_	_	O
fast	_	_	B-VAR
balls	_	_	I-VAR
.	_	_	O
Each	_	_	O
slow	_	_	B-VAR
ball	_	_	I-VAR
hit	_	_	O
is	_	_	O
3	_	_	B-PARAM
points	_	_	B-OBJ_NAME
and	_	_	O
each	_	_	O
fast	_	_	B-VAR
ball	_	_	I-VAR
hit	_	_	O
is	_	_	O
5	_	_	B-PARAM
points	_	_	B-OBJ_NAME
.	_	_	O
You	_	_	O
have	_	_	O
to	_	_	O
hit	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
slow	_	_	B-VAR
balls	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-LIMIT
fast	_	_	B-VAR
balls	_	_	I-VAR
.	_	_	O
However	_	_	O
you	_	_	O
can	_	_	O
hit	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
8	_	_	B-LIMIT
slow	_	_	B-VAR
balls	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
8	_	_	B-LIMIT
fast	_	_	B-VAR
balls	_	_	I-VAR
.	_	_	O
In	_	_	O
total	_	_	O
,	_	_	O
you	_	_	O
can	_	_	O
hit	_	_	O
no	_	_	B-CONST_DIR
more	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
12	_	_	B-LIMIT
balls	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
ball	_	_	O
should	_	_	O
you	_	_	O
hit	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
your	_	_	O
points	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
car	_	_	O
company	_	_	O
sells	_	_	O
electric	_	_	B-VAR
and	_	_	O
gas	_	_	B-VAR
cars	_	_	I-VAR
.	_	_	O
Two	_	_	O
different	_	_	O
factories	_	_	O
produce	_	_	O
these	_	_	O
cars	_	_	O
.	_	_	O
The	_	_	O
electric	_	_	B-VAR
car	_	_	I-VAR
factory	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
3	_	_	B-LIMIT
electric	_	_	B-VAR
cars	_	_	I-VAR
per	_	_	O
day	_	_	O
while	_	_	O
the	_	_	O
gas	_	_	B-VAR
car	_	_	I-VAR
factory	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
5	_	_	B-LIMIT
gas	_	_	B-VAR
cars	_	_	I-VAR
per	_	_	O
day	_	_	O
.	_	_	O
All	_	_	O
cars	_	_	O
have	_	_	O
to	_	_	O
go	_	_	O
through	_	_	O
a	_	_	O
third	_	_	O
factory	_	_	O
where	_	_	O
finishing	_	_	O
touches	_	_	O
are	_	_	O
added	_	_	O
and	_	_	O
this	_	_	O
factory	_	_	O
can	_	_	O
process	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
5	_	_	B-LIMIT
cars	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
electric	_	_	B-VAR
car	_	_	I-VAR
is	_	_	O
$	_	_	O
5000	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
gas	_	_	B-VAR
car	_	_	I-VAR
is	_	_	O
$	_	_	O
3000	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
phone	_	_	O
company	_	_	O
makes	_	_	O
regular	_	_	B-VAR
phones	_	_	I-VAR
and	_	_	O
premium	_	_	B-VAR
phones	_	_	I-VAR
.	_	_	O
Let	_	_	O
's	_	_	O
say	_	_	O
they	_	_	O
make	_	_	O
x1	_	_	O
regular	_	_	B-VAR
phones	_	_	I-VAR
per	_	_	O
day	_	_	O
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
200	_	_	B-PARAM
each	_	_	O
and	_	_	O
x2	_	_	O
premium	_	_	B-VAR
phone	_	_	I-VAR
per	_	_	O
day	_	_	O
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
300	_	_	B-PARAM
each	_	_	O
(	_	_	O
x1	_	_	O
and	_	_	O
x2	_	_	O
are	_	_	O
both	_	_	O
greater	_	_	O
than	_	_	O
or	_	_	O
equal	_	_	O
to	_	_	O
0	_	_	O
)	_	_	O
.	_	_	O
Note	_	_	O
that	_	_	O
the	_	_	O
daily	_	_	O
demand	_	_	O
for	_	_	O
regular	_	_	B-VAR
phones	_	_	I-VAR
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
20	_	_	B-LIMIT
and	_	_	O
the	_	_	O
daily	_	_	O
demand	_	_	O
for	_	_	O
premium	_	_	B-VAR
phones	_	_	I-VAR
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
15	_	_	B-LIMIT
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
the	_	_	O
company	_	_	O
can	_	_	O
only	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
phones	_	_	O
total	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
phones	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
small	_	_	O
town	_	_	O
has	_	_	O
$	_	_	O
100000	_	_	B-LIMIT
available	_	_	B-CONST_DIR
to	_	_	O
invest	_	_	O
in	_	_	O
a	_	_	O
12	_	_	O
-	_	_	O
month	_	_	O
commitment	_	_	O
.	_	_	O
They	_	_	O
have	_	_	O
decided	_	_	O
to	_	_	O
invest	_	_	O
in	_	_	O
both	_	_	O
the	_	_	O
mining	_	_	B-VAR
and	_	_	O
logging	_	_	B-VAR
industries	_	_	I-VAR
.	_	_	O
After	_	_	O
consulting	_	_	O
an	_	_	O
advisor	_	_	O
,	_	_	O
the	_	_	O
town	_	_	O
has	_	_	O
decided	_	_	O
to	_	_	O
invest	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
30	_	_	B-LIMIT
%	_	_	O
in	_	_	O
the	_	_	O
mining	_	_	B-VAR
industry	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
55	_	_	B-LIMIT
%	_	_	O
in	_	_	O
the	_	_	O
logging	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
The	_	_	O
money	_	_	O
placed	_	_	O
in	_	_	O
the	_	_	O
mining	_	_	B-VAR
industry	_	_	I-VAR
yields	_	_	O
a	_	_	O
9	_	_	B-PARAM
%	_	_	O
return	_	_	B-OBJ_NAME
and	_	_	O
the	_	_	O
money	_	_	O
placed	_	_	O
in	_	_	O
the	_	_	O
logging	_	_	B-VAR
industry	_	_	I-VAR
yields	_	_	O
a	_	_	O
5	_	_	B-PARAM
%	_	_	O
return	_	_	B-OBJ_NAME
.	_	_	O
How	_	_	O
much	_	_	O
should	_	_	O
the	_	_	O
town	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
industry	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
its	_	_	O
return	_	_	B-OBJ_NAME
on	_	_	O
investment	_	_	O
?	_	_	O

A	_	_	O
retired	_	_	O
professor	_	_	O
wants	_	_	O
to	_	_	O
invest	_	_	O
up	_	_	B-CONST_DIR
to	_	_	I-CONST_DIR
$	_	_	O
50000	_	_	B-LIMIT
in	_	_	O
the	_	_	O
airline	_	_	B-VAR
and	_	_	O
railway	_	_	B-VAR
industries	_	_	I-VAR
.	_	_	O
Each	_	_	O
dollar	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
airline	_	_	B-VAR
industry	_	_	I-VAR
yields	_	_	O
a	_	_	O
$	_	_	O
0.30	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
and	_	_	O
each	_	_	O
dollar	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
railway	_	_	B-VAR
industry	_	_	I-VAR
yields	_	_	O
a	_	_	O
$	_	_	O
0.10	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
.	_	_	O
A	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
10000	_	_	B-LIMIT
must	_	_	O
be	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
railway	_	_	B-VAR
industry	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
25	_	_	B-LIMIT
%	_	_	O
of	_	_	O
all	_	_	O
money	_	_	O
invested	_	_	O
must	_	_	O
be	_	_	O
in	_	_	O
the	_	_	O
airline	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
that	_	_	O
can	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
professor	_	_	O
's	_	_	O
profit	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
butcher	_	_	O
shop	_	_	O
has	_	_	B-CONST_DIR
1000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
ground	_	_	O
meat	_	_	O
to	_	_	O
make	_	_	O
both	_	_	O
burgers	_	_	B-VAR
and	_	_	O
sausages	_	_	B-VAR
.	_	_	O
Each	_	_	O
burger	_	_	B-VAR
requires	_	_	O
20	_	_	B-PARAM
grams	_	_	O
of	_	_	O
ground	_	_	O
meat	_	_	O
while	_	_	O
each	_	_	O
sausage	_	_	B-VAR
requires	_	_	O
10	_	_	B-PARAM
grams	_	_	O
of	_	_	O
ground	_	_	O
meat	_	_	O
.	_	_	O
Past	_	_	O
sales	_	_	O
have	_	_	O
indicated	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
sausages	_	_	B-VAR
are	_	_	O
needed	_	_	O
than	_	_	O
burgers	_	_	B-VAR
.	_	_	O
There	_	_	O
also	_	_	O
needs	_	_	O
to	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
burgers	_	_	B-VAR
made	_	_	O
.	_	_	O
Each	_	_	O
burger	_	_	B-VAR
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
each	_	_	O
sausage	_	_	B-VAR
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
3	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
item	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
electronics	_	_	O
store	_	_	O
must	_	_	O
determine	_	_	O
how	_	_	O
many	_	_	O
monitors	_	_	B-VAR
and	_	_	O
gaming	_	_	B-VAR
stations	_	_	I-VAR
to	_	_	O
keep	_	_	O
in	_	_	O
stock	_	_	O
.	_	_	O
A	_	_	O
monitor	_	_	B-VAR
requires	_	_	O
8	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
of	_	_	O
floor	_	_	O
space	_	_	O
,	_	_	O
whereas	_	_	O
a	_	_	O
gaming	_	_	B-VAR
station	_	_	I-VAR
requires	_	_	O
12	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
150	_	_	B-LIMIT
sq	_	_	O
ft	_	_	O
of	_	_	O
floor	_	_	O
space	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
monitor	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
40	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
gaming	_	_	B-VAR
station	_	_	I-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
80	_	_	B-PARAM
.	_	_	O
The	_	_	O
store	_	_	O
stocks	_	_	O
only	_	_	O
monitors	_	_	B-VAR
and	_	_	O
gaming	_	_	B-VAR
stations	_	_	I-VAR
.	_	_	O
Marketing	_	_	O
requirements	_	_	O
dictate	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
40	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
all	_	_	O
items	_	_	O
in	_	_	O
stock	_	_	O
be	_	_	O
gaming	_	_	B-VAR
stations	_	_	I-VAR
.	_	_	O
Finally	_	_	O
,	_	_	O
a	_	_	O
monitor	_	_	B-VAR
ties	_	_	O
up	_	_	O
$	_	_	O
180	_	_	B-PARAM
in	_	_	O
capital	_	_	O
,	_	_	O
and	_	_	O
a	_	_	O
gaming	_	_	B-VAR
station	_	_	I-VAR
,	_	_	O
$	_	_	O
260	_	_	B-PARAM
.	_	_	O
The	_	_	O
store	_	_	O
wants	_	_	O
to	_	_	O
have	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
4,000	_	_	B-LIMIT
worth	_	_	O
of	_	_	O
capital	_	_	O
tied	_	_	O
up	_	_	O
at	_	_	O
any	_	_	O
time	_	_	O
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
that	_	_	O
can	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
film	_	_	O
production	_	_	O
company	_	_	O
wants	_	_	O
to	_	_	O
advertise	_	_	O
the	_	_	O
release	_	_	O
of	_	_	O
their	_	_	O
new	_	_	O
movie	_	_	O
using	_	_	O
ads	_	_	O
in	_	_	O
three	_	_	O
areas	_	_	O
:	_	_	O
malls	_	_	B-VAR
,	_	_	O
bus	_	_	B-VAR
stops	_	_	I-VAR
,	_	_	O
and	_	_	O
theatres	_	_	B-VAR
.	_	_	O
They	_	_	O
have	_	_	O
a	_	_	O
weekly	_	_	O
advertising	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
30000	_	_	B-LIMIT
.	_	_	O
The	_	_	O
cost	_	_	O
of	_	_	O
an	_	_	O
ad	_	_	O
in	_	_	O
each	_	_	O
area	_	_	O
and	_	_	O
their	_	_	O
audience	_	_	O
reach	_	_	O
is	_	_	O
given	_	_	O
.	_	_	O
An	_	_	O
ad	_	_	O
in	_	_	O
a	_	_	O
mall	_	_	B-VAR
costs	_	_	O
$	_	_	O
5000	_	_	B-PARAM
and	_	_	O
reaches	_	_	O
50000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
An	_	_	O
ad	_	_	O
at	_	_	O
a	_	_	O
bus	_	_	B-VAR
stop	_	_	I-VAR
costs	_	_	O
$	_	_	O
1000	_	_	B-PARAM
and	_	_	O
reaches	_	_	O
10000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
An	_	_	O
ad	_	_	O
in	_	_	O
a	_	_	O
theatre	_	_	B-VAR
costs	_	_	O
$	_	_	O
3000	_	_	B-PARAM
and	_	_	O
reaches	_	_	O
20000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
city	_	_	O
limits	_	_	B-CONST_DIR
the	_	_	I-CONST_DIR
number	_	_	I-CONST_DIR
of	_	_	O
ads	_	_	O
at	_	_	O
a	_	_	O
bus	_	_	B-VAR
stop	_	_	I-VAR
from	_	_	O
a	_	_	O
single	_	_	O
company	_	_	O
to	_	_	O
20	_	_	B-LIMIT
.	_	_	O
In	_	_	O
order	_	_	O
to	_	_	O
maintain	_	_	O
balance	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
a	_	_	O
third	_	_	B-LIMIT
of	_	_	O
the	_	_	O
total	_	_	O
number	_	_	O
of	_	_	O
ads	_	_	O
should	_	_	O
be	_	_	O
in	_	_	O
theatres	_	_	B-VAR
and	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
20	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
ads	_	_	O
should	_	_	O
be	_	_	O
in	_	_	O
malls	_	_	B-VAR
.	_	_	O
How	_	_	O
many	_	_	O
ads	_	_	O
should	_	_	O
be	_	_	O
run	_	_	O
in	_	_	O
each	_	_	O
of	_	_	O
the	_	_	O
three	_	_	O
areas	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
viewership	_	_	B-OBJ_NAME
?	_	_	O

Lucy	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
30000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
the	_	_	O
automotive	_	_	B-VAR
and	_	_	O
textile	_	_	B-VAR
industries	_	_	I-VAR
.	_	_	O
The	_	_	O
money	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
automotive	_	_	B-VAR
industry	_	_	I-VAR
earns	_	_	B-OBJ_NAME
10	_	_	B-PARAM
%	_	_	I-PARAM
while	_	_	O
the	_	_	O
money	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
textile	_	_	B-VAR
industry	_	_	I-VAR
earns	_	_	B-OBJ_NAME
8	_	_	B-PARAM
%	_	_	I-PARAM
.	_	_	O
She	_	_	O
has	_	_	O
decided	_	_	O
that	_	_	O
the	_	_	O
money	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
automotive	_	_	B-VAR
industry	_	_	I-VAR
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	O
as	_	_	O
much	_	_	O
as	_	_	O
the	_	_	O
money	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
textile	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
the	_	_	O
money	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
automotive	_	_	B-VAR
industry	_	_	I-VAR
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
24000	_	_	B-LIMIT
.	_	_	O
How	_	_	O
much	_	_	O
should	_	_	O
she	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
industry	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
long	_	_	O
haul	_	_	O
bus	_	_	O
carries	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
passengers	_	_	O
.	_	_	O
A	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
50	_	_	B-PARAM
is	_	_	O
made	_	_	O
for	_	_	O
each	_	_	O
premium	_	_	B-VAR
class	_	_	I-VAR
seat	_	_	O
with	_	_	O
extra	_	_	O
leg	_	_	O
room	_	_	O
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
30	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
regular	_	_	B-VAR
class	_	_	I-VAR
seat	_	_	O
.	_	_	O
The	_	_	O
bus	_	_	O
reserves	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
seats	_	_	O
for	_	_	O
the	_	_	O
premium	_	_	B-VAR
class	_	_	I-VAR
seats	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-PARAM
as	_	_	O
many	_	_	O
passengers	_	_	O
prefer	_	_	O
to	_	_	O
save	_	_	O
money	_	_	O
and	_	_	O
travel	_	_	O
by	_	_	O
regular	_	_	B-VAR
class	_	_	I-VAR
than	_	_	O
by	_	_	O
premium	_	_	B-VAR
class	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
seats	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
be	_	_	O
sold	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
restaurant	_	_	O
employs	_	_	O
waiters	_	_	B-VAR
earning	_	_	B-OBJ_NAME
$	_	_	O
147	_	_	B-PARAM
per	_	_	O
week	_	_	O
and	_	_	O
cooks	_	_	B-VAR
earning	_	_	B-OBJ_NAME
$	_	_	O
290	_	_	B-PARAM
per	_	_	O
week	_	_	O
.	_	_	O
It	_	_	O
is	_	_	O
required	_	_	O
to	_	_	O
keep	_	_	O
the	_	_	O
weekly	_	_	O
wage	_	_	O
bill	_	_	O
below	_	_	B-CONST_DIR
$	_	_	O
17,600	_	_	B-LIMIT
.	_	_	O
The	_	_	O
restaurant	_	_	O
requires	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
50	_	_	B-LIMIT
staff	_	_	O
,	_	_	O
of	_	_	O
whom	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
12	_	_	B-LIMIT
must	_	_	O
be	_	_	O
cooks	_	_	B-VAR
.	_	_	O
Union	_	_	O
regulations	_	_	O
require	_	_	O
that	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
cooks	_	_	B-VAR
should	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
one	_	_	B-PARAM
third	_	_	I-PARAM
the	_	_	O
number	_	_	O
of	_	_	O
waiters	_	_	B-VAR
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
wage	_	_	B-OBJ_NAME
bill	_	_	I-OBJ_NAME
.	_	_	O

A	_	_	O
retired	_	_	O
teacher	_	_	O
is	_	_	O
deciding	_	_	O
where	_	_	O
to	_	_	O
invest	_	_	O
his	_	_	O
money	_	_	O
.	_	_	O
He	_	_	O
has	_	_	O
$	_	_	O
300000	_	_	B-LIMIT
available	_	_	B-CONST_DIR
and	_	_	O
has	_	_	O
decided	_	_	O
to	_	_	O
invest	_	_	O
in	_	_	O
the	_	_	O
energy	_	_	B-VAR
,	_	_	O
telecom	_	_	B-VAR
,	_	_	O
utilities	_	_	B-VAR
,	_	_	O
and	_	_	O
health	_	_	B-VAR
care	_	_	I-VAR
industries	_	_	O
.	_	_	O
The	_	_	O
annual	_	_	O
rate	_	_	O
of	_	_	O
return	_	_	B-OBJ_NAME
on	_	_	O
an	_	_	O
investment	_	_	O
in	_	_	O
each	_	_	O
of	_	_	O
the	_	_	O
industries	_	_	O
is	_	_	O
as	_	_	O
follows	_	_	O
:	_	_	O
energy	_	_	B-VAR
,	_	_	O
5	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
telecom	_	_	B-VAR
,	_	_	O
8	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
utilities	_	_	B-VAR
,	_	_	O
3	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
health	_	_	B-VAR
care	_	_	I-VAR
,	_	_	O
9	_	_	B-PARAM
%	_	_	I-PARAM
.	_	_	O
A	_	_	O
financial	_	_	O
advisor	_	_	O
has	_	_	O
given	_	_	O
him	_	_	O
the	_	_	O
following	_	_	O
advice	_	_	O
.	_	_	O
The	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
health	_	_	B-VAR
care	_	_	I-VAR
industry	_	_	O
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
energy	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
Also	_	_	O
,	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
telecom	_	_	B-VAR
industry	_	_	I-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
utilities	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
Finally	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
33	_	_	B-LIMIT
%	_	_	O
of	_	_	O
the	_	_	O
total	_	_	O
amount	_	_	O
of	_	_	O
money	_	_	O
can	_	_	O
be	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
health	_	_	B-VAR
care	_	_	I-VAR
industry	_	_	O
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
return	_	_	B-OBJ_NAME
on	_	_	O
investment	_	_	O
.	_	_	O

A	_	_	O
bookstore	_	_	O
can	_	_	O
display	_	_	O
and	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
500	_	_	B-LIMIT
books	_	_	O
.	_	_	O
A	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
5	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
hardcover	_	_	B-VAR
book	_	_	I-VAR
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
2	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
paperback	_	_	B-VAR
book	_	_	I-VAR
.	_	_	O
The	_	_	O
bookstore	_	_	O
makes	_	_	O
sure	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
50	_	_	B-LIMIT
books	_	_	O
displayed	_	_	O
are	_	_	O
hardcover	_	_	B-VAR
.	_	_	O
However	_	_	O
,	_	_	O
due	_	_	O
to	_	_	O
their	_	_	O
convenience	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
reader	_	_	O
prefer	_	_	O
paperback	_	_	B-VAR
books	_	_	I-VAR
to	_	_	O
hardcover	_	_	B-VAR
books	_	_	I-VAR
.	_	_	O
Assuming	_	_	O
the	_	_	O
bookstore	_	_	O
can	_	_	O
sell	_	_	O
all	_	_	O
their	_	_	O
books	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
book	_	_	O
type	_	_	O
,	_	_	O
hardcover	_	_	O
and	_	_	O
softcover	_	_	O
,	_	_	O
should	_	_	O
be	_	_	O
displayed	_	_	O
and	_	_	O
sold	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
keyboard	_	_	O
factory	_	_	O
makes	_	_	O
regular	_	_	B-VAR
and	_	_	O
mechanical	_	_	B-VAR
keyboards	_	_	I-VAR
.	_	_	O
Projections	_	_	O
indicate	_	_	O
a	_	_	O
demand	_	_	O
of	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
165	_	_	B-LIMIT
regular	_	_	B-VAR
keyboards	_	_	I-VAR
and	_	_	O
70	_	_	B-LIMIT
mechanical	_	_	B-VAR
keyboards	_	_	I-VAR
each	_	_	O
day	_	_	O
.	_	_	O
Because	_	_	O
of	_	_	O
the	_	_	O
manual	_	_	O
labor	_	_	O
involved	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
300	_	_	B-LIMIT
regular	_	_	B-VAR
keyboards	_	_	I-VAR
and	_	_	O
150	_	_	B-LIMIT
mechanical	_	_	B-VAR
keyboards	_	_	I-VAR
can	_	_	O
be	_	_	O
made	_	_	O
each	_	_	O
day	_	_	O
.	_	_	O
To	_	_	O
satisfy	_	_	O
a	_	_	O
contract	_	_	O
with	_	_	O
an	_	_	O
electronics	_	_	O
shop	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
250	_	_	B-LIMIT
keyboards	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
must	_	_	O
be	_	_	O
made	_	_	O
each	_	_	O
day	_	_	O
.	_	_	O
The	_	_	O
factory	_	_	O
makes	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
30	_	_	B-PARAM
per	_	_	O
regular	_	_	B-VAR
keyboard	_	_	I-VAR
and	_	_	O
$	_	_	O
60	_	_	B-PARAM
per	_	_	O
mechanical	_	_	B-VAR
keyboard	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
keyboard	_	_	O
should	_	_	O
the	_	_	O
factory	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
bubble	_	_	O
tea	_	_	O
store	_	_	O
sells	_	_	O
peach	_	_	B-VAR
and	_	_	O
mango	_	_	B-VAR
flavored	_	_	O
drinks	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
150	_	_	B-LIMIT
drinks	_	_	O
total	_	_	O
.	_	_	O
To	_	_	O
stay	_	_	O
in	_	_	O
business	_	_	O
,	_	_	O
they	_	_	O
must	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
60	_	_	B-LIMIT
mango	_	_	B-VAR
drinks	_	_	I-VAR
and	_	_	O
40	_	_	B-LIMIT
peach	_	_	B-VAR
drinks	_	_	I-VAR
.	_	_	O
Due	_	_	O
to	_	_	O
fruit	_	_	O
shortages	_	_	O
however	_	_	O
,	_	_	O
they	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
120	_	_	B-LIMIT
mango	_	_	B-VAR
drinks	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
70	_	_	B-LIMIT
peach	_	_	B-VAR
drinks	_	_	I-VAR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
mango	_	_	B-VAR
drink	_	_	I-VAR
is	_	_	O
$	_	_	O
2	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
peach	_	_	B-VAR
drink	_	_	I-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
drink	_	_	O
should	_	_	O
they	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

You	_	_	O
decide	_	_	O
to	_	_	O
take	_	_	O
part	_	_	O
in	_	_	O
a	_	_	O
math	_	_	O
contest	_	_	O
with	_	_	O
algebra	_	_	B-VAR
questions	_	_	I-VAR
worth	_	_	O
1	_	_	B-PARAM
point	_	_	B-OBJ_NAME
each	_	_	O
and	_	_	O
calculus	_	_	B-VAR
questions	_	_	I-VAR
worth	_	_	O
3	_	_	B-PARAM
points	_	_	B-OBJ_NAME
each	_	_	O
.	_	_	O
In	_	_	O
this	_	_	O
contest	_	_	O
,	_	_	O
you	_	_	O
can	_	_	O
answer	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
25	_	_	B-LIMIT
questions	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
you	_	_	O
must	_	_	O
answer	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
algebra	_	_	B-VAR
questions	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
6	_	_	B-LIMIT
calculus	_	_	B-VAR
questions	_	_	I-VAR
.	_	_	O
Time	_	_	O
restricts	_	_	O
you	_	_	O
from	_	_	O
answering	_	_	O
more	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
15	_	_	B-LIMIT
of	_	_	O
either	_	_	O
type	_	_	O
.	_	_	O
Assuming	_	_	O
all	_	_	O
your	_	_	O
answers	_	_	O
are	_	_	O
correct	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
question	_	_	O
should	_	_	O
you	_	_	O
answer	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
your	_	_	O
score	_	_	B-OBJ_NAME
?	_	_	O
What	_	_	O
is	_	_	O
your	_	_	O
maximum	_	_	O
score	_	_	O
?	_	_	O

A	_	_	O
wine	_	_	O
company	_	_	O
sells	_	_	O
two	_	_	O
products	_	_	O
.	_	_	O
Its	_	_	O
regular	_	_	B-VAR
wine	_	_	I-VAR
and	_	_	O
a	_	_	O
premium	_	_	B-VAR
aged	_	_	I-VAR
wine	_	_	I-VAR
.	_	_	O
The	_	_	O
company	_	_	O
makes	_	_	O
x1	_	_	O
bottles	_	_	O
of	_	_	O
the	_	_	O
regular	_	_	B-VAR
wine	_	_	I-VAR
per	_	_	O
day	_	_	O
and	_	_	O
x2	_	_	O
bottled	_	_	O
of	_	_	O
the	_	_	O
premium	_	_	B-VAR
wine	_	_	I-VAR
per	_	_	O
day	_	_	O
(	_	_	O
x1	_	_	O
and	_	_	O
x2	_	_	O
are	_	_	O
unknown	_	_	O
values	_	_	O
greater	_	_	O
than	_	_	O
or	_	_	O
equal	_	_	O
to	_	_	O
0	_	_	O
)	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
bottle	_	_	O
of	_	_	O
regular	_	_	B-VAR
wine	_	_	I-VAR
is	_	_	O
$	_	_	O
20	_	_	B-PARAM
ad	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
bottle	_	_	O
of	_	_	O
the	_	_	O
premium	_	_	B-VAR
wine	_	_	I-VAR
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
.	_	_	O
Current	_	_	O
demand	_	_	O
for	_	_	O
the	_	_	O
wine	_	_	O
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
80	_	_	B-LIMIT
bottles	_	_	O
of	_	_	O
the	_	_	O
regular	_	_	B-VAR
wine	_	_	I-VAR
per	_	_	O
day	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
50	_	_	B-LIMIT
bottles	_	_	O
of	_	_	O
the	_	_	O
premium	_	_	B-VAR
wine	_	_	I-VAR
per	_	_	O
day	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
only	_	_	B-CONST_DIR
has	_	_	O
enough	_	_	O
supply	_	_	O
to	_	_	O
make	_	_	O
120	_	_	B-LIMIT
bottles	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
each	_	_	O
day	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
bottles	_	_	O
of	_	_	O
each	_	_	O
wine	_	_	O
,	_	_	O
regular	_	_	B-VAR
and	_	_	O
premium	_	_	B-VAR
,	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
company	_	_	O
is	_	_	O
looking	_	_	O
to	_	_	O
diversify	_	_	O
its	_	_	O
investments	_	_	O
and	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
300000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
a	_	_	O
12	_	_	O
month	_	_	O
commitment	_	_	O
.	_	_	O
They	_	_	O
can	_	_	O
invest	_	_	O
in	_	_	O
the	_	_	O
paper	_	_	B-VAR
industry	_	_	I-VAR
yielding	_	_	O
a	_	_	O
2	_	_	B-PARAM
%	_	_	I-PARAM
return	_	_	B-OBJ_NAME
or	_	_	O
in	_	_	O
the	_	_	O
glass	_	_	B-VAR
industry	_	_	I-VAR
yielding	_	_	O
a	_	_	O
5	_	_	B-PARAM
%	_	_	I-PARAM
return	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
board	_	_	O
of	_	_	O
directors	_	_	O
requires	_	_	O
that	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
30	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
investment	_	_	O
be	_	_	O
placed	_	_	O
in	_	_	O
the	_	_	O
paper	_	_	B-VAR
industry	_	_	I-VAR
and	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
50	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
investment	_	_	O
be	_	_	O
placed	_	_	O
in	_	_	O
the	_	_	O
glass	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
How	_	_	O
much	_	_	O
money	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
industry	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
its	_	_	O
return	_	_	B-OBJ_NAME
on	_	_	O
investments	_	_	O
?	_	_	O

Frank	_	_	O
has	_	_	O
up	_	_	B-CONST_DIR
to	_	_	I-CONST_DIR
$	_	_	O
5000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
the	_	_	O
cigarette	_	_	B-VAR
and	_	_	O
tobacco	_	_	B-VAR
industries	_	_	I-VAR
.	_	_	O
After	_	_	O
talking	_	_	O
to	_	_	O
his	_	_	O
friends	_	_	O
,	_	_	O
he	_	_	O
has	_	_	O
decided	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
40	_	_	B-LIMIT
%	_	_	O
of	_	_	O
all	_	_	O
the	_	_	O
money	_	_	O
invested	_	_	O
must	_	_	O
be	_	_	O
in	_	_	O
the	_	_	O
cigarette	_	_	B-VAR
industry	_	_	I-VAR
and	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
$	_	_	O
1000	_	_	B-LIMIT
must	_	_	O
be	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
tobacco	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
Each	_	_	O
dollar	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
cigarette	_	_	B-VAR
industry	_	_	I-VAR
yields	_	_	O
a	_	_	O
$	_	_	O
0.30	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
while	_	_	O
each	_	_	O
dollar	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
tobacco	_	_	B-VAR
industry	_	_	I-VAR
yields	_	_	O
a	_	_	O
$	_	_	O
0.45	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
Frank	_	_	O
's	_	_	O
investment	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
soup	_	_	O
kitchen	_	_	O
has	_	_	B-CONST_DIR
50000	_	_	B-LIMIT
ml	_	_	O
of	_	_	O
soup	_	_	O
to	_	_	O
serve	_	_	O
.	_	_	O
They	_	_	O
sell	_	_	O
both	_	_	O
individual	_	_	B-VAR
servings	_	_	I-VAR
and	_	_	O
family	_	_	B-VAR
servings	_	_	I-VAR
.	_	_	O
An	_	_	O
individual	_	_	B-VAR
serving	_	_	I-VAR
has	_	_	O
250	_	_	B-PARAM
ml	_	_	O
of	_	_	O
soup	_	_	O
while	_	_	O
a	_	_	O
family	_	_	B-VAR
serving	_	_	I-VAR
has	_	_	O
1200	_	_	B-PARAM
ml	_	_	O
of	_	_	O
soup	_	_	O
.	_	_	O
The	_	_	O
soup	_	_	O
kitchen	_	_	O
knows	_	_	O
that	_	_	O
they	_	_	O
need	_	_	O
to	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
individual	_	_	B-VAR
servings	_	_	I-VAR
than	_	_	O
the	_	_	O
family	_	_	B-VAR
servings	_	_	I-VAR
.	_	_	O
They	_	_	O
also	_	_	O
know	_	_	O
that	_	_	O
that	_	_	O
they	_	_	O
need	_	_	O
to	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
family	_	_	B-VAR
servings	_	_	I-VAR
.	_	_	O
Each	_	_	O
individual	_	_	B-VAR
serving	_	_	I-VAR
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
3	_	_	B-PARAM
and	_	_	O
each	_	_	O
family	_	_	B-VAR
serving	_	_	I-VAR
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
10	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
serving	_	_	O
needs	_	_	O
to	_	_	O
be	_	_	O
made	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
kitchen	_	_	O
appliance	_	_	O
store	_	_	O
sells	_	_	O
only	_	_	O
fridges	_	_	B-VAR
and	_	_	O
stoves	_	_	B-VAR
.	_	_	O
They	_	_	O
have	_	_	O
1000	_	_	B-LIMIT
sq	_	_	O
ft	_	_	O
of	_	_	O
floor	_	_	O
space	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
A	_	_	O
fridge	_	_	B-VAR
requires	_	_	O
10	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
of	_	_	O
floor	_	_	O
space	_	_	O
while	_	_	O
a	_	_	O
stove	_	_	B-VAR
requires	_	_	O
15	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
of	_	_	O
floor	_	_	O
space	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
fridge	_	_	B-VAR
is	_	_	O
$	_	_	O
400	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
stove	_	_	B-VAR
is	_	_	O
$	_	_	O
500	_	_	B-PARAM
.	_	_	O
Management	_	_	O
requires	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
40	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
all	_	_	O
appliances	_	_	O
in	_	_	O
stock	_	_	O
be	_	_	O
fridges	_	_	B-VAR
.	_	_	O
While	_	_	O
a	_	_	O
fridge	_	_	B-VAR
ties	_	_	O
up	_	_	O
$	_	_	O
1000	_	_	B-PARAM
in	_	_	O
capital	_	_	O
,	_	_	O
a	_	_	O
stove	_	_	B-VAR
ties	_	_	O
up	_	_	O
$	_	_	O
1200	_	_	B-PARAM
in	_	_	O
capital	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
wants	_	_	O
to	_	_	O
have	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
40000	_	_	B-LIMIT
worth	_	_	O
of	_	_	O
capital	_	_	O
tied	_	_	O
up	_	_	O
at	_	_	O
any	_	_	O
time	_	_	O
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
store	_	_	O
's	_	_	O
profit	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
hockey	_	_	O
store	_	_	O
can	_	_	O
spend	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
20000	_	_	B-LIMIT
on	_	_	O
hockey	_	_	B-VAR
sticks	_	_	I-VAR
and	_	_	O
pucks	_	_	B-VAR
.	_	_	O
A	_	_	O
hockey	_	_	B-VAR
stick	_	_	I-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
75	_	_	B-PARAM
and	_	_	O
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
50	_	_	B-PARAM
.	_	_	O
A	_	_	O
puck	_	_	B-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
2	_	_	B-PARAM
and	_	_	O
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
5	_	_	B-PARAM
.	_	_	O
The	_	_	O
store	_	_	O
owner	_	_	O
estimates	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
but	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
110	_	_	B-LIMIT
hockey	_	_	B-VAR
sticks	_	_	I-VAR
are	_	_	O
sold	_	_	O
each	_	_	O
month	_	_	O
.	_	_	O
The	_	_	O
owner	_	_	O
also	_	_	O
estimates	_	_	O
that	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
pucks	_	_	B-VAR
sold	_	_	O
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
hockey	_	_	B-VAR
sticks	_	_	I-VAR
sold	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
item	_	_	O
,	_	_	O
hockey	_	_	B-VAR
sticks	_	_	I-VAR
and	_	_	O
pucks	_	_	B-VAR
,	_	_	O
should	_	_	O
be	_	_	O
sold	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
movie	_	_	O
theatre	_	_	O
can	_	_	O
seat	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
people	_	_	O
.	_	_	O
A	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
15	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
moving	_	_	B-VAR
seat	_	_	I-VAR
ticket	_	_	O
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
10	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
regular	_	_	B-VAR
seat	_	_	I-VAR
ticket	_	_	O
.	_	_	O
The	_	_	O
theatre	_	_	O
reserves	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
15	_	_	B-LIMIT
seats	_	_	O
to	_	_	O
be	_	_	O
moving	_	_	B-VAR
seats	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
because	_	_	O
many	_	_	O
people	_	_	O
find	_	_	O
them	_	_	O
nauseating	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
people	_	_	O
prefer	_	_	O
sitting	_	_	O
in	_	_	O
regular	_	_	B-VAR
seats	_	_	I-VAR
than	_	_	O
in	_	_	O
moving	_	_	B-VAR
seats	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
tickets	_	_	O
for	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
seat	_	_	O
must	_	_	O
be	_	_	O
sold	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
banana	_	_	O
farmer	_	_	O
has	_	_	O
to	_	_	O
transport	_	_	O
his	_	_	O
bananas	_	_	O
using	_	_	O
cars	_	_	B-VAR
and	_	_	O
motor	_	_	B-VAR
bikes	_	_	I-VAR
.	_	_	O
Each	_	_	O
car	_	_	B-VAR
can	_	_	O
take	_	_	O
100	_	_	B-PARAM
bananas	_	_	B-OBJ_NAME
and	_	_	O
each	_	_	O
bike	_	_	B-VAR
can	_	_	O
take	_	_	O
30	_	_	B-PARAM
bananas	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
cost	_	_	O
of	_	_	O
running	_	_	O
each	_	_	O
car	_	_	B-VAR
is	_	_	O
$	_	_	O
10	_	_	B-PARAM
per	_	_	O
trip	_	_	O
and	_	_	O
the	_	_	O
cost	_	_	O
of	_	_	O
running	_	_	O
each	_	_	O
bike	_	_	B-VAR
is	_	_	O
$	_	_	O
6	_	_	B-PARAM
per	_	_	O
trip	_	_	O
.	_	_	O
The	_	_	O
farmer	_	_	O
wants	_	_	O
to	_	_	O
spend	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
200	_	_	B-LIMIT
on	_	_	O
transporting	_	_	O
his	_	_	O
bananas	_	_	O
.	_	_	O
Due	_	_	O
to	_	_	O
traffic	_	_	O
laws	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
cars	_	_	B-VAR
must	_	_	O
be	_	_	O
less	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
bikes	_	_	B-VAR
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	O
of	_	_	O
bananas	_	_	B-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
transported	_	_	O
.	_	_	O

A	_	_	O
hotel	_	_	O
employs	_	_	O
cleaners	_	_	B-VAR
and	_	_	O
receptionists	_	_	B-VAR
.	_	_	O
Cleaners	_	_	B-VAR
earn	_	_	B-OBJ_NAME
$	_	_	O
500	_	_	B-PARAM
per	_	_	O
week	_	_	O
and	_	_	O
receptionists	_	_	B-VAR
earn	_	_	B-OBJ_NAME
$	_	_	O
350	_	_	B-PARAM
per	_	_	O
week	_	_	O
.	_	_	O
The	_	_	O
hotel	_	_	O
requires	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
100	_	_	B-LIMIT
workers	_	_	O
of	_	_	O
whom	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
must	_	_	O
be	_	_	O
receptionists	_	_	B-VAR
.	_	_	O
To	_	_	O
keep	_	_	O
the	_	_	O
hotel	_	_	O
clean	_	_	O
and	_	_	O
running	_	_	O
smoothly	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
receptionists	_	_	B-VAR
should	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
a	_	_	O
third	_	_	B-PARAM
of	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
cleaners	_	_	B-VAR
.	_	_	O
The	_	_	O
hotel	_	_	O
wants	_	_	O
to	_	_	O
keep	_	_	O
the	_	_	O
weekly	_	_	O
wage	_	_	O
bill	_	_	O
below	_	_	B-CONST_DIR
$	_	_	O
30000	_	_	B-LIMIT
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
wage	_	_	B-OBJ_NAME
bill	_	_	I-OBJ_NAME
.	_	_	O

George	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
1000000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
the	_	_	O
oil	_	_	B-VAR
and	_	_	I-VAR
gas	_	_	I-VAR
,	_	_	O
tech	_	_	B-VAR
,	_	_	O
mining	_	_	B-VAR
,	_	_	O
and	_	_	O
retail	_	_	B-VAR
industries	_	_	I-VAR
.	_	_	O
George	_	_	O
is	_	_	O
a	_	_	O
smart	_	_	O
investor	_	_	O
and	_	_	O
he	_	_	O
knows	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
retail	_	_	B-VAR
industry	_	_	I-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
oil	_	_	B-VAR
and	_	_	I-VAR
gas	_	_	I-VAR
industry	_	_	O
.	_	_	O
Also	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
tech	_	_	B-VAR
industry	_	_	I-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
mining	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
Finally	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
28	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
total	_	_	O
amount	_	_	O
invested	_	_	O
can	_	_	O
be	_	_	O
in	_	_	O
the	_	_	O
retail	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
The	_	_	O
return	_	_	B-OBJ_NAME
on	_	_	O
investment	_	_	O
in	_	_	O
each	_	_	O
of	_	_	O
the	_	_	O
industries	_	_	O
is	_	_	O
as	_	_	O
follows	_	_	O
:	_	_	O
oil	_	_	B-VAR
and	_	_	I-VAR
gas	_	_	I-VAR
,	_	_	O
6	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
tech	_	_	B-VAR
,	_	_	O
8	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
mining	_	_	B-VAR
,	_	_	O
9	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
retail	_	_	B-VAR
,	_	_	O
11	_	_	B-PARAM
%	_	_	I-PARAM
.	_	_	O
George	_	_	O
wants	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
return	_	_	B-OBJ_NAME
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
that	_	_	O
will	_	_	O
allow	_	_	O
him	_	_	O
to	_	_	O
achieve	_	_	O
this	_	_	O
goal	_	_	O
.	_	_	O

A	_	_	O
hockey	_	_	O
arena	_	_	O
can	_	_	O
hold	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
300	_	_	B-LIMIT
people	_	_	O
and	_	_	O
has	_	_	O
both	_	_	O
heated	_	_	B-VAR
and	_	_	O
regular	_	_	B-VAR
seats	_	_	I-VAR
.	_	_	O
A	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
30	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
heated	_	_	B-VAR
seat	_	_	I-VAR
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
20	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
regular	_	_	B-VAR
seat	_	_	I-VAR
.	_	_	O
The	_	_	O
arena	_	_	O
reserves	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
50	_	_	B-LIMIT
seats	_	_	O
to	_	_	O
be	_	_	O
heated	_	_	B-VAR
seats	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
since	_	_	O
it	_	_	O
is	_	_	O
not	_	_	O
too	_	_	O
cold	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
people	_	_	O
prefer	_	_	O
to	_	_	O
sit	_	_	O
in	_	_	O
regular	_	_	B-VAR
seats	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
seat	_	_	O
must	_	_	O
be	_	_	O
sold	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O
What	_	_	O
is	_	_	O
the	_	_	O
maximum	_	_	O
profit	_	_	O
?	_	_	O

A	_	_	O
jacket	_	_	O
company	_	_	O
makes	_	_	O
winter	_	_	B-VAR
jackets	_	_	I-VAR
and	_	_	O
rain	_	_	B-VAR
jackets	_	_	I-VAR
.	_	_	O
Due	_	_	O
to	_	_	O
factory	_	_	O
limitations	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
60	_	_	B-LIMIT
winter	_	_	B-VAR
jackets	_	_	I-VAR
and	_	_	O
70	_	_	B-LIMIT
rain	_	_	B-VAR
jackets	_	_	I-VAR
can	_	_	O
be	_	_	O
made	_	_	O
daily	_	_	O
.	_	_	O
Projections	_	_	O
indicate	_	_	O
a	_	_	O
demand	_	_	O
of	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
winter	_	_	B-VAR
jackets	_	_	I-VAR
and	_	_	O
35	_	_	B-LIMIT
rain	_	_	B-VAR
jackets	_	_	I-VAR
daily	_	_	O
.	_	_	O
To	_	_	O
satisfy	_	_	O
a	_	_	O
contract	_	_	O
with	_	_	O
a	_	_	O
retail	_	_	O
store	_	_	O
,	_	_	O
a	_	_	O
total	_	_	O
of	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
80	_	_	B-LIMIT
jackets	_	_	O
must	_	_	O
be	_	_	O
made	_	_	O
daily	_	_	O
.	_	_	O
Because	_	_	O
the	_	_	O
factory	_	_	O
wants	_	_	O
to	_	_	O
get	_	_	O
rid	_	_	O
of	_	_	O
material	_	_	O
,	_	_	O
each	_	_	O
winter	_	_	B-VAR
jacket	_	_	I-VAR
sold	_	_	O
results	_	_	O
in	_	_	O
a	_	_	O
$	_	_	O
5	_	_	B-PARAM
loss	_	_	B-OBJ_NAME
.	_	_	O
However	_	_	O
,	_	_	O
each	_	_	O
rain	_	_	B-VAR
jacket	_	_	I-VAR
sold	_	_	O
results	_	_	O
in	_	_	O
a	_	_	O
$	_	_	O
50	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
jacket	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
daily	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
sandwich	_	_	O
store	_	_	O
makes	_	_	O
peanut	_	_	B-VAR
butter	_	_	I-VAR
sandwiches	_	_	I-VAR
and	_	_	O
chocolate	_	_	B-VAR
spread	_	_	I-VAR
sandwiches	_	_	I-VAR
.	_	_	O
The	_	_	O
store	_	_	O
only	_	_	O
has	_	_	O
enough	_	_	O
bread	_	_	O
to	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
150	_	_	B-LIMIT
sandwiches	_	_	O
.	_	_	O
To	_	_	O
stay	_	_	O
in	_	_	O
business	_	_	O
,	_	_	O
they	_	_	O
must	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
45	_	_	B-LIMIT
peanut	_	_	B-VAR
butter	_	_	I-VAR
sandwiches	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
65	_	_	B-LIMIT
chocolate	_	_	B-VAR
spread	_	_	I-VAR
sandwiches	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
they	_	_	O
only	_	_	O
have	_	_	O
enough	_	_	O
spread	_	_	O
,	_	_	O
peanut	_	_	O
butter	_	_	O
and	_	_	O
chocolate	_	_	O
,	_	_	O
to	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
80	_	_	B-LIMIT
peanut	_	_	B-VAR
butter	_	_	I-VAR
sandwiches	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
chocolate	_	_	B-VAR
spread	_	_	I-VAR
sandwiches	_	_	I-VAR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
peanut	_	_	B-VAR
butter	_	_	I-VAR
sandwich	_	_	I-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
chocolate	_	_	B-VAR
spread	_	_	I-VAR
sandwich	_	_	I-VAR
is	_	_	O
$	_	_	O
2	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
sandwich	_	_	O
should	_	_	O
the	_	_	O
store	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

You	_	_	O
are	_	_	O
playing	_	_	O
a	_	_	O
game	_	_	O
where	_	_	O
you	_	_	O
have	_	_	O
to	_	_	O
throw	_	_	O
a	_	_	O
ball	_	_	O
at	_	_	O
a	_	_	O
target	_	_	O
.	_	_	O
Throwing	_	_	O
a	_	_	O
small	_	_	B-VAR
ball	_	_	I-VAR
is	_	_	O
worth	_	_	O
5	_	_	B-PARAM
points	_	_	B-OBJ_NAME
and	_	_	O
throwing	_	_	O
a	_	_	O
large	_	_	B-VAR
ball	_	_	I-VAR
is	_	_	O
worth	_	_	O
2	_	_	B-PARAM
points	_	_	B-OBJ_NAME
.	_	_	O
You	_	_	O
can	_	_	O
throw	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
20	_	_	B-LIMIT
balls	_	_	O
total	_	_	O
.	_	_	O
You	_	_	O
must	_	_	O
also	_	_	O
throw	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
6	_	_	B-LIMIT
small	_	_	B-VAR
balls	_	_	I-VAR
and	_	_	O
5	_	_	B-LIMIT
large	_	_	B-VAR
balls	_	_	I-VAR
.	_	_	O
You	_	_	O
can	_	_	O
not	_	_	O
throw	_	_	O
more	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
12	_	_	B-LIMIT
of	_	_	O
either	_	_	O
type	_	_	O
.	_	_	O
Assuming	_	_	O
you	_	_	O
always	_	_	O
hit	_	_	O
the	_	_	O
target	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
balls	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
you	_	_	O
throw	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
your	_	_	O
score	_	_	B-OBJ_NAME
?	_	_	O
What	_	_	O
is	_	_	O
that	_	_	O
score	_	_	O
?	_	_	O

A	_	_	O
luggage	_	_	O
company	_	_	O
makes	_	_	O
carry	_	_	B-VAR
-	_	_	I-VAR
on	_	_	I-VAR
and	_	_	O
large	_	_	B-VAR
suitcases	_	_	I-VAR
in	_	_	O
their	_	_	O
factory	_	_	O
.	_	_	O
A	_	_	O
different	_	_	O
team	_	_	O
produces	_	_	O
each	_	_	O
kind	_	_	O
of	_	_	O
suitcase	_	_	O
and	_	_	O
each	_	_	O
team	_	_	O
has	_	_	O
a	_	_	O
different	_	_	O
maximum	_	_	B-CONST_DIR
production	_	_	O
rate	_	_	O
:	_	_	O
15	_	_	B-LIMIT
carry	_	_	B-VAR
-	_	_	I-VAR
on	_	_	I-VAR
suitcases	_	_	I-VAR
per	_	_	O
day	_	_	O
and	_	_	O
20	_	_	B-LIMIT
large	_	_	B-VAR
suitcases	_	_	I-VAR
per	_	_	O
day	_	_	O
respectively	_	_	O
.	_	_	O
Both	_	_	O
teams	_	_	O
require	_	_	O
use	_	_	O
of	_	_	O
a	_	_	O
sewing	_	_	O
machine	_	_	O
and	_	_	O
this	_	_	O
machine	_	_	O
can	_	_	O
process	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
25	_	_	B-LIMIT
suitcases	_	_	O
per	_	_	O
day	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
.	_	_	O
While	_	_	O
the	_	_	O
carry	_	_	B-VAR
-	_	_	I-VAR
on	_	_	I-VAR
suitcases	_	_	I-VAR
generate	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
100	_	_	B-PARAM
per	_	_	O
suitcase	_	_	O
,	_	_	O
the	_	_	O
large	_	_	B-VAR
suitcases	_	_	I-VAR
generate	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
150	_	_	B-PARAM
per	_	_	O
suitcase	_	_	O
.	_	_	O
Assuming	_	_	O
the	_	_	O
company	_	_	O
can	_	_	O
sell	_	_	O
all	_	_	O
the	_	_	O
suitcases	_	_	O
they	_	_	O
make	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
suitcase	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
family	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
500000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
both	_	_	O
the	_	_	O
textile	_	_	B-VAR
and	_	_	O
telecom	_	_	B-VAR
industries	_	_	I-VAR
.	_	_	O
Money	_	_	O
placed	_	_	O
in	_	_	O
the	_	_	O
textile	_	_	B-VAR
industry	_	_	I-VAR
yields	_	_	O
a	_	_	O
6	_	_	B-PARAM
%	_	_	I-PARAM
return	_	_	B-OBJ_NAME
while	_	_	O
money	_	_	O
placed	_	_	O
in	_	_	O
the	_	_	O
telecom	_	_	B-VAR
industry	_	_	I-VAR
yields	_	_	O
a	_	_	O
8	_	_	B-PARAM
%	_	_	I-PARAM
return	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
family	_	_	O
wants	_	_	O
to	_	_	O
place	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
30	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
investment	_	_	O
in	_	_	O
the	_	_	O
textile	_	_	B-VAR
industry	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
50	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
investment	_	_	O
in	_	_	O
the	_	_	O
telecom	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
How	_	_	O
much	_	_	O
money	_	_	O
should	_	_	O
be	_	_	O
placed	_	_	O
in	_	_	O
each	_	_	O
industry	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
return	_	_	B-OBJ_NAME
on	_	_	O
investment	_	_	O
?	_	_	O

A	_	_	O
costume	_	_	O
store	_	_	O
sells	_	_	O
police	_	_	B-VAR
officer	_	_	I-VAR
costumes	_	_	I-VAR
and	_	_	O
fireman	_	_	B-VAR
costumes	_	_	I-VAR
.	_	_	O
It	_	_	O
takes	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
police	_	_	B-VAR
officer	_	_	I-VAR
costume	_	_	I-VAR
and	_	_	O
12	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
fireman	_	_	B-VAR
costume	_	_	I-VAR
.	_	_	O
Due	_	_	O
to	_	_	O
popularity	_	_	O
,	_	_	O
the	_	_	O
store	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
fireman	_	_	B-VAR
costumes	_	_	I-VAR
as	_	_	O
police	_	_	B-VAR
officer	_	_	I-VAR
costumes	_	_	I-VAR
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
3000	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
to	_	_	O
make	_	_	O
costumes	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
police	_	_	B-VAR
officer	_	_	I-VAR
costume	_	_	I-VAR
is	_	_	O
$	_	_	O
10	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
fireman	_	_	B-VAR
costume	_	_	I-VAR
is	_	_	O
$	_	_	O
12	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Jacob	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
3000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
the	_	_	O
logging	_	_	B-VAR
and	_	_	O
shipping	_	_	B-VAR
industries	_	_	I-VAR
.	_	_	O
Each	_	_	O
dollar	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
logging	_	_	B-VAR
industry	_	_	I-VAR
yields	_	_	O
a	_	_	O
$	_	_	O
0.06	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
while	_	_	O
each	_	_	O
dollar	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
shipping	_	_	B-VAR
industry	_	_	I-VAR
yields	_	_	O
a	_	_	O
$	_	_	O
0.03	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
.	_	_	O
A	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
50	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
money	_	_	O
has	_	_	O
to	_	_	O
be	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
logging	_	_	B-VAR
industry	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
$	_	_	O
1000	_	_	B-LIMIT
has	_	_	O
to	_	_	O
be	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
shipping	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
How	_	_	O
much	_	_	O
should	_	_	O
he	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
bakery	_	_	O
only	_	_	B-CONST_DIR
has	_	_	O
1000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
blueberries	_	_	O
to	_	_	O
make	_	_	O
pies	_	_	B-VAR
and	_	_	O
small	_	_	O
tarts	_	_	B-VAR
.	_	_	O
Each	_	_	O
pie	_	_	B-VAR
needs	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
blueberries	_	_	O
and	_	_	O
each	_	_	O
tart	_	_	B-VAR
needs	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
blueberries	_	_	O
.	_	_	O
Since	_	_	O
tarts	_	_	B-VAR
are	_	_	O
easier	_	_	O
to	_	_	O
eat	_	_	O
quickly	_	_	O
,	_	_	O
the	_	_	O
bakery	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
tarts	_	_	B-VAR
as	_	_	O
pies	_	_	B-VAR
.	_	_	O
However	_	_	O
,	_	_	O
the	_	_	O
bakery	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
pies	_	_	B-VAR
.	_	_	O
If	_	_	O
each	_	_	O
pie	_	_	B-VAR
sold	_	_	O
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
8	_	_	B-PARAM
and	_	_	O
each	_	_	O
tart	_	_	B-VAR
sold	_	_	O
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
5	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
bakery	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
outlet	_	_	O
buys	_	_	O
and	_	_	O
sells	_	_	O
both	_	_	O
sofas	_	_	B-VAR
and	_	_	O
beds	_	_	B-VAR
.	_	_	O
Each	_	_	O
sofa	_	_	B-VAR
takes	_	_	O
8	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
of	_	_	O
space	_	_	O
while	_	_	O
each	_	_	O
bed	_	_	B-VAR
takes	_	_	O
12	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
of	_	_	O
space	_	_	O
.	_	_	O
The	_	_	O
outlet	_	_	O
has	_	_	O
500	_	_	B-LIMIT
sq	_	_	O
ft	_	_	O
of	_	_	O
space	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
Buying	_	_	O
a	_	_	O
sofa	_	_	B-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
buying	_	_	O
a	_	_	O
bed	_	_	B-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
300	_	_	B-PARAM
.	_	_	O
The	_	_	O
outlet	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
12500	_	_	B-PARAM
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
items	_	_	O
in	_	_	O
stock	_	_	O
have	_	_	O
to	_	_	O
be	_	_	O
sofas	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
sofa	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
100	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
bed	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
outlet	_	_	O
buy	_	_	O
and	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
young	_	_	O
entrepreneur	_	_	O
buys	_	_	O
and	_	_	O
sells	_	_	O
t	_	_	B-VAR
-	_	_	I-VAR
shirts	_	_	I-VAR
and	_	_	O
sweaters	_	_	B-VAR
.	_	_	O
He	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
1000	_	_	B-LIMIT
and	_	_	O
each	_	_	O
t	_	_	B-VAR
-	_	_	I-VAR
shirt	_	_	I-VAR
costs	_	_	O
$	_	_	O
20	_	_	B-PARAM
and	_	_	O
each	_	_	O
sweater	_	_	B-VAR
costs	_	_	O
$	_	_	O
30	_	_	B-PARAM
.	_	_	O
Each	_	_	O
t	_	_	B-VAR
-	_	_	I-VAR
shirt	_	_	I-VAR
is	_	_	O
then	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
15	_	_	B-PARAM
and	_	_	O
each	_	_	O
sweater	_	_	B-VAR
is	_	_	O
then	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
20	_	_	B-PARAM
.	_	_	O
The	_	_	O
young	_	_	O
man	_	_	O
estimates	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
but	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
40	_	_	B-LIMIT
t	_	_	B-VAR
-	_	_	I-VAR
shirts	_	_	I-VAR
are	_	_	O
sold	_	_	O
.	_	_	O
He	_	_	O
also	_	_	O
estimates	_	_	O
that	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
sweaters	_	_	B-VAR
sold	_	_	O
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
half	_	_	B-PARAM
the	_	_	O
number	_	_	O
of	_	_	O
t	_	_	B-VAR
-	_	_	I-VAR
shirts	_	_	I-VAR
sold	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
item	_	_	O
should	_	_	O
he	_	_	O
buy	_	_	O
and	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
company	_	_	O
wants	_	_	O
to	_	_	O
buy	_	_	O
ads	_	_	O
to	_	_	O
advertise	_	_	O
their	_	_	O
new	_	_	O
product	_	_	O
.	_	_	O
They	_	_	O
can	_	_	O
purchase	_	_	O
ads	_	_	O
to	_	_	O
be	_	_	O
placed	_	_	O
on	_	_	O
planes	_	_	B-VAR
,	_	_	O
blimps	_	_	B-VAR
,	_	_	O
and	_	_	O
hot	_	_	B-VAR
air	_	_	I-VAR
balloons	_	_	I-VAR
.	_	_	O
The	_	_	O
cost	_	_	O
for	_	_	O
an	_	_	O
ad	_	_	O
on	_	_	O
each	_	_	O
as	_	_	O
well	_	_	O
as	_	_	O
the	_	_	O
expected	_	_	O
viewership	_	_	O
is	_	_	O
given	_	_	O
.	_	_	O
On	_	_	O
planes	_	_	B-VAR
an	_	_	O
ad	_	_	O
costs	_	_	O
$	_	_	O
5000	_	_	B-PARAM
and	_	_	O
reaches	_	_	O
100000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
On	_	_	O
blimps	_	_	B-VAR
an	_	_	O
ad	_	_	O
costs	_	_	O
$	_	_	O
2000	_	_	B-PARAM
and	_	_	O
reaches	_	_	O
50000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
On	_	_	O
hot	_	_	B-VAR
air	_	_	I-VAR
balloons	_	_	I-VAR
an	_	_	O
ad	_	_	O
costs	_	_	O
$	_	_	O
1000	_	_	B-PARAM
and	_	_	O
reaches	_	_	O
20000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
airline	_	_	B-VAR
industry	_	_	O
limits	_	_	B-CONST_DIR
the	_	_	I-CONST_DIR
number	_	_	I-CONST_DIR
of	_	_	O
ads	_	_	O
from	_	_	O
the	_	_	O
same	_	_	O
to	_	_	O
company	_	_	O
to	_	_	O
5	_	_	B-LIMIT
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
half	_	_	B-LIMIT
the	_	_	O
total	_	_	O
number	_	_	O
of	_	_	O
ads	_	_	O
can	_	_	O
occur	_	_	O
on	_	_	O
hot	_	_	B-VAR
air	_	_	I-VAR
balloons	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
%	_	_	I-LIMIT
should	_	_	O
occur	_	_	O
on	_	_	O
blimps	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
company	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
50000	_	_	B-LIMIT
,	_	_	O
how	_	_	O
many	_	_	O
ads	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
they	_	_	O
purchase	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
viewership	_	_	B-OBJ_NAME
.	_	_	O

Jon	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
30000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
both	_	_	O
the	_	_	O
milk	_	_	B-VAR
and	_	_	O
cheese	_	_	B-VAR
industries	_	_	I-VAR
.	_	_	O
He	_	_	O
has	_	_	O
decided	_	_	O
that	_	_	O
the	_	_	O
money	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
milk	_	_	B-VAR
industry	_	_	I-VAR
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	O
as	_	_	O
much	_	_	O
as	_	_	O
the	_	_	O
money	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
cheese	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
he	_	_	O
has	_	_	O
limited	_	_	O
himself	_	_	O
to	_	_	O
invest	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
25000	_	_	B-LIMIT
in	_	_	O
the	_	_	O
milk	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
If	_	_	O
investments	_	_	O
in	_	_	O
the	_	_	O
milk	_	_	B-VAR
industry	_	_	I-VAR
earn	_	_	B-OBJ_NAME
8	_	_	B-PARAM
%	_	_	I-PARAM
and	_	_	O
investments	_	_	O
in	_	_	O
the	_	_	O
cheese	_	_	B-VAR
industry	_	_	I-VAR
earn	_	_	B-OBJ_NAME
6	_	_	B-PARAM
%	_	_	I-PARAM
,	_	_	O
how	_	_	O
much	_	_	O
should	_	_	O
he	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
earnings	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
tour	_	_	O
bus	_	_	O
has	_	_	B-CONST_DIR
100	_	_	B-LIMIT
seats	_	_	O
,	_	_	O
premium	_	_	B-VAR
seats	_	_	I-VAR
with	_	_	O
TV	_	_	O
's	_	_	O
and	_	_	O
regular	_	_	B-VAR
seats	_	_	I-VAR
.	_	_	O
A	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
40	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
premium	_	_	B-VAR
seat	_	_	I-VAR
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
20	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
regular	_	_	B-VAR
seat	_	_	I-VAR
.	_	_	O
The	_	_	O
tour	_	_	O
bus	_	_	O
reserves	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
seats	_	_	O
to	_	_	O
be	_	_	O
premium	_	_	B-VAR
but	_	_	O
because	_	_	O
there	_	_	O
is	_	_	O
usually	_	_	O
nothing	_	_	O
good	_	_	O
on	_	_	O
tv	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
people	_	_	O
prefer	_	_	O
regular	_	_	B-VAR
seats	_	_	I-VAR
to	_	_	O
premium	_	_	B-VAR
seats	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
tickets	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
be	_	_	O
sold	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
orange	_	_	O
farm	_	_	O
is	_	_	O
trying	_	_	O
to	_	_	O
send	_	_	O
their	_	_	O
oranges	_	_	O
to	_	_	O
the	_	_	O
city	_	_	O
.	_	_	O
They	_	_	O
can	_	_	O
either	_	_	O
send	_	_	O
them	_	_	O
by	_	_	O
train	_	_	B-VAR
or	_	_	O
by	_	_	O
car	_	_	B-VAR
.	_	_	O
Each	_	_	O
train	_	_	B-VAR
trip	_	_	I-VAR
costs	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
can	_	_	O
take	_	_	O
500	_	_	B-PARAM
oranges	_	_	B-OBJ_NAME
while	_	_	O
each	_	_	O
car	_	_	B-VAR
trip	_	_	I-VAR
costs	_	_	O
$	_	_	O
30	_	_	B-PARAM
and	_	_	O
can	_	_	O
take	_	_	O
200	_	_	B-PARAM
oranges	_	_	B-OBJ_NAME
.	_	_	O
Due	_	_	O
to	_	_	O
scheduling	_	_	O
issues	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
train	_	_	B-VAR
trips	_	_	I-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
car	_	_	B-VAR
trips	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
farm	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
500	_	_	B-LIMIT
,	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
oranges	_	_	I-OBJ_NAME
they	_	_	O
can	_	_	O
send	_	_	O
.	_	_	O

A	_	_	O
research	_	_	O
lab	_	_	O
employs	_	_	O
undergraduate	_	_	B-VAR
students	_	_	I-VAR
earning	_	_	B-OBJ_NAME
$	_	_	O
100	_	_	B-PARAM
a	_	_	O
week	_	_	O
and	_	_	O
graduate	_	_	B-VAR
students	_	_	I-VAR
earning	_	_	B-OBJ_NAME
$	_	_	O
300	_	_	B-PARAM
a	_	_	O
week	_	_	O
.	_	_	O
The	_	_	O
lab	_	_	O
requires	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
students	_	_	O
,	_	_	O
of	_	_	O
whom	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
must	_	_	O
be	_	_	O
graduate	_	_	B-VAR
students	_	_	I-VAR
.	_	_	O
To	_	_	O
make	_	_	O
sure	_	_	O
there	_	_	O
is	_	_	O
enough	_	_	O
experience	_	_	O
in	_	_	O
the	_	_	O
lab	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
graduate	_	_	B-VAR
students	_	_	I-VAR
should	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
a	_	_	O
third	_	_	B-PARAM
the	_	_	O
number	_	_	O
of	_	_	O
undergraduate	_	_	B-VAR
students	_	_	I-VAR
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
weekly	_	_	O
wages	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
woman	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
300000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
a	_	_	O
chocolate	_	_	B-VAR
company	_	_	I-VAR
,	_	_	O
a	_	_	O
coffee	_	_	B-VAR
company	_	_	I-VAR
,	_	_	O
a	_	_	O
peanut	_	_	B-VAR
butter	_	_	I-VAR
company	_	_	I-VAR
,	_	_	O
and	_	_	O
a	_	_	O
maple	_	_	B-VAR
syrup	_	_	I-VAR
company	_	_	I-VAR
.	_	_	O
The	_	_	O
return	_	_	B-OBJ_NAME
on	_	_	O
investment	_	_	O
for	_	_	O
each	_	_	O
company	_	_	O
is	_	_	O
as	_	_	O
follows	_	_	O
:	_	_	O
chocolate	_	_	B-VAR
company	_	_	I-VAR
,	_	_	O
5	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
coffee	_	_	B-VAR
company	_	_	I-VAR
,	_	_	O
10	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
peanut	_	_	B-VAR
butter	_	_	I-VAR
company	_	_	I-VAR
,	_	_	O
7	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
maple	_	_	B-VAR
syrup	_	_	I-VAR
company	_	_	I-VAR
6	_	_	B-PARAM
%	_	_	I-PARAM
.	_	_	O
There	_	_	O
are	_	_	O
some	_	_	O
restrictions	_	_	O
on	_	_	O
her	_	_	O
investment	_	_	O
.	_	_	O
The	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
chocolate	_	_	B-VAR
company	_	_	I-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
maple	_	_	B-VAR
syrup	_	_	I-VAR
company	_	_	I-VAR
.	_	_	O
Also	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
coffee	_	_	B-VAR
company	_	_	I-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
peanut	_	_	B-VAR
butter	_	_	I-VAR
company	_	_	I-VAR
.	_	_	O
If	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
20	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
her	_	_	O
money	_	_	O
can	_	_	O
be	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
maple	_	_	B-VAR
syrup	_	_	I-VAR
company	_	_	I-VAR
,	_	_	O
how	_	_	O
much	_	_	O
should	_	_	O
she	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
return	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
gardener	_	_	O
has	_	_	O
50	_	_	B-LIMIT
acres	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
growing	_	_	O
lavender	_	_	B-VAR
and	_	_	O
tulips	_	_	B-VAR
.	_	_	O
The	_	_	O
gardener	_	_	O
must	_	_	O
grow	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
lavender	_	_	B-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
8	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
tulips	_	_	B-VAR
.	_	_	O
Even	_	_	O
though	_	_	O
lavenders	_	_	B-VAR
sell	_	_	O
better	_	_	O
,	_	_	O
the	_	_	O
gardener	_	_	O
can	_	_	O
grow	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
twice	_	_	B-PARAM
the	_	_	O
amount	_	_	O
of	_	_	O
lavender	_	_	B-VAR
as	_	_	O
tulips	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
lavender	_	_	B-VAR
is	_	_	O
$	_	_	O
250	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
tulips	_	_	B-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
grown	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
tower	_	_	O
which	_	_	O
is	_	_	O
a	_	_	O
tourist	_	_	O
attraction	_	_	O
offers	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
tickets	_	_	O
.	_	_	O
There	_	_	O
is	_	_	O
a	_	_	O
premium	_	_	B-VAR
ticket	_	_	I-VAR
which	_	_	O
takes	_	_	O
you	_	_	O
to	_	_	O
the	_	_	O
very	_	_	O
top	_	_	O
,	_	_	O
and	_	_	O
a	_	_	O
regular	_	_	B-VAR
ticket	_	_	I-VAR
that	_	_	O
takes	_	_	O
you	_	_	O
to	_	_	O
the	_	_	O
viewing	_	_	O
deck	_	_	O
.	_	_	O
The	_	_	O
attraction	_	_	O
sells	_	_	B-CONST_DIR
500	_	_	B-LIMIT
tickets	_	_	O
,	_	_	O
of	_	_	O
which	_	_	O
they	_	_	O
reserve	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
to	_	_	O
be	_	_	O
premium	_	_	B-VAR
.	_	_	O
Since	_	_	O
most	_	_	O
people	_	_	O
just	_	_	O
want	_	_	O
to	_	_	O
go	_	_	O
to	_	_	O
the	_	_	O
viewing	_	_	O
deck	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
people	_	_	O
prefer	_	_	O
regular	_	_	B-VAR
tickets	_	_	I-VAR
than	_	_	O
premium	_	_	B-VAR
tickets	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
premium	_	_	B-VAR
ticket	_	_	I-VAR
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
regular	_	_	B-VAR
ticker	_	_	I-VAR
is	_	_	O
$	_	_	O
30	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
sold	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
bakery	_	_	O
makes	_	_	O
chocolate	_	_	B-VAR
and	_	_	O
maple	_	_	B-VAR
donuts	_	_	I-VAR
.	_	_	O
There	_	_	O
is	_	_	O
a	_	_	O
daily	_	_	O
demand	_	_	O
of	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
chocolate	_	_	B-VAR
donuts	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
75	_	_	B-LIMIT
maple	_	_	B-VAR
donuts	_	_	I-VAR
.	_	_	O
However	_	_	O
the	_	_	O
bakery	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
chocolate	_	_	B-VAR
donuts	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
150	_	_	B-LIMIT
maple	_	_	B-VAR
donuts	_	_	I-VAR
.	_	_	O
They	_	_	O
have	_	_	O
a	_	_	O
contract	_	_	O
with	_	_	O
a	_	_	O
local	_	_	O
grocery	_	_	O
store	_	_	O
and	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
200	_	_	B-LIMIT
donuts	_	_	O
total	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
chocolate	_	_	B-VAR
donut	_	_	I-VAR
is	_	_	O
$	_	_	O
2	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
maple	_	_	B-VAR
donut	_	_	I-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
food	_	_	O
truck	_	_	O
sells	_	_	O
fries	_	_	B-VAR
and	_	_	O
onion	_	_	B-VAR
rings	_	_	I-VAR
.	_	_	O
To	_	_	O
stay	_	_	O
in	_	_	O
business	_	_	O
,	_	_	O
they	_	_	O
must	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
orders	_	_	O
of	_	_	O
fries	_	_	B-VAR
but	_	_	O
they	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
50	_	_	B-LIMIT
orders	_	_	O
of	_	_	O
fries	_	_	B-VAR
.	_	_	O
Also	_	_	O
,	_	_	O
they	_	_	O
must	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
orders	_	_	O
of	_	_	O
onion	_	_	B-VAR
rings	_	_	I-VAR
but	_	_	O
they	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
40	_	_	B-LIMIT
orders	_	_	O
of	_	_	O
onion	_	_	B-VAR
rings	_	_	I-VAR
.	_	_	O
Due	_	_	O
to	_	_	O
limited	_	_	O
fryer	_	_	O
time	_	_	O
,	_	_	O
the	_	_	O
food	_	_	O
truck	_	_	O
can	_	_	O
only	_	_	B-CONST_DIR
sell	_	_	O
50	_	_	B-LIMIT
orders	_	_	O
total	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
order	_	_	O
of	_	_	O
fries	_	_	B-VAR
is	_	_	O
$	_	_	O
4	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
order	_	_	O
of	_	_	O
onion	_	_	B-VAR
rings	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
orders	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

In	_	_	O
a	_	_	O
spelling	_	_	O
bee	_	_	O
,	_	_	O
you	_	_	O
can	_	_	O
spell	_	_	O
short	_	_	B-VAR
words	_	_	I-VAR
worth	_	_	O
3	_	_	B-PARAM
points	_	_	B-OBJ_NAME
or	_	_	O
long	_	_	B-VAR
words	_	_	I-VAR
worth	_	_	O
6	_	_	B-PARAM
points	_	_	B-OBJ_NAME
.	_	_	O
You	_	_	O
must	_	_	O
spell	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
short	_	_	B-VAR
words	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
2	_	_	B-LIMIT
long	_	_	B-VAR
words	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
due	_	_	O
to	_	_	O
time	_	_	O
restrictions	_	_	O
you	_	_	O
can	_	_	O
spell	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
10	_	_	B-LIMIT
short	_	_	B-VAR
words	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
5	_	_	B-LIMIT
long	_	_	B-VAR
words	_	_	I-VAR
.	_	_	O
In	_	_	O
total	_	_	O
,	_	_	O
you	_	_	O
can	_	_	O
spell	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
10	_	_	B-LIMIT
words	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
length	_	_	O
of	_	_	O
word	_	_	O
should	_	_	O
you	_	_	O
spell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
your	_	_	O
points	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
jewelry	_	_	O
company	_	_	O
makes	_	_	O
sapphire	_	_	B-VAR
and	_	_	O
ruby	_	_	B-VAR
rings	_	_	I-VAR
.	_	_	O
The	_	_	O
sapphire	_	_	B-VAR
rings	_	_	I-VAR
are	_	_	O
made	_	_	O
by	_	_	O
a	_	_	O
team	_	_	O
who	_	_	O
cam	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
10	_	_	B-LIMIT
sapphire	_	_	B-VAR
rings	_	_	I-VAR
per	_	_	O
day	_	_	O
.	_	_	O
The	_	_	O
ruby	_	_	B-VAR
rings	_	_	I-VAR
are	_	_	O
made	_	_	O
by	_	_	O
a	_	_	O
team	_	_	O
who	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
15	_	_	B-LIMIT
ruby	_	_	B-VAR
rings	_	_	I-VAR
per	_	_	O
day	_	_	O
.	_	_	O
All	_	_	O
rings	_	_	O
have	_	_	O
to	_	_	O
be	_	_	O
approved	_	_	O
by	_	_	O
a	_	_	O
master	_	_	O
jeweler	_	_	O
and	_	_	O
he	_	_	O
can	_	_	O
check	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
15	_	_	B-LIMIT
rings	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
sapphire	_	_	B-VAR
ring	_	_	I-VAR
is	_	_	O
$	_	_	O
500	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
ruby	_	_	B-VAR
ring	_	_	I-VAR
is	_	_	O
$	_	_	O
400	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
jewelry	_	_	O
company	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
pen	_	_	O
store	_	_	O
sells	_	_	O
regular	_	_	B-VAR
pens	_	_	I-VAR
and	_	_	O
premium	_	_	B-VAR
pens	_	_	I-VAR
made	_	_	O
of	_	_	O
higher	_	_	O
quality	_	_	O
material	_	_	O
.	_	_	O
They	_	_	O
can	_	_	O
sell	_	_	O
x1	_	_	O
regular	_	_	B-VAR
pens	_	_	I-VAR
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
3	_	_	B-PARAM
each	_	_	O
and	_	_	O
x2	_	_	O
premium	_	_	B-VAR
pens	_	_	I-VAR
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
8	_	_	B-PARAM
each	_	_	O
(	_	_	O
x1	_	_	O
nd	_	_	O
x2	_	_	O
are	_	_	O
both	_	_	O
greater	_	_	O
than	_	_	O
or	_	_	O
equal	_	_	O
to	_	_	O
0	_	_	O
)	_	_	O
.	_	_	O
Daily	_	_	O
demand	_	_	O
for	_	_	O
regular	_	_	B-VAR
pens	_	_	I-VAR
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
and	_	_	O
daily	_	_	O
demand	_	_	O
for	_	_	O
premium	_	_	B-VAR
pens	_	_	I-VAR
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
50	_	_	B-LIMIT
.	_	_	O
If	_	_	O
the	_	_	O
store	_	_	O
can	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
75	_	_	B-LIMIT
pens	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
per	_	_	O
day	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
pen	_	_	O
should	_	_	O
they	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Amanda	_	_	O
has	_	_	B-CONST_DIR
4000	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
to	_	_	O
grow	_	_	O
apple	_	_	B-VAR
and	_	_	O
peach	_	_	B-VAR
trees	_	_	I-VAR
.	_	_	O
Apple	_	_	B-VAR
trees	_	_	I-VAR
cost	_	_	O
$	_	_	O
50	_	_	B-PARAM
for	_	_	O
their	_	_	O
saplings	_	_	O
,	_	_	O
and	_	_	O
they	_	_	O
take	_	_	O
3	_	_	B-PARAM
hours	_	_	O
to	_	_	O
maintain	_	_	O
per	_	_	O
acre	_	_	O
.	_	_	O
Peach	_	_	B-VAR
trees	_	_	I-VAR
cost	_	_	O
$	_	_	O
80	_	_	B-PARAM
for	_	_	O
their	_	_	O
saplings	_	_	O
and	_	_	O
take	_	_	O
5	_	_	B-PARAM
hours	_	_	O
to	_	_	O
maintain	_	_	O
per	_	_	O
acre	_	_	O
.	_	_	O
Amanda	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
30000	_	_	B-LIMIT
for	_	_	O
saplings	_	_	O
and	_	_	O
has	_	_	O
600	_	_	B-LIMIT
available	_	_	B-CONST_DIR
hours	_	_	O
for	_	_	O
maintenance	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
apples	_	_	B-VAR
is	_	_	O
$	_	_	O
15	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
peaches	_	_	B-VAR
is	_	_	O
$	_	_	O
25	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
grown	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
cafe	_	_	O
makes	_	_	O
lattes	_	_	B-VAR
and	_	_	O
cappuccinos	_	_	B-VAR
.	_	_	O
Both	_	_	O
of	_	_	O
which	_	_	O
require	_	_	O
milk	_	_	O
and	_	_	O
coffee	_	_	O
.	_	_	O
Each	_	_	O
latte	_	_	B-VAR
needs	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
milk	_	_	O
and	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
coffee	_	_	O
.	_	_	O
Each	_	_	O
cappuccino	_	_	B-VAR
requires	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
milk	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
coffee	_	_	O
.	_	_	O
The	_	_	O
cafe	_	_	O
has	_	_	O
a	_	_	B-CONST_DIR
total	_	_	I-CONST_DIR
of	_	_	I-CONST_DIR
80	_	_	B-LIMIT
units	_	_	O
of	_	_	O
milk	_	_	O
and	_	_	O
50	_	_	B-LIMIT
units	_	_	O
of	_	_	O
coffee	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
latte	_	_	B-VAR
is	_	_	O
$	_	_	O
2	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
cappuccino	_	_	B-VAR
is	_	_	O
$	_	_	O
1	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
sandwich	_	_	O
shop	_	_	O
produces	_	_	O
premium	_	_	B-VAR
and	_	_	O
regular	_	_	B-VAR
versions	_	_	O
of	_	_	O
their	_	_	O
sandwiches	_	_	O
.	_	_	O
A	_	_	O
premium	_	_	B-VAR
sandwich	_	_	I-VAR
takes	_	_	O
6	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
preparation	_	_	O
and	_	_	O
requires	_	_	O
5	_	_	B-PARAM
slices	_	_	O
of	_	_	O
meat	_	_	O
to	_	_	O
make	_	_	O
.	_	_	O
A	_	_	O
regular	_	_	B-VAR
sandwich	_	_	I-VAR
takes	_	_	O
4	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
preparation	_	_	O
and	_	_	O
requires	_	_	O
1	_	_	B-PARAM
slice	_	_	O
of	_	_	O
meat	_	_	O
to	_	_	O
make	_	_	O
.	_	_	O
The	_	_	O
shop	_	_	O
has	_	_	O
in	_	_	B-CONST_DIR
total	_	_	I-CONST_DIR
400	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
preparation	_	_	O
time	_	_	O
and	_	_	O
100	_	_	B-LIMIT
slices	_	_	O
of	_	_	O
meat	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
premium	_	_	B-VAR
sandwich	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
regular	_	_	B-VAR
sandwich	_	_	I-VAR
is	_	_	O
$	_	_	O
1	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
tutoring	_	_	O
company	_	_	O
wants	_	_	O
to	_	_	O
advertise	_	_	O
their	_	_	O
service	_	_	O
using	_	_	O
advertisements	_	_	O
on	_	_	O
the	_	_	O
internet	_	_	O
.	_	_	O
They	_	_	O
decided	_	_	O
to	_	_	O
use	_	_	O
three	_	_	O
types	_	_	O
of	_	_	O
advertisements	_	_	O
:	_	_	O
advertisements	_	_	O
on	_	_	O
search	_	_	B-VAR
engines	_	_	I-VAR
,	_	_	O
advertisements	_	_	O
on	_	_	O
videos	_	_	B-VAR
,	_	_	O
and	_	_	O
advertisements	_	_	O
on	_	_	O
social	_	_	B-VAR
media	_	_	I-VAR
.	_	_	O
The	_	_	O
cost	_	_	O
and	_	_	O
expected	_	_	O
influence	_	_	B-OBJ_NAME
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
advertisement	_	_	O
are	_	_	O
given	_	_	O
as	_	_	O
follows	_	_	O
.	_	_	O
An	_	_	O
advertisement	_	_	O
on	_	_	O
a	_	_	O
search	_	_	B-VAR
engine	_	_	I-VAR
costs	_	_	O
$	_	_	O
50000	_	_	B-PARAM
and	_	_	O
reaches	_	_	B-OBJ_NAME
100000	_	_	B-PARAM
users	_	_	O
.	_	_	O
An	_	_	O
advertisement	_	_	O
on	_	_	O
a	_	_	O
video	_	_	B-VAR
costs	_	_	O
$	_	_	O
5000	_	_	B-PARAM
and	_	_	O
reaches	_	_	B-OBJ_NAME
7000	_	_	B-PARAM
users	_	_	O
.	_	_	O
Finally	_	_	O
,	_	_	O
an	_	_	O
advertisement	_	_	O
on	_	_	O
social	_	_	B-VAR
media	_	_	I-VAR
costs	_	_	O
$	_	_	O
1000	_	_	B-PARAM
and	_	_	O
reaches	_	_	B-OBJ_NAME
800	_	_	B-PARAM
users	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
4	_	_	B-LIMIT
advertisements	_	_	O
on	_	_	O
videos	_	_	B-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
a	_	_	O
half	_	_	B-LIMIT
of	_	_	O
all	_	_	O
advertisements	_	_	O
must	_	_	O
be	_	_	O
on	_	_	O
social	_	_	B-VAR
media	_	_	I-VAR
.	_	_	O
Finally	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
advertisements	_	_	O
should	_	_	O
be	_	_	O
on	_	_	O
search	_	_	B-VAR
engines	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
weekly	_	_	O
budget	_	_	B-CONST_DIR
is	_	_	O
$	_	_	O
850000	_	_	B-LIMIT
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
commercial	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
influence	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
sauce	_	_	O
factory	_	_	O
mass	_	_	O
produces	_	_	O
pasta	_	_	B-VAR
sauce	_	_	I-VAR
and	_	_	O
barbecue	_	_	B-VAR
sauce	_	_	I-VAR
on	_	_	O
an	_	_	O
assembly	_	_	O
line	_	_	O
.	_	_	O
Each	_	_	O
jar	_	_	O
of	_	_	O
pasta	_	_	B-VAR
sauce	_	_	I-VAR
takes	_	_	O
1	_	_	B-PARAM
minute	_	_	O
on	_	_	O
the	_	_	O
filling	_	_	O
machine	_	_	O
and	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
jarring	_	_	O
machine	_	_	O
.	_	_	O
Each	_	_	O
jar	_	_	O
of	_	_	O
barbecue	_	_	B-VAR
sauce	_	_	I-VAR
takes	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
filling	_	_	O
machine	_	_	O
and	_	_	O
4	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
jarring	_	_	O
machine	_	_	O
.	_	_	O
The	_	_	O
filling	_	_	O
machine	_	_	O
is	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
12500	_	_	B-LIMIT
minutes	_	_	O
while	_	_	O
the	_	_	O
jarring	_	_	O
machine	_	_	O
is	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
20000	_	_	B-LIMIT
minutes	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
jar	_	_	O
of	_	_	O
pasta	_	_	B-VAR
sauce	_	_	I-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
jar	_	_	O
of	_	_	O
barbecue	_	_	B-VAR
sauce	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
jars	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
vacuum	_	_	O
repair	_	_	O
company	_	_	O
repairs	_	_	O
home	_	_	B-VAR
vacuums	_	_	I-VAR
and	_	_	O
shop	_	_	B-VAR
vacuums	_	_	I-VAR
.	_	_	O
Each	_	_	O
shop	_	_	B-VAR
vacuum	_	_	I-VAR
requires	_	_	O
1	_	_	B-PARAM
hour	_	_	O
of	_	_	O
disassembly	_	_	O
and	_	_	O
2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
repair	_	_	O
.	_	_	O
Each	_	_	O
home	_	_	B-VAR
vacuum	_	_	I-VAR
requires	_	_	O
0.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
disassembly	_	_	O
and	_	_	O
1	_	_	B-PARAM
hour	_	_	O
of	_	_	O
repair	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
300	_	_	B-LIMIT
hours	_	_	O
for	_	_	O
disassembly	_	_	O
and	_	_	O
400	_	_	B-LIMIT
hours	_	_	O
for	_	_	O
repair	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
home	_	_	B-VAR
vacuum	_	_	I-VAR
repaired	_	_	O
is	_	_	O
$	_	_	O
20	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
shop	_	_	B-VAR
vacuum	_	_	I-VAR
repaired	_	_	O
is	_	_	O
$	_	_	O
35	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
repair	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
brunch	_	_	O
restaurant	_	_	O
makes	_	_	O
eggs	_	_	B-VAR
benedicts	_	_	I-VAR
and	_	_	O
hashbrowns	_	_	B-VAR
.	_	_	I-VAR
Each	_	_	O
eggs	_	_	B-VAR
benedict	_	_	I-VAR
requires	_	_	O
10	_	_	B-PARAM
grams	_	_	O
of	_	_	O
butter	_	_	O
and	_	_	O
1	_	_	B-PARAM
egg	_	_	O
.	_	_	O
Each	_	_	O
hashbrown	_	_	B-VAR
requires	_	_	O
5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
butter	_	_	O
and	_	_	O
2	_	_	B-PARAM
eggs	_	_	O
.	_	_	O
The	_	_	O
restaurant	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
5000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
butter	_	_	O
and	_	_	O
600	_	_	B-LIMIT
eggs	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
eggs	_	_	B-VAR
benedict	_	_	I-VAR
is	_	_	O
$	_	_	O
4	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
hashbrown	_	_	B-VAR
is	_	_	O
$	_	_	O
2	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
lighting	_	_	O
company	_	_	O
makes	_	_	O
desk	_	_	B-VAR
lamps	_	_	I-VAR
and	_	_	O
chandeliers	_	_	B-VAR
.	_	_	O
Each	_	_	O
desk	_	_	B-VAR
lamp	_	_	I-VAR
takes	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
manufacturing	_	_	O
time	_	_	O
and	_	_	O
1	_	_	B-PARAM
light	_	_	O
bulb	_	_	O
.	_	_	O
Each	_	_	O
chandelier	_	_	B-VAR
takes	_	_	O
60	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
manufacturing	_	_	O
time	_	_	O
and	_	_	O
requires	_	_	O
15	_	_	B-PARAM
light	_	_	O
bulbs	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
40	_	_	B-LIMIT
desk	_	_	B-VAR
lamps	_	_	I-VAR
.	_	_	O
They	_	_	O
have	_	_	O
1500	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
manufacturing	_	_	O
time	_	_	O
available	_	_	B-CONST_DIR
and	_	_	O
300	_	_	B-LIMIT
light	_	_	O
bulbs	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
desk	_	_	B-VAR
lamp	_	_	I-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
chandelier	_	_	B-VAR
is	_	_	O
$	_	_	O
500	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Kevin	_	_	O
needs	_	_	O
vitamins	_	_	O
to	_	_	O
supplement	_	_	O
his	_	_	O
diet	_	_	O
.	_	_	O
He	_	_	O
needs	_	_	O
to	_	_	O
get	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
25	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamin	_	_	O
A	_	_	O
and	_	_	O
40	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamin	_	_	O
B	_	_	O
everyday	_	_	O
.	_	_	O
In	_	_	O
order	_	_	O
to	_	_	O
do	_	_	O
so	_	_	O
,	_	_	O
he	_	_	O
can	_	_	O
buy	_	_	O
capsules	_	_	O
named	_	_	O
Special	_	_	B-VAR
Formula	_	_	I-VAR
and	_	_	O
One	_	_	B-VAR
Daily	_	_	I-VAR
.	_	_	O
Each	_	_	O
capsule	_	_	O
of	_	_	O
Special	_	_	B-VAR
Formula	_	_	I-VAR
contains	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
A	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
B.	_	_	O
Each	_	_	O
capsule	_	_	O
of	_	_	O
One	_	_	B-VAR
Daily	_	_	I-VAR
contains	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
A	_	_	O
and	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
B.	_	_	O
If	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
Special	_	_	B-VAR
Formula	_	_	I-VAR
capsule	_	_	O
is	_	_	O
$	_	_	O
0.50	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
One	_	_	B-VAR
Daily	_	_	I-VAR
capsule	_	_	O
is	_	_	O
$	_	_	O
0.20	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
buy	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
cost	_	_	B-OBJ_NAME
?	_	_	O

Two	_	_	O
different	_	_	O
food	_	_	O
groups	_	_	O
,	_	_	O
grains	_	_	B-VAR
and	_	_	O
vegetables	_	_	B-VAR
,	_	_	O
are	_	_	O
eaten	_	_	O
everyday	_	_	O
to	_	_	O
get	_	_	O
iron	_	_	O
and	_	_	O
fiber	_	_	O
.	_	_	O
A	_	_	O
serving	_	_	O
of	_	_	O
vegetables	_	_	B-VAR
contains	_	_	O
15	_	_	B-PARAM
grams	_	_	O
of	_	_	O
iron	_	_	O
and	_	_	O
25	_	_	B-PARAM
grams	_	_	O
of	_	_	O
fiber	_	_	O
.	_	_	O
A	_	_	O
serving	_	_	O
of	_	_	O
grains	_	_	B-VAR
contains	_	_	O
30	_	_	B-PARAM
grams	_	_	O
of	_	_	O
iron	_	_	O
and	_	_	O
5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
fiber	_	_	O
.	_	_	O
Daily	_	_	O
requirements	_	_	O
are	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
iron	_	_	O
and	_	_	O
150	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
fiber	_	_	O
.	_	_	O
If	_	_	O
a	_	_	O
serving	_	_	O
of	_	_	O
grains	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
0.40	_	_	B-PARAM
and	_	_	O
a	_	_	O
serving	_	_	O
of	_	_	O
vegetables	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
0.60	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
eaten	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
dessert	_	_	O
restaurant	_	_	O
makes	_	_	O
cakes	_	_	B-VAR
and	_	_	O
cupcakes	_	_	B-VAR
.	_	_	O
Each	_	_	O
type	_	_	O
of	_	_	O
dessert	_	_	O
requires	_	_	O
time	_	_	O
in	_	_	O
the	_	_	O
oven	_	_	O
and	_	_	O
cooling	_	_	O
rack	_	_	O
.	_	_	O
A	_	_	O
batch	_	_	O
of	_	_	O
cupcakes	_	_	B-VAR
requires	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
in	_	_	O
the	_	_	O
oven	_	_	O
and	_	_	O
60	_	_	B-PARAM
minutes	_	_	O
cooling	_	_	O
.	_	_	O
A	_	_	O
batch	_	_	O
of	_	_	O
cakes	_	_	B-VAR
requires	_	_	O
60	_	_	B-PARAM
minutes	_	_	O
in	_	_	O
the	_	_	O
oven	_	_	O
and	_	_	O
120	_	_	B-PARAM
minutes	_	_	O
cooling	_	_	O
.	_	_	O
Additionally	_	_	O
,	_	_	O
the	_	_	O
oven	_	_	O
is	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
9000	_	_	B-LIMIT
minutes	_	_	O
per	_	_	O
month	_	_	O
,	_	_	O
the	_	_	O
cooling	_	_	O
rack	_	_	O
is	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
12000	_	_	B-LIMIT
minutes	_	_	O
per	_	_	O
month	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
batch	_	_	O
of	_	_	O
cupcakes	_	_	B-VAR
is	_	_	O
$	_	_	O
10	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
batch	_	_	O
of	_	_	O
cake	_	_	B-VAR
is	_	_	O
$	_	_	O
25	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
batches	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
apple	_	_	O
farm	_	_	O
produces	_	_	O
Granny	_	_	B-VAR
Smith	_	_	I-VAR
apples	_	_	I-VAR
and	_	_	O
McIntosh	_	_	B-VAR
apples	_	_	I-VAR
.	_	_	O
They	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
Granny	_	_	B-VAR
Smith	_	_	I-VAR
apples	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
120	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
McIntosh	_	_	B-VAR
apples	_	_	I-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
they	_	_	O
must	_	_	O
supply	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
25	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
Granny	_	_	B-VAR
Smith	_	_	I-VAR
apples	_	_	I-VAR
and	_	_	O
50	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
McIntosh	_	_	B-VAR
apples	_	_	I-VAR
per	_	_	O
day	_	_	O
.	_	_	O
Both	_	_	O
require	_	_	O
time	_	_	O
in	_	_	O
a	_	_	O
cleaning	_	_	O
machine	_	_	O
.	_	_	O
Each	_	_	O
kg	_	_	O
of	_	_	O
Granny	_	_	B-VAR
Smith	_	_	I-VAR
apples	_	_	I-VAR
and	_	_	O
McIntosh	_	_	B-VAR
apples	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
hours	_	_	O
at	_	_	O
the	_	_	O
cleaning	_	_	O
machine	_	_	O
.	_	_	O
The	_	_	O
cleaning	_	_	O
machine	_	_	O
is	_	_	O
available	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
15	_	_	B-LIMIT
hours	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
kg	_	_	O
of	_	_	O
Granny	_	_	B-VAR
Smith	_	_	I-VAR
apples	_	_	I-VAR
is	_	_	O
$	_	_	O
2	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
kg	_	_	O
of	_	_	O
McIntosh	_	_	B-VAR
apples	_	_	I-VAR
is	_	_	O
$	_	_	O
1	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
kg	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Samuel	_	_	O
has	_	_	B-CONST_DIR
90	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
to	_	_	O
grow	_	_	O
wheat	_	_	B-VAR
and	_	_	O
corn	_	_	B-VAR
.	_	_	O
Each	_	_	O
acre	_	_	O
of	_	_	O
wheat	_	_	B-VAR
requires	_	_	O
$	_	_	O
10	_	_	B-PARAM
in	_	_	O
maintenance	_	_	O
and	_	_	O
4	_	_	B-PARAM
hours	_	_	O
of	_	_	O
care	_	_	O
.	_	_	O
Each	_	_	O
acre	_	_	O
of	_	_	O
corn	_	_	B-VAR
requires	_	_	O
$	_	_	O
20	_	_	B-PARAM
in	_	_	O
maintenance	_	_	O
and	_	_	O
3	_	_	B-PARAM
hours	_	_	O
of	_	_	O
care	_	_	O
.	_	_	O
He	_	_	O
has	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
1400	_	_	B-LIMIT
to	_	_	O
spend	_	_	O
on	_	_	O
maintenance	_	_	O
and	_	_	O
90	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
time	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
care	_	_	O
keeping	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
wheat	_	_	B-VAR
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
corn	_	_	B-VAR
is	_	_	O
$	_	_	O
90	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
grown	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
investor	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
500000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
two	_	_	O
software	_	_	O
companies	_	_	O
,	_	_	O
company	_	_	B-VAR
A	_	_	I-VAR
and	_	_	O
company	_	_	B-VAR
B.	_	_	I-VAR
He	_	_	O
has	_	_	O
decided	_	_	O
to	_	_	O
invest	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
two	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
much	_	_	O
money	_	_	O
in	_	_	O
company	_	_	B-VAR
A	_	_	I-VAR
than	_	_	O
in	_	_	O
company	_	_	B-VAR
B.	_	_	I-VAR
In	_	_	O
addition	_	_	O
,	_	_	O
he	_	_	O
can	_	_	O
invest	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
200000	_	_	B-LIMIT
in	_	_	O
company	_	_	B-VAR
B.	_	_	I-VAR
If	_	_	O
investments	_	_	O
in	_	_	O
company	_	_	B-VAR
A	_	_	I-VAR
yield	_	_	O
9	_	_	B-PARAM
%	_	_	I-PARAM
returns	_	_	B-OBJ_NAME
and	_	_	O
investments	_	_	O
in	_	_	O
company	_	_	B-VAR
B	_	_	I-VAR
yield	_	_	O
12	_	_	B-PARAM
%	_	_	I-PARAM
returns	_	_	B-OBJ_NAME
,	_	_	O
how	_	_	O
much	_	_	O
should	_	_	O
he	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
earnings	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
sign	_	_	O
shop	_	_	O
makes	_	_	O
storefront	_	_	B-VAR
signs	_	_	I-VAR
and	_	_	O
street	_	_	B-VAR
signs	_	_	I-VAR
.	_	_	O
Each	_	_	O
requires	_	_	O
time	_	_	O
for	_	_	O
cutting	_	_	O
,	_	_	O
printing	_	_	O
,	_	_	O
and	_	_	O
assembly	_	_	O
.	_	_	O
Each	_	_	O
storefront	_	_	B-VAR
sign	_	_	I-VAR
takes	_	_	O
2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
cutting	_	_	O
,	_	_	O
1	_	_	B-PARAM
hour	_	_	O
of	_	_	O
printing	_	_	O
,	_	_	O
and	_	_	O
2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
assembly	_	_	O
.	_	_	O
Each	_	_	O
street	_	_	B-VAR
sign	_	_	I-VAR
takes	_	_	O
1	_	_	B-PARAM
hour	_	_	O
of	_	_	O
cutting	_	_	O
,	_	_	O
0.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
printing	_	_	O
,	_	_	O
and	_	_	O
0.8	_	_	B-PARAM
hours	_	_	O
of	_	_	O
assembly	_	_	O
.	_	_	O
The	_	_	O
sign	_	_	O
shop	_	_	O
has	_	_	O
100	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
cutting	_	_	O
,	_	_	O
50	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
printing	_	_	O
,	_	_	O
and	_	_	O
60	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
assembly	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
storefront	_	_	B-VAR
sign	_	_	I-VAR
is	_	_	O
$	_	_	O
400	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
street	_	_	B-VAR
sign	_	_	I-VAR
is	_	_	O
$	_	_	O
120	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
salad	_	_	O
shop	_	_	O
sells	_	_	O
two	_	_	O
salads	_	_	O
,	_	_	O
Caesar	_	_	B-VAR
salad	_	_	I-VAR
and	_	_	O
Mediterranean	_	_	B-VAR
salad	_	_	I-VAR
.	_	_	O
Each	_	_	O
salad	_	_	O
uses	_	_	O
different	_	_	O
amounts	_	_	O
of	_	_	O
lettuce	_	_	O
,	_	_	O
sauce	_	_	O
,	_	_	O
and	_	_	O
cheese	_	_	O
.	_	_	O
Caesar	_	_	B-VAR
salad	_	_	I-VAR
uses	_	_	O
100	_	_	B-PARAM
g	_	_	O
of	_	_	O
lettuce	_	_	O
,	_	_	O
10	_	_	B-PARAM
g	_	_	O
of	_	_	O
sauce	_	_	O
,	_	_	O
and	_	_	O
5	_	_	B-PARAM
g	_	_	O
of	_	_	O
cheese	_	_	O
.	_	_	O
Mediterranean	_	_	B-VAR
salad	_	_	I-VAR
uses	_	_	O
150	_	_	B-PARAM
g	_	_	O
of	_	_	O
lettuce	_	_	O
,	_	_	O
15	_	_	B-PARAM
g	_	_	O
of	_	_	O
sauce	_	_	O
,	_	_	O
and	_	_	O
15	_	_	B-PARAM
g	_	_	O
of	_	_	O
cheese	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
20000	_	_	B-LIMIT
g	_	_	O
of	_	_	O
lettuce	_	_	O
,	_	_	O
2000	_	_	B-LIMIT
g	_	_	O
of	_	_	O
sauce	_	_	O
,	_	_	O
and	_	_	O
3000	_	_	B-LIMIT
g	_	_	O
of	_	_	O
cheese	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
Caesar	_	_	B-VAR
salad	_	_	I-VAR
is	_	_	O
$	_	_	O
7	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
Mediterranean	_	_	B-VAR
salad	_	_	I-VAR
is	_	_	O
$	_	_	O
9	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
salad	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
pasta	_	_	O
restaurant	_	_	O
is	_	_	O
going	_	_	O
to	_	_	O
purchase	_	_	O
pasta	_	_	O
rollers	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
two	_	_	O
models	_	_	O
available	_	_	O
.	_	_	O
Roller	_	_	B-VAR
v2	_	_	I-VAR
can	_	_	O
make	_	_	O
15	_	_	B-PARAM
kg	_	_	O
of	_	_	O
spaghetti	_	_	O
per	_	_	O
cycle	_	_	O
,	_	_	O
requires	_	_	O
60	_	_	B-PARAM
grams	_	_	O
of	_	_	O
fuel	_	_	O
per	_	_	O
cycle	_	_	O
,	_	_	O
and	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
9000	_	_	B-PARAM
.	_	_	O
Roller	_	_	B-VAR
v1	_	_	I-VAR
can	_	_	O
make	_	_	O
9	_	_	B-PARAM
kg	_	_	O
of	_	_	O
pasta	_	_	O
per	_	_	O
cycle	_	_	O
,	_	_	O
requires	_	_	O
70	_	_	B-PARAM
grams	_	_	O
of	_	_	O
fuel	_	_	O
per	_	_	O
cycle	_	_	O
,	_	_	O
and	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
4000	_	_	B-PARAM
.	_	_	O
The	_	_	O
pasta	_	_	O
restaurant	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
150	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
spaghetti	_	_	O
per	_	_	O
cycle	_	_	O
and	_	_	O
use	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
900	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
fuel	_	_	O
per	_	_	O
cycle	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
pasta	_	_	O
roller	_	_	O
should	_	_	O
they	_	_	O
purchase	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
bubble	_	_	O
tea	_	_	O
shop	_	_	O
makes	_	_	O
taro	_	_	B-VAR
and	_	_	O
mango	_	_	B-VAR
bubble	_	_	I-VAR
teas	_	_	I-VAR
.	_	_	O
Three	_	_	O
ingredients	_	_	O
are	_	_	O
needed	_	_	O
to	_	_	O
make	_	_	O
the	_	_	O
bubble	_	_	O
teas	_	_	O
:	_	_	O
milk	_	_	O
tea	_	_	O
,	_	_	O
taro	_	_	O
,	_	_	O
and	_	_	O
mango	_	_	O
.	_	_	O
One	_	_	O
taro	_	_	B-VAR
bubble	_	_	I-VAR
tea	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
taro	_	_	O
and	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
milk	_	_	O
.	_	_	O
One	_	_	O
mango	_	_	B-VAR
bubble	_	_	I-VAR
tea	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
mango	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
milk	_	_	O
.	_	_	O
The	_	_	O
shop	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
60	_	_	B-LIMIT
units	_	_	O
of	_	_	O
taro	_	_	O
,	_	_	O
60	_	_	B-LIMIT
units	_	_	O
of	_	_	O
mango	_	_	O
,	_	_	O
and	_	_	O
140	_	_	B-LIMIT
units	_	_	O
of	_	_	O
milk	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
taro	_	_	B-VAR
bubble	_	_	I-VAR
tea	_	_	I-VAR
is	_	_	O
$	_	_	O
4	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
mango	_	_	B-VAR
bubble	_	_	I-VAR
tea	_	_	I-VAR
is	_	_	O
$	_	_	O
6	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
company	_	_	O
produces	_	_	O
action	_	_	B-VAR
figures	_	_	I-VAR
and	_	_	O
toy	_	_	B-VAR
cars	_	_	I-VAR
.	_	_	O
Each	_	_	O
action	_	_	B-VAR
figure	_	_	I-VAR
takes	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
production	_	_	O
time	_	_	O
and	_	_	O
$	_	_	O
2	_	_	B-PARAM
worth	_	_	O
of	_	_	O
plastic	_	_	O
.	_	_	O
Each	_	_	O
toy	_	_	B-VAR
car	_	_	I-VAR
takes	_	_	O
8	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
production	_	_	O
time	_	_	O
and	_	_	O
$	_	_	O
2.50	_	_	B-PARAM
worth	_	_	O
of	_	_	O
plastic	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
1000	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
production	_	_	O
and	_	_	O
$	_	_	O
1000	_	_	B-LIMIT
worth	_	_	O
of	_	_	O
plastic	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
company	_	_	O
earns	_	_	B-OBJ_NAME
$	_	_	O
2	_	_	B-PARAM
per	_	_	O
action	_	_	B-VAR
figure	_	_	I-VAR
and	_	_	O
$	_	_	O
3	_	_	B-PARAM
per	_	_	O
toy	_	_	B-VAR
car	_	_	I-VAR
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
produce	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
their	_	_	O
earnings	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
teddy	_	_	O
bear	_	_	O
shop	_	_	O
makes	_	_	O
two	_	_	O
sizes	_	_	O
of	_	_	O
teddy	_	_	O
bears	_	_	O
-	_	_	O
small	_	_	B-VAR
and	_	_	O
large	_	_	B-VAR
.	_	_	O
Both	_	_	O
require	_	_	O
time	_	_	O
for	_	_	O
filling	_	_	O
and	_	_	O
stitching	_	_	O
.	_	_	O
A	_	_	O
small	_	_	B-VAR
teddy	_	_	I-VAR
bear	_	_	I-VAR
requires	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
filling	_	_	O
and	_	_	O
25	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
stitching	_	_	O
.	_	_	O
A	_	_	O
large	_	_	B-VAR
teddy	_	_	I-VAR
bear	_	_	I-VAR
requires	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
filling	_	_	O
and	_	_	O
35	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
stitching	_	_	O
.	_	_	O
The	_	_	O
shop	_	_	O
has	_	_	O
700	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
per	_	_	O
day	_	_	O
for	_	_	O
filling	_	_	O
and	_	_	O
900	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
per	_	_	O
day	_	_	O
for	_	_	O
stitching	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
small	_	_	B-VAR
teddy	_	_	I-VAR
bear	_	_	I-VAR
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
large	_	_	B-VAR
teddy	_	_	I-VAR
bear	_	_	I-VAR
is	_	_	O
$	_	_	O
8	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
teddy	_	_	O
bear	_	_	O
should	_	_	O
the	_	_	O
shop	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
their	_	_	O
profits	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
fast	_	_	O
food	_	_	O
restaurant	_	_	O
makes	_	_	O
cheeseburgers	_	_	B-VAR
and	_	_	O
fries	_	_	B-VAR
.	_	_	O
They	_	_	O
make	_	_	O
x1	_	_	O
cheeseburgers	_	_	B-VAR
per	_	_	O
day	_	_	O
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
1.50	_	_	B-PARAM
per	_	_	O
cheeseburger	_	_	B-VAR
and	_	_	O
x2	_	_	O
fries	_	_	B-VAR
per	_	_	O
day	_	_	O
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
1	_	_	B-PARAM
per	_	_	O
fries	_	_	B-VAR
(	_	_	O
x1	_	_	O
and	_	_	O
x2	_	_	O
must	_	_	O
be	_	_	O
greater	_	_	O
than	_	_	O
or	_	_	O
equal	_	_	O
to	_	_	O
0	_	_	O
)	_	_	O
.	_	_	O
There	_	_	O
is	_	_	O
a	_	_	O
daily	_	_	O
demand	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
110	_	_	B-LIMIT
cheeseburgers	_	_	B-VAR
and	_	_	O
80	_	_	B-LIMIT
fries	_	_	B-VAR
.	_	_	O
The	_	_	O
restaurant	_	_	O
only	_	_	O
has	_	_	O
capacity	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
150	_	_	B-LIMIT
items	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
produce	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
chef	_	_	O
mixes	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
seasoning	_	_	O
to	_	_	O
ensure	_	_	O
the	_	_	O
new	_	_	O
mixture	_	_	O
contains	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
5	_	_	B-LIMIT
units	_	_	O
of	_	_	O
pepper	_	_	O
and	_	_	O
6	_	_	B-LIMIT
units	_	_	O
of	_	_	O
salt	_	_	O
.	_	_	O
Seasoning	_	_	B-VAR
A	_	_	I-VAR
contains	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
pepper	_	_	O
and	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
salt	_	_	O
per	_	_	O
kg	_	_	O
.	_	_	O
Seasoning	_	_	B-VAR
B	_	_	I-VAR
contains	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
pepper	_	_	O
and	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
salt	_	_	O
per	_	_	O
kg	_	_	O
.	_	_	O
If	_	_	O
it	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
1.50	_	_	B-PARAM
per	_	_	O
kg	_	_	O
of	_	_	O
seasoning	_	_	B-VAR
A	_	_	I-VAR
and	_	_	O
$	_	_	O
3	_	_	B-PARAM
per	_	_	O
kg	_	_	O
of	_	_	O
seasoning	_	_	B-VAR
B	_	_	I-VAR
,	_	_	O
how	_	_	O
many	_	_	O
kg	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
chef	_	_	O
buy	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
her	_	_	O
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
city	_	_	O
planner	_	_	O
has	_	_	B-CONST_DIR
120	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
on	_	_	O
which	_	_	O
he	_	_	O
can	_	_	O
build	_	_	O
solar	_	_	B-VAR
panels	_	_	I-VAR
and	_	_	O
windmills	_	_	B-VAR
.	_	_	O
Per	_	_	O
acre	_	_	O
of	_	_	O
solar	_	_	B-VAR
panels	_	_	I-VAR
,	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
resources	_	_	O
are	_	_	O
required	_	_	O
.	_	_	O
Per	_	_	O
acre	_	_	O
of	_	_	O
windmills	_	_	B-VAR
,	_	_	O
40	_	_	B-PARAM
units	_	_	O
of	_	_	O
resources	_	_	O
are	_	_	O
required	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
the	_	_	O
city	_	_	O
planner	_	_	O
only	_	_	O
has	_	_	O
2000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
resources	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
If	_	_	O
the	_	_	O
savings	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
solar	_	_	B-VAR
panels	_	_	I-VAR
is	_	_	O
$	_	_	O
500	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
windmills	_	_	B-VAR
is	_	_	O
$	_	_	O
1000	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
built	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
savings	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
neighbourhood	_	_	O
community	_	_	O
builds	_	_	O
and	_	_	O
paints	_	_	O
sheds	_	_	B-VAR
and	_	_	O
treehouses	_	_	B-VAR
.	_	_	O
Each	_	_	O
shed	_	_	B-VAR
takes	_	_	O
4	_	_	B-PARAM
hours	_	_	O
to	_	_	O
build	_	_	O
and	_	_	O
2	_	_	B-PARAM
hours	_	_	O
to	_	_	O
paint	_	_	O
.	_	_	O
Each	_	_	O
treehouse	_	_	B-VAR
takes	_	_	O
2	_	_	B-PARAM
hours	_	_	O
to	_	_	O
build	_	_	O
and	_	_	O
1.5	_	_	B-PARAM
hours	_	_	O
to	_	_	O
paint	_	_	O
.	_	_	O
The	_	_	O
neighbourhood	_	_	O
community	_	_	O
has	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
40	_	_	B-LIMIT
hours	_	_	O
available	_	_	O
for	_	_	O
building	_	_	O
and	_	_	O
30	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
painting	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
neighbourhood	_	_	O
community	_	_	O
makes	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
700	_	_	B-PARAM
per	_	_	O
shed	_	_	B-VAR
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
500	_	_	B-PARAM
per	_	_	O
treehouse	_	_	B-VAR
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
their	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
gardener	_	_	O
mixes	_	_	O
soil	_	_	O
to	_	_	O
produce	_	_	O
his	_	_	O
own	_	_	O
soil	_	_	O
mix	_	_	O
to	_	_	O
fulfill	_	_	O
his	_	_	O
compost	_	_	O
and	_	_	O
loam	_	_	O
requirements	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
soil	_	_	O
,	_	_	O
an	_	_	O
outdoor	_	_	B-VAR
soil	_	_	I-VAR
and	_	_	O
an	_	_	O
indoor	_	_	B-VAR
soil	_	_	I-VAR
.	_	_	O
The	_	_	O
indoor	_	_	B-VAR
soil	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
2	_	_	B-PARAM
and	_	_	O
contains	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
compost	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
loam	_	_	O
.	_	_	O
The	_	_	O
outdoor	_	_	B-VAR
soil	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
3	_	_	B-PARAM
and	_	_	O
contains	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
compost	_	_	O
and	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
loam	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
gardener	_	_	O
requires	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
80	_	_	B-LIMIT
units	_	_	O
of	_	_	O
compost	_	_	O
and	_	_	O
70	_	_	B-LIMIT
units	_	_	O
of	_	_	O
loam	_	_	O
per	_	_	O
week	_	_	O
,	_	_	O
how	_	_	O
much	_	_	O
of	_	_	O
each	_	_	O
soil	_	_	O
should	_	_	O
he	_	_	O
purchase	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
cost	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
company	_	_	O
makes	_	_	O
kayaks	_	_	B-VAR
and	_	_	O
canoes	_	_	B-VAR
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
8000	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
assembly	_	_	O
and	_	_	O
4000	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
quality	_	_	O
checking	_	_	O
.	_	_	O
Each	_	_	O
kayak	_	_	B-VAR
takes	_	_	O
60	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
assembly	_	_	O
and	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
quality	_	_	O
checking	_	_	O
.	_	_	O
Each	_	_	O
canoe	_	_	B-VAR
takes	_	_	O
80	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
assembly	_	_	O
and	_	_	O
25	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
quality	_	_	O
checking	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
kayak	_	_	B-VAR
is	_	_	O
$	_	_	O
300	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
canoe	_	_	B-VAR
is	_	_	O
$	_	_	O
450	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Sid	_	_	O
has	_	_	O
to	_	_	O
meet	_	_	O
his	_	_	O
daily	_	_	O
requirements	_	_	B-CONST_DIR
of	_	_	O
2	_	_	B-LIMIT
servings	_	_	O
of	_	_	O
meat	_	_	O
,	_	_	O
1	_	_	B-LIMIT
serving	_	_	O
of	_	_	O
dairy	_	_	O
,	_	_	O
4	_	_	B-LIMIT
servings	_	_	O
of	_	_	O
vegetables	_	_	O
,	_	_	O
and	_	_	O
3	_	_	B-LIMIT
servings	_	_	O
of	_	_	O
grains	_	_	O
.	_	_	O
He	_	_	O
can	_	_	O
eat	_	_	O
a	_	_	O
hamburger	_	_	B-VAR
,	_	_	O
which	_	_	O
has	_	_	O
1	_	_	B-PARAM
serving	_	_	O
of	_	_	O
meat	_	_	O
,	_	_	O
0.5	_	_	B-PARAM
servings	_	_	O
of	_	_	O
dairy	_	_	O
,	_	_	O
1	_	_	B-PARAM
serving	_	_	O
of	_	_	O
vegetables	_	_	O
and	_	_	O
1	_	_	B-PARAM
serving	_	_	O
of	_	_	O
grains	_	_	O
or	_	_	O
he	_	_	O
can	_	_	O
eat	_	_	O
a	_	_	O
plate	_	_	O
of	_	_	O
pasta	_	_	B-VAR
,	_	_	O
which	_	_	O
has	_	_	O
0	_	_	B-PARAM
servings	_	_	O
of	_	_	O
meat	_	_	O
,	_	_	O
1	_	_	B-PARAM
serving	_	_	O
of	_	_	O
dairy	_	_	O
,	_	_	O
1	_	_	B-PARAM
serving	_	_	O
of	_	_	O
vegetables	_	_	O
and	_	_	O
2	_	_	B-PARAM
servings	_	_	O
of	_	_	O
grains	_	_	O
.	_	_	O
If	_	_	O
a	_	_	O
hamburger	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
3	_	_	B-PARAM
and	_	_	O
a	_	_	O
plate	_	_	O
of	_	_	O
pasta	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
4	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
item	_	_	O
should	_	_	O
he	_	_	O
buy	_	_	O
to	_	_	O
meet	_	_	O
his	_	_	O
requirements	_	_	O
at	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
?	_	_	O

Martin	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
2000000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
the	_	_	O
following	_	_	O
technology	_	_	O
sectors	_	_	O
:	_	_	O
GPUs	_	_	B-VAR
,	_	_	O
CPUs	_	_	B-VAR
,	_	_	O
software	_	_	B-VAR
and	_	_	O
mobile	_	_	B-VAR
devices	_	_	I-VAR
.	_	_	O
The	_	_	O
annual	_	_	O
rate	_	_	O
of	_	_	O
return	_	_	B-OBJ_NAME
for	_	_	O
each	_	_	O
is	_	_	O
as	_	_	O
follows	_	_	O
:	_	_	O
GPUs	_	_	B-VAR
,	_	_	O
4	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
CPUs	_	_	B-VAR
,	_	_	O
6	_	_	B-PARAM
%	_	_	I-PARAM
,	_	_	O
software	_	_	B-VAR
,	_	_	O
11	_	_	B-PARAM
%	_	_	I-PARAM
,	_	_	O
mobile	_	_	B-VAR
devices	_	_	I-VAR
,	_	_	O
8	_	_	B-PARAM
%	_	_	I-PARAM
.	_	_	O
Martin	_	_	O
has	_	_	O
the	_	_	O
following	_	_	O
conditions	_	_	O
.	_	_	O
The	_	_	O
amount	_	_	O
he	_	_	O
invests	_	_	O
in	_	_	O
GPUs	_	_	B-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
CPUs	_	_	B-VAR
.	_	_	O
Similarly	_	_	O
,	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
mobile	_	_	B-VAR
devices	_	_	I-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
software	_	_	B-VAR
.	_	_	O
Lastly	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
9	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
investment	_	_	O
can	_	_	O
be	_	_	O
in	_	_	O
GPUs	_	_	B-VAR
.	_	_	O
How	_	_	O
much	_	_	O
money	_	_	O
should	_	_	O
Martin	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
sector	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
return	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
farmer	_	_	O
has	_	_	B-CONST_DIR
200	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
to	_	_	O
grow	_	_	O
oranges	_	_	B-VAR
and	_	_	O
grapefruits	_	_	B-VAR
.	_	_	O
He	_	_	O
must	_	_	O
grow	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
60	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
oranges	_	_	B-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
grapefruits	_	_	B-VAR
.	_	_	O
The	_	_	O
farmer	_	_	O
prefers	_	_	O
to	_	_	O
grow	_	_	O
more	_	_	B-CONST_DIR
grapefruits	_	_	B-VAR
than	_	_	O
oranges	_	_	B-VAR
but	_	_	O
due	_	_	O
to	_	_	O
a	_	_	O
shortage	_	_	O
,	_	_	O
he	_	_	O
can	_	_	O
grow	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
twice	_	_	B-PARAM
the	_	_	O
amount	_	_	O
of	_	_	O
grapefruits	_	_	B-VAR
as	_	_	O
oranges	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
oranges	_	_	B-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
,	_	_	O
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
grapefruits	_	_	B-VAR
is	_	_	O
$	_	_	O
220	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
grown	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
framing	_	_	O
company	_	_	O
frames	_	_	O
printed	_	_	B-VAR
art	_	_	I-VAR
and	_	_	O
paintings	_	_	B-VAR
.	_	_	O
Each	_	_	O
printed	_	_	B-VAR
art	_	_	I-VAR
takes	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
for	_	_	O
printing	_	_	O
and	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
for	_	_	O
framing	_	_	O
.	_	_	O
Each	_	_	O
painting	_	_	B-VAR
takes	_	_	O
0	_	_	B-PARAM
minutes	_	_	O
for	_	_	O
printing	_	_	O
and	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
for	_	_	O
framing	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
150	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
printing	_	_	O
and	_	_	O
400	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
framing	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
printed	_	_	B-VAR
art	_	_	I-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
painting	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
8	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
produce	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profits	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
cyclist	_	_	O
only	_	_	O
eats	_	_	O
chicken	_	_	B-VAR
and	_	_	O
potatoes	_	_	B-VAR
.	_	_	O
He	_	_	O
wants	_	_	O
to	_	_	O
make	_	_	O
sure	_	_	O
he	_	_	O
gets	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
80	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
50	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
fat	_	_	O
,	_	_	O
and	_	_	O
100	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
carbs	_	_	O
.	_	_	O
Chicken	_	_	B-VAR
contains	_	_	O
20	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
4	_	_	B-PARAM
grams	_	_	O
of	_	_	O
fat	_	_	O
,	_	_	O
and	_	_	O
4	_	_	B-PARAM
grams	_	_	O
of	_	_	O
carbs	_	_	O
.	_	_	O
Potatoes	_	_	B-VAR
contain	_	_	O
2	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
3	_	_	B-PARAM
grams	_	_	O
of	_	_	O
fat	_	_	O
,	_	_	O
and	_	_	O
7	_	_	B-PARAM
grams	_	_	O
of	_	_	O
carbs	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
chicken	_	_	B-VAR
is	_	_	O
$	_	_	O
6	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
potato	_	_	B-VAR
is	_	_	O
$	_	_	O
2	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
buy	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
construction	_	_	O
company	_	_	O
installs	_	_	O
hardwood	_	_	B-VAR
flooring	_	_	I-VAR
and	_	_	O
carpet	_	_	B-VAR
.	_	_	O
It	_	_	O
takes	_	_	O
1	_	_	B-PARAM
hour	_	_	O
of	_	_	O
cutting	_	_	O
and	_	_	O
3	_	_	B-PARAM
hours	_	_	O
of	_	_	O
installation	_	_	O
for	_	_	O
hardwood	_	_	B-VAR
flooring	_	_	I-VAR
.	_	_	O
It	_	_	O
takes	_	_	O
0.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
cutting	_	_	O
and	_	_	O
4	_	_	B-PARAM
hours	_	_	O
of	_	_	O
installation	_	_	O
for	_	_	O
carpet	_	_	B-VAR
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
200	_	_	B-LIMIT
hours	_	_	O
for	_	_	O
cutting	_	_	O
and	_	_	O
400	_	_	B-LIMIT
hours	_	_	O
for	_	_	O
installation	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
hardwood	_	_	B-VAR
flooring	_	_	I-VAR
is	_	_	O
$	_	_	O
400	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
carpet	_	_	B-VAR
is	_	_	O
$	_	_	O
650	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
installed	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
berry	_	_	O
farmer	_	_	O
has	_	_	B-CONST_DIR
300	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
to	_	_	O
grow	_	_	O
blueberries	_	_	B-VAR
and	_	_	O
raspberries	_	_	B-VAR
.	_	_	O
Each	_	_	O
acre	_	_	O
of	_	_	O
blueberries	_	_	B-VAR
costs	_	_	O
$	_	_	O
60	_	_	B-PARAM
for	_	_	O
fertilizer	_	_	O
and	_	_	O
takes	_	_	O
3	_	_	B-PARAM
hours	_	_	O
of	_	_	O
picking	_	_	O
.	_	_	O
Each	_	_	O
acre	_	_	O
of	_	_	O
raspberries	_	_	B-VAR
costs	_	_	O
$	_	_	O
40	_	_	B-PARAM
for	_	_	O
fertilizer	_	_	O
and	_	_	O
takes	_	_	O
4	_	_	B-PARAM
hours	_	_	O
of	_	_	O
picking	_	_	O
.	_	_	O
The	_	_	O
farmer	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
$	_	_	O
20000	_	_	B-LIMIT
to	_	_	O
spend	_	_	O
on	_	_	O
fertilizer	_	_	O
and	_	_	O
400	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
picking	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
blueberries	_	_	B-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
raspberries	_	_	B-VAR
is	_	_	O
$	_	_	O
250	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
grown	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
dessert	_	_	O
factory	_	_	O
makes	_	_	O
cakes	_	_	B-VAR
and	_	_	O
pies	_	_	B-VAR
.	_	_	O
Each	_	_	O
cake	_	_	B-VAR
requires	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
sugar	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
flour	_	_	O
.	_	_	O
Each	_	_	O
pie	_	_	B-VAR
requires	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
sugar	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
flour	_	_	O
.	_	_	O
The	_	_	O
factory	_	_	O
has	_	_	O
1000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
sugar	_	_	O
and	_	_	O
1200	_	_	B-LIMIT
units	_	_	O
of	_	_	O
flour	_	_	O
agent	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
If	_	_	O
the	_	_	O
revenue	_	_	B-OBJ_NAME
per	_	_	O
cake	_	_	B-VAR
made	_	_	O
is	_	_	O
$	_	_	O
4	_	_	B-PARAM
and	_	_	O
the	_	_	O
revenue	_	_	B-OBJ_NAME
per	_	_	O
pie	_	_	B-VAR
made	_	_	O
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
revenue	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
company	_	_	O
makes	_	_	O
regular	_	_	B-VAR
desks	_	_	I-VAR
and	_	_	O
standing	_	_	B-VAR
desks	_	_	I-VAR
.	_	_	O
Regular	_	_	B-VAR
desks	_	_	I-VAR
require	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
wood	_	_	O
while	_	_	O
standing	_	_	B-VAR
desks	_	_	I-VAR
require	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
wood	_	_	O
.	_	_	O
Regular	_	_	B-VAR
desks	_	_	I-VAR
take	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
package	_	_	O
while	_	_	O
standing	_	_	B-VAR
desks	_	_	I-VAR
take	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
package	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
4000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
wood	_	_	O
available	_	_	B-CONST_DIR
and	_	_	O
1500	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
packaging	_	_	O
time	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
regular	_	_	B-VAR
desk	_	_	I-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
the	_	_	O
standing	_	_	B-VAR
desk	_	_	I-VAR
is	_	_	O
$	_	_	O
300	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
wood	_	_	O
artist	_	_	O
makes	_	_	O
cutting	_	_	B-VAR
boards	_	_	I-VAR
and	_	_	O
chairs	_	_	B-VAR
.	_	_	O
Each	_	_	O
cutting	_	_	B-VAR
board	_	_	I-VAR
takes	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
make	_	_	O
while	_	_	O
each	_	_	O
chair	_	_	B-VAR
takes	_	_	O
70	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
make	_	_	O
.	_	_	O
In	_	_	O
a	_	_	O
week	_	_	O
,	_	_	O
the	_	_	O
artist	_	_	O
only	_	_	O
has	_	_	O
1500	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
to	_	_	O
do	_	_	O
woodworking	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
he	_	_	O
only	_	_	B-CONST_DIR
has	_	_	O
enough	_	_	O
wood	_	_	O
to	_	_	O
make	_	_	O
40	_	_	B-LIMIT
items	_	_	O
total	_	_	O
.	_	_	O
If	_	_	O
he	_	_	O
makes	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
14	_	_	B-PARAM
per	_	_	O
cutting	_	_	B-VAR
board	_	_	I-VAR
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
25	_	_	B-PARAM
per	_	_	O
chair	_	_	B-VAR
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

In	_	_	O
a	_	_	O
video	_	_	O
game	_	_	O
,	_	_	O
Alison	_	_	O
has	_	_	B-CONST_DIR
to	_	_	I-CONST_DIR
collect	_	_	I-CONST_DIR
40	_	_	B-LIMIT
stars	_	_	O
and	_	_	O
80	_	_	B-LIMIT
snowballs	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
two	_	_	O
areas	_	_	O
.	_	_	O
Starry	_	_	B-VAR
Mountain	_	_	I-VAR
and	_	_	O
Frosty	_	_	B-VAR
Hills	_	_	I-VAR
,	_	_	O
where	_	_	O
she	_	_	O
can	_	_	O
find	_	_	O
these	_	_	O
resources	_	_	O
.	_	_	O
For	_	_	O
each	_	_	B-OBJ_NAME
hour	_	_	I-OBJ_NAME
in	_	_	O
Starry	_	_	B-VAR
Mountain	_	_	I-VAR
that	_	_	O
she	_	_	O
spends	_	_	O
,	_	_	O
she	_	_	O
gets	_	_	O
5	_	_	B-PARAM
stars	_	_	O
and	_	_	O
2	_	_	B-PARAM
snowballs	_	_	O
.	_	_	O
For	_	_	O
each	_	_	B-OBJ_NAME
hour	_	_	I-OBJ_NAME
in	_	_	O
Frosty	_	_	B-VAR
Hills	_	_	I-VAR
that	_	_	O
she	_	_	O
spends	_	_	O
,	_	_	O
she	_	_	O
gets	_	_	O
1	_	_	B-PARAM
star	_	_	O
and	_	_	O
12	_	_	B-PARAM
snowballs	_	_	O
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
time	_	_	I-OBJ_NAME
spent	_	_	O
in	_	_	O
both	_	_	O
areas	_	_	O
.	_	_	O

A	_	_	O
car	_	_	O
dealership	_	_	O
stocks	_	_	O
cars	_	_	B-VAR
and	_	_	O
trucks	_	_	B-VAR
.	_	_	O
Each	_	_	O
car	_	_	B-VAR
takes	_	_	O
30	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
of	_	_	O
space	_	_	O
while	_	_	O
each	_	_	O
truck	_	_	B-VAR
takes	_	_	O
45	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
of	_	_	O
space	_	_	O
.	_	_	O
The	_	_	O
dealership	_	_	O
has	_	_	O
a	_	_	B-CONST_DIR
total	_	_	I-CONST_DIR
of	_	_	I-CONST_DIR
450	_	_	B-LIMIT
sq	_	_	O
ft	_	_	O
of	_	_	O
space	_	_	O
available	_	_	O
.	_	_	O
Based	_	_	O
on	_	_	O
past	_	_	O
seasons	_	_	O
,	_	_	O
the	_	_	O
dealership	_	_	O
makes	_	_	O
sure	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
60	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
all	_	_	O
items	_	_	O
in	_	_	O
stock	_	_	O
are	_	_	O
cars	_	_	B-VAR
.	_	_	O
In	_	_	O
terms	_	_	O
of	_	_	O
capital	_	_	O
,	_	_	O
the	_	_	O
dealership	_	_	O
wants	_	_	O
to	_	_	O
spend	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
800000	_	_	B-LIMIT
.	_	_	O
Each	_	_	O
car	_	_	B-VAR
costs	_	_	O
the	_	_	O
dealership	_	_	O
$	_	_	O
30000	_	_	B-PARAM
and	_	_	O
each	_	_	O
truck	_	_	B-VAR
costs	_	_	O
the	_	_	O
dealership	_	_	O
$	_	_	O
40000	_	_	B-PARAM
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
car	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
2000	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
truck	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
4000	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
stocked	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
small	_	_	O
family	_	_	O
business	_	_	O
makes	_	_	O
homemade	_	_	O
apple	_	_	B-VAR
pies	_	_	I-VAR
and	_	_	O
blueberry	_	_	B-VAR
pies	_	_	I-VAR
.	_	_	O
It	_	_	O
takes	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
make	_	_	O
one	_	_	O
apple	_	_	B-VAR
pie	_	_	I-VAR
and	_	_	O
40	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
blueberry	_	_	B-VAR
pie	_	_	I-VAR
.	_	_	O
The	_	_	O
family	_	_	O
business	_	_	O
only	_	_	B-CONST_DIR
operates	_	_	O
for	_	_	O
4500	_	_	B-LIMIT
minutes	_	_	O
per	_	_	O
week	_	_	O
.	_	_	O
Due	_	_	O
to	_	_	O
fruit	_	_	O
availability	_	_	O
,	_	_	O
they	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
70	_	_	B-LIMIT
apple	_	_	B-VAR
pies	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
60	_	_	B-LIMIT
blueberry	_	_	B-VAR
pies	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
apple	_	_	B-VAR
pie	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
blueberry	_	_	B-VAR
pie	_	_	I-VAR
is	_	_	O
$	_	_	O
6	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
pie	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
their	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
sign	_	_	O
company	_	_	O
makes	_	_	O
neon	_	_	B-VAR
and	_	_	O
metal	_	_	B-VAR
signs	_	_	I-VAR
.	_	_	O
Each	_	_	O
neon	_	_	B-VAR
sign	_	_	I-VAR
takes	_	_	O
3	_	_	B-PARAM
hours	_	_	O
for	_	_	O
crafting	_	_	O
and	_	_	O
2	_	_	B-PARAM
hours	_	_	O
for	_	_	O
installation	_	_	O
.	_	_	O
Each	_	_	O
metal	_	_	B-VAR
sign	_	_	I-VAR
takes	_	_	O
2	_	_	B-PARAM
hours	_	_	O
for	_	_	O
crafting	_	_	O
and	_	_	O
1.5	_	_	B-PARAM
hours	_	_	O
for	_	_	O
installation	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
950	_	_	B-LIMIT
hours	_	_	O
for	_	_	O
crafting	_	_	O
and	_	_	O
400	_	_	B-LIMIT
hours	_	_	O
for	_	_	O
installation	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
neon	_	_	B-VAR
sign	_	_	I-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
metal	_	_	B-VAR
sign	_	_	I-VAR
is	_	_	O
$	_	_	O
100	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
craft	_	_	O
and	_	_	O
install	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
cafe	_	_	O
company	_	_	O
has	_	_	O
two	_	_	O
locations	_	_	O
,	_	_	O
a	_	_	O
university	_	_	B-VAR
cafe	_	_	I-VAR
and	_	_	O
a	_	_	O
downtown	_	_	B-VAR
cafe	_	_	I-VAR
.	_	_	O
The	_	_	O
university	_	_	B-VAR
cafe	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
400	_	_	B-PARAM
to	_	_	O
run	_	_	O
for	_	_	O
1	_	_	O
hour	_	_	O
while	_	_	O
the	_	_	O
downtown	_	_	B-VAR
cafe	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
700	_	_	B-PARAM
to	_	_	O
run	_	_	O
for	_	_	O
1	_	_	O
hour	_	_	O
.	_	_	O
In	_	_	O
an	_	_	O
hour	_	_	O
,	_	_	O
the	_	_	O
university	_	_	B-VAR
cafe	_	_	I-VAR
yields	_	_	O
30	_	_	B-PARAM
cappuccinos	_	_	O
,	_	_	O
40	_	_	B-PARAM
lattes	_	_	O
,	_	_	O
and	_	_	O
60	_	_	B-PARAM
regular	_	_	O
coffees	_	_	O
.	_	_	O
In	_	_	O
an	_	_	O
hour	_	_	O
,	_	_	O
the	_	_	O
downtown	_	_	B-VAR
cafe	_	_	I-VAR
yields	_	_	O
40	_	_	B-PARAM
cappuccinos	_	_	O
,	_	_	O
70	_	_	B-PARAM
lattes	_	_	O
,	_	_	O
and	_	_	O
110	_	_	B-PARAM
regular	_	_	O
coffees	_	_	O
.	_	_	O
The	_	_	O
cafe	_	_	O
company	_	_	O
must	_	_	O
produce	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
900	_	_	B-LIMIT
cappuccinos	_	_	O
,	_	_	O
700	_	_	B-LIMIT
lattes	_	_	O
,	_	_	O
and	_	_	O
1400	_	_	B-LIMIT
regular	_	_	O
coffees	_	_	O
in	_	_	O
total	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
hours	_	_	O
should	_	_	O
each	_	_	O
cafe	_	_	O
be	_	_	O
run	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
tea	_	_	O
company	_	_	O
makes	_	_	O
low	_	_	B-VAR
,	_	_	O
medium	_	_	B-VAR
,	_	_	O
and	_	_	O
high	_	_	B-VAR
quality	_	_	I-VAR
tea	_	_	I-VAR
.	_	_	O
A	_	_	O
low	_	_	B-VAR
quality	_	_	I-VAR
tea	_	_	I-VAR
contains	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
rare	_	_	O
additives	_	_	O
and	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
tea	_	_	O
leaves	_	_	O
.	_	_	O
A	_	_	O
medium	_	_	B-VAR
quality	_	_	I-VAR
tea	_	_	I-VAR
contains	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
rare	_	_	O
additives	_	_	O
and	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
tea	_	_	O
leaves	_	_	O
.	_	_	O
A	_	_	O
high	_	_	B-VAR
quality	_	_	I-VAR
tea	_	_	I-VAR
contains	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
rare	_	_	O
additives	_	_	O
and	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
tea	_	_	O
leaves	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
200	_	_	B-LIMIT
units	_	_	O
of	_	_	O
rare	_	_	O
additives	_	_	O
and	_	_	O
400	_	_	B-LIMIT
units	_	_	O
of	_	_	O
tea	_	_	O
leaves	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
low	_	_	B-VAR
quality	_	_	I-VAR
tea	_	_	I-VAR
is	_	_	O
$	_	_	O
1	_	_	B-PARAM
,	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
medium	_	_	B-VAR
quality	_	_	I-VAR
tea	_	_	I-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
,	_	_	O
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
high	_	_	B-VAR
quality	_	_	I-VAR
tea	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profits	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
dietician	_	_	O
recommends	_	_	O
that	_	_	O
his	_	_	O
patient	_	_	O
eat	_	_	O
gummy	_	_	O
vitamins	_	_	O
to	_	_	O
get	_	_	O
his	_	_	O
mineral	_	_	O
requirements	_	_	O
.	_	_	O
Each	_	_	O
blue	_	_	B-VAR
gummy	_	_	I-VAR
contains	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
calcium	_	_	O
,	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
A	_	_	O
,	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
iron	_	_	O
.	_	_	O
Each	_	_	O
red	_	_	B-VAR
gummy	_	_	I-VAR
contains	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
calcium	_	_	O
,	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
A	_	_	O
,	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
iron	_	_	O
.	_	_	O
The	_	_	O
patient	_	_	O
must	_	_	O
get	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
40	_	_	B-LIMIT
units	_	_	O
of	_	_	O
calcium	_	_	O
,	_	_	O
45	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamin	_	_	O
A	_	_	O
,	_	_	O
and	_	_	O
20	_	_	B-LIMIT
units	_	_	O
of	_	_	O
iron	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
blue	_	_	B-VAR
gummy	_	_	I-VAR
is	_	_	O
$	_	_	O
2	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
red	_	_	B-VAR
gummy	_	_	I-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
gummy	_	_	O
should	_	_	O
the	_	_	O
patient	_	_	O
purchase	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
company	_	_	O
makes	_	_	O
small	_	_	B-VAR
and	_	_	O
large	_	_	B-VAR
chessboards	_	_	I-VAR
.	_	_	O
Each	_	_	O
small	_	_	B-VAR
chessboard	_	_	I-VAR
takes	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
cutting	_	_	O
and	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
assembly	_	_	O
.	_	_	O
Each	_	_	O
large	_	_	B-VAR
chessboard	_	_	I-VAR
takes	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
cutting	_	_	O
and	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
assembly	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
400	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
cutting	_	_	O
and	_	_	O
700	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
assembly	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
small	_	_	B-VAR
chessboard	_	_	I-VAR
is	_	_	O
$	_	_	O
4	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
large	_	_	B-VAR
chessboard	_	_	I-VAR
is	_	_	O
$	_	_	O
8	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
battery	_	_	O
store	_	_	O
sells	_	_	O
AA	_	_	B-VAR
and	_	_	O
D	_	_	B-VAR
batteries	_	_	I-VAR
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
1000	_	_	B-LIMIT
and	_	_	O
each	_	_	O
AA	_	_	B-VAR
battery	_	_	I-VAR
costs	_	_	O
$	_	_	O
1	_	_	B-PARAM
and	_	_	O
each	_	_	O
D	_	_	B-VAR
battery	_	_	I-VAR
costs	_	_	O
$	_	_	O
3	_	_	B-PARAM
.	_	_	O
The	_	_	O
monthly	_	_	O
demand	_	_	O
for	_	_	O
both	_	_	O
batteries	_	_	O
will	_	_	O
not	_	_	B-CONST_DIR
exceed	_	_	I-CONST_DIR
1000	_	_	B-LIMIT
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
AA	_	_	B-VAR
battery	_	_	I-VAR
is	_	_	O
$	_	_	O
0.50	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
D	_	_	B-VAR
battery	_	_	I-VAR
is	_	_	O
$	_	_	O
1	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
store	_	_	O
stock	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
sandwich	_	_	O
store	_	_	O
makes	_	_	O
subs	_	_	B-VAR
and	_	_	O
flatbreads	_	_	B-VAR
.	_	_	O
Each	_	_	O
sub	_	_	B-VAR
takes	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
preparation	_	_	O
and	_	_	O
2	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
toasting	_	_	O
.	_	_	O
Each	_	_	O
flatbread	_	_	B-VAR
takes	_	_	O
4	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
preparation	_	_	O
and	_	_	O
1	_	_	B-PARAM
minute	_	_	O
of	_	_	O
toasting	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
2000	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
preparation	_	_	O
and	_	_	O
2200	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
toasting	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
sub	_	_	B-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
flatbread	_	_	B-VAR
is	_	_	O
$	_	_	O
2.50	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
ferry	_	_	O
can	_	_	O
carry	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
120	_	_	B-LIMIT
people	_	_	O
and	_	_	O
sells	_	_	O
regular	_	_	B-VAR
rate	_	_	I-VAR
tickets	_	_	I-VAR
and	_	_	O
concession	_	_	B-VAR
rate	_	_	I-VAR
tickets	_	_	I-VAR
.	_	_	O
A	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
2	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
regular	_	_	B-VAR
rate	_	_	I-VAR
ticket	_	_	I-VAR
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
0.50	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
concession	_	_	B-VAR
rate	_	_	I-VAR
ticket	_	_	I-VAR
.	_	_	O
The	_	_	O
ferry	_	_	O
reserves	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
15	_	_	B-LIMIT
tickets	_	_	O
for	_	_	O
concession	_	_	B-VAR
rate	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
many	_	_	O
tickets	_	_	O
sold	_	_	O
are	_	_	O
regular	_	_	B-VAR
rate	_	_	I-VAR
tickets	_	_	I-VAR
than	_	_	O
concession	_	_	B-VAR
rate	_	_	I-VAR
tickets	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
ticket	_	_	O
should	_	_	O
be	_	_	O
sold	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
factory	_	_	O
produces	_	_	O
1st	_	_	B-VAR
and	_	_	O
2nd	_	_	B-VAR
generation	_	_	I-VAR
motherboards	_	_	I-VAR
.	_	_	O
A	_	_	O
1st	_	_	B-VAR
generation	_	_	I-VAR
motherboard	_	_	I-VAR
requires	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
silicon	_	_	O
while	_	_	O
a	_	_	O
2nd	_	_	B-VAR
generation	_	_	I-VAR
motherboard	_	_	I-VAR
requires	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
silicon	_	_	O
.	_	_	O
A	_	_	O
1st	_	_	B-VAR
generation	_	_	I-VAR
motherboard	_	_	I-VAR
requires	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
assembly	_	_	O
and	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
soldering	_	_	O
while	_	_	O
a	_	_	O
2nd	_	_	B-VAR
generation	_	_	I-VAR
motherboard	_	_	I-VAR
requires	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
assembly	_	_	O
and	_	_	O
40	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
soldering	_	_	O
.	_	_	O
The	_	_	O
factory	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
450	_	_	B-LIMIT
units	_	_	O
of	_	_	O
silicon	_	_	O
,	_	_	O
900	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
assembly	_	_	O
time	_	_	O
,	_	_	O
and	_	_	O
500	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
soldering	_	_	O
time	_	_	O
.	_	_	O
They	_	_	O
also	_	_	O
want	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
6	_	_	B-LIMIT
1st	_	_	B-VAR
generation	_	_	I-VAR
motherboards	_	_	I-VAR
and	_	_	O
7	_	_	B-LIMIT
2nd	_	_	B-VAR
generation	_	_	I-VAR
motherboards	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
1st	_	_	B-VAR
generation	_	_	I-VAR
motherboard	_	_	I-VAR
is	_	_	O
$	_	_	O
100	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
2nd	_	_	B-VAR
generation	_	_	I-VAR
motherboard	_	_	I-VAR
is	_	_	O
$	_	_	O
125	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
factory	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
snack	_	_	O
company	_	_	O
wants	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
special	_	_	O
mix	_	_	O
using	_	_	O
previous	_	_	O
snack	_	_	O
mixes	_	_	O
,	_	_	O
snack	_	_	B-VAR
mix	_	_	I-VAR
A	_	_	I-VAR
and	_	_	O
snack	_	_	B-VAR
mix	_	_	I-VAR
B.	_	_	I-VAR
Each	_	_	O
snack	_	_	B-VAR
mix	_	_	I-VAR
A	_	_	I-VAR
has	_	_	O
20	_	_	B-PARAM
cashews	_	_	O
and	_	_	O
30	_	_	B-PARAM
peanuts	_	_	O
.	_	_	O
Each	_	_	O
snack	_	_	B-VAR
mix	_	_	I-VAR
B	_	_	I-VAR
has	_	_	O
10	_	_	B-PARAM
cashews	_	_	O
and	_	_	O
45	_	_	B-PARAM
peanuts	_	_	O
.	_	_	O
The	_	_	O
special	_	_	O
mix	_	_	O
must	_	_	O
contain	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
90	_	_	B-LIMIT
cashews	_	_	O
and	_	_	O
80	_	_	B-LIMIT
peanuts	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
there	_	_	O
can	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
12	_	_	B-LIMIT
of	_	_	O
snack	_	_	B-VAR
mix	_	_	I-VAR
A	_	_	I-VAR
in	_	_	O
the	_	_	O
mixture	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
snack	_	_	B-VAR
mix	_	_	I-VAR
A	_	_	I-VAR
is	_	_	O
$	_	_	O
1.00	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
snack	_	_	B-VAR
mix	_	_	I-VAR
B	_	_	I-VAR
is	_	_	O
$	_	_	O
1.20	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
in	_	_	O
the	_	_	O
mixture	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
company	_	_	O
sells	_	_	O
tea	_	_	B-VAR
and	_	_	O
coffee	_	_	B-VAR
in	_	_	O
small	_	_	O
tins	_	_	O
.	_	_	O
Each	_	_	O
tea	_	_	B-VAR
tin	_	_	I-VAR
takes	_	_	O
4	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
fill	_	_	O
and	_	_	O
1	_	_	B-PARAM
minute	_	_	O
to	_	_	O
label	_	_	O
.	_	_	O
Each	_	_	O
coffee	_	_	B-VAR
tin	_	_	I-VAR
takes	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
fill	_	_	O
and	_	_	O
2	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
label	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
500	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
filling	_	_	O
and	_	_	O
600	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
labeling	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
tea	_	_	B-VAR
tin	_	_	I-VAR
is	_	_	O
$	_	_	O
11	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
coffee	_	_	B-VAR
tin	_	_	I-VAR
is	_	_	O
$	_	_	O
13	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
pet	_	_	O
store	_	_	O
feeds	_	_	O
their	_	_	O
dogs	_	_	O
by	_	_	O
making	_	_	O
a	_	_	O
mixture	_	_	O
from	_	_	O
two	_	_	O
bags	_	_	O
.	_	_	O
Bag	_	_	B-VAR
A	_	_	I-VAR
contains	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
calcium	_	_	O
per	_	_	O
bag	_	_	O
.	_	_	O
Bag	_	_	B-VAR
B	_	_	I-VAR
contains	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
calcium	_	_	O
per	_	_	O
bag	_	_	O
.	_	_	O
The	_	_	O
mixture	_	_	O
must	_	_	O
contain	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
units	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
35	_	_	B-LIMIT
units	_	_	O
of	_	_	O
calcium	_	_	O
.	_	_	O
Bag	_	_	B-VAR
A	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
3.50	_	_	B-PARAM
per	_	_	O
bag	_	_	O
and	_	_	O
Bag	_	_	B-VAR
B	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
2.50	_	_	B-PARAM
per	_	_	O
bag	_	_	O
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
cost	_	_	B-OBJ_NAME
for	_	_	O
the	_	_	O
mixture	_	_	O
.	_	_	O

A	_	_	O
sandwich	_	_	O
store	_	_	O
makes	_	_	O
meatballs	_	_	B-VAR
and	_	_	O
ham	_	_	B-VAR
sandwiches	_	_	I-VAR
.	_	_	O
Each	_	_	O
meatball	_	_	B-VAR
sandwich	_	_	I-VAR
requires	_	_	O
25	_	_	B-PARAM
grams	_	_	O
of	_	_	O
meat	_	_	O
,	_	_	O
10	_	_	B-PARAM
grams	_	_	O
of	_	_	O
cheese	_	_	O
,	_	_	O
and	_	_	O
50	_	_	B-PARAM
grams	_	_	O
of	_	_	O
sauce	_	_	O
.	_	_	O
Each	_	_	O
ham	_	_	B-VAR
sandwich	_	_	I-VAR
requires	_	_	O
30	_	_	B-PARAM
grams	_	_	O
of	_	_	O
meat	_	_	O
,	_	_	O
25	_	_	B-PARAM
grams	_	_	O
of	_	_	O
cheese	_	_	O
,	_	_	O
and	_	_	O
20	_	_	B-PARAM
grams	_	_	O
of	_	_	O
sauce	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
4000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
meat	_	_	O
,	_	_	O
5000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
cheese	_	_	O
,	_	_	O
and	_	_	O
5200	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
sauce	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
meatball	_	_	B-VAR
sandwich	_	_	I-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
ham	_	_	B-VAR
sandwich	_	_	I-VAR
is	_	_	O
$	_	_	O
3.50	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
telecommunications	_	_	O
company	_	_	O
installs	_	_	O
internet	_	_	B-VAR
service	_	_	I-VAR
and	_	_	O
TV	_	_	B-VAR
service	_	_	I-VAR
in	_	_	O
buildings	_	_	O
.	_	_	O
Each	_	_	O
internet	_	_	B-VAR
service	_	_	I-VAR
takes	_	_	O
60	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
wiring	_	_	O
time	_	_	O
and	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
box	_	_	O
installation	_	_	O
time	_	_	O
.	_	_	O
Each	_	_	O
TV	_	_	B-VAR
service	_	_	I-VAR
takes	_	_	O
50	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
wiring	_	_	O
time	_	_	O
and	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
box	_	_	O
installation	_	_	O
time	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
7000	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
wiring	_	_	O
time	_	_	O
and	_	_	O
4000	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
box	_	_	O
installation	_	_	O
time	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
internet	_	_	B-VAR
service	_	_	I-VAR
installation	_	_	O
is	_	_	O
$	_	_	O
100	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
TV	_	_	B-VAR
service	_	_	I-VAR
installation	_	_	O
is	_	_	O
$	_	_	O
120	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
installed	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
makeup	_	_	O
company	_	_	O
hand	_	_	O
fills	_	_	O
perfume	_	_	B-VAR
and	_	_	O
cologne	_	_	B-VAR
bottles	_	_	I-VAR
.	_	_	O
Each	_	_	O
perfume	_	_	B-VAR
bottle	_	_	I-VAR
takes	_	_	O
2	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
fill	_	_	O
and	_	_	O
each	_	_	O
cologne	_	_	B-VAR
bottle	_	_	I-VAR
takes	_	_	O
2.5	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
fill	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
must	_	_	O
fill	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
60	_	_	B-LIMIT
perfume	_	_	B-VAR
bottles	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
40	_	_	B-LIMIT
cologne	_	_	B-VAR
bottles	_	_	I-VAR
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
700	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
perfume	_	_	B-VAR
bottle	_	_	I-VAR
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
cologne	_	_	B-VAR
bottle	_	_	I-VAR
is	_	_	O
$	_	_	O
60	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
filled	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
steel	_	_	O
shop	_	_	O
makes	_	_	O
fences	_	_	B-VAR
and	_	_	O
doors	_	_	B-VAR
using	_	_	O
stainless	_	_	O
steel	_	_	O
and	_	_	O
aluminum	_	_	O
.	_	_	O
Each	_	_	O
fence	_	_	B-VAR
requires	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
stainless	_	_	O
steel	_	_	O
and	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
aluminum	_	_	O
.	_	_	O
Each	_	_	O
door	_	_	B-VAR
requires	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
stainless	_	_	O
steel	_	_	O
and	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
aluminum	_	_	O
.	_	_	O
The	_	_	O
steel	_	_	O
shop	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
400	_	_	B-LIMIT
units	_	_	O
of	_	_	O
stainless	_	_	O
steel	_	_	O
and	_	_	O
500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
aluminum	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
fence	_	_	B-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
door	_	_	B-VAR
is	_	_	O
$	_	_	O
100	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

You	_	_	O
need	_	_	O
to	_	_	O
buy	_	_	O
cabinets	_	_	O
to	_	_	O
store	_	_	O
your	_	_	O
seasonings	_	_	B-OBJ_NAME
and	_	_	I-OBJ_NAME
spices	_	_	I-OBJ_NAME
.	_	_	O
A	_	_	O
small	_	_	B-VAR
cabinet	_	_	I-VAR
takes	_	_	O
4	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
of	_	_	O
space	_	_	O
and	_	_	O
costs	_	_	O
$	_	_	O
70	_	_	B-PARAM
.	_	_	O
A	_	_	O
large	_	_	B-VAR
cabinet	_	_	I-VAR
takes	_	_	O
8	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
and	_	_	O
costs	_	_	O
$	_	_	O
120	_	_	B-PARAM
.	_	_	O
You	_	_	O
have	_	_	O
200	_	_	B-LIMIT
sq	_	_	O
ft	_	_	O
of	_	_	O
space	_	_	O
available	_	_	B-CONST_DIR
in	_	_	O
your	_	_	O
kitchen	_	_	O
and	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
1400	_	_	B-LIMIT
.	_	_	O
If	_	_	O
the	_	_	O
small	_	_	B-VAR
cabinet	_	_	I-VAR
can	_	_	O
hold	_	_	O
30	_	_	B-PARAM
seasonings	_	_	B-OBJ_NAME
and	_	_	I-OBJ_NAME
spices	_	_	I-OBJ_NAME
and	_	_	O
a	_	_	O
large	_	_	B-VAR
cabinet	_	_	I-VAR
can	_	_	O
hold	_	_	O
40	_	_	B-PARAM
seasonings	_	_	B-OBJ_NAME
and	_	_	I-OBJ_NAME
spices	_	_	I-OBJ_NAME
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
you	_	_	O
buy	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	O
of	_	_	O
seasonings	_	_	B-OBJ_NAME
and	_	_	I-OBJ_NAME
spices	_	_	I-OBJ_NAME
you	_	_	O
can	_	_	O
store	_	_	O
.	_	_	O

You	_	_	O
have	_	_	O
two	_	_	O
instant	_	_	O
coffees	_	_	O
that	_	_	O
contain	_	_	O
caffeine	_	_	O
and	_	_	O
sugar	_	_	O
.	_	_	O
Vanilla	_	_	B-VAR
flavor	_	_	I-VAR
contains	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
caffeine	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
sugar	_	_	O
per	_	_	O
package	_	_	O
.	_	_	O
Mocha	_	_	B-VAR
flavor	_	_	I-VAR
contains	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
caffeine	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
sugar	_	_	O
per	_	_	O
package	_	_	O
.	_	_	O
You	_	_	O
must	_	_	O
consume	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
60	_	_	B-LIMIT
units	_	_	O
of	_	_	O
caffeine	_	_	O
and	_	_	O
50	_	_	B-LIMIT
units	_	_	O
of	_	_	O
sugar	_	_	O
.	_	_	O
If	_	_	O
a	_	_	O
package	_	_	O
of	_	_	O
vanilla	_	_	B-VAR
flavor	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
2	_	_	B-PARAM
and	_	_	O
a	_	_	O
package	_	_	O
of	_	_	O
mocha	_	_	B-VAR
flavor	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
3	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
you	_	_	O
buy	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

You	_	_	O
have	_	_	B-CONST_DIR
40	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
on	_	_	O
which	_	_	O
you	_	_	O
grow	_	_	O
corn	_	_	B-VAR
and	_	_	O
peas	_	_	B-VAR
.	_	_	O
Each	_	_	O
acre	_	_	O
of	_	_	O
corn	_	_	B-VAR
requires	_	_	O
$	_	_	O
50	_	_	B-PARAM
worth	_	_	O
of	_	_	O
fertilizer	_	_	O
and	_	_	O
60	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
time	_	_	O
to	_	_	O
lay	_	_	O
the	_	_	O
fertilizer	_	_	O
.	_	_	O
Each	_	_	O
acre	_	_	O
of	_	_	O
peas	_	_	B-VAR
requires	_	_	O
$	_	_	O
60	_	_	B-PARAM
worth	_	_	O
of	_	_	O
fertilizer	_	_	O
and	_	_	O
90	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
time	_	_	O
to	_	_	O
lay	_	_	O
the	_	_	O
fertilizer	_	_	O
.	_	_	O
You	_	_	O
have	_	_	O
available	_	_	B-CONST_DIR
$	_	_	O
4350	_	_	B-LIMIT
to	_	_	O
spend	_	_	O
on	_	_	O
fertilizer	_	_	O
and	_	_	O
6000	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
to	_	_	O
lay	_	_	O
the	_	_	O
fertilizer	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
corn	_	_	B-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
peas	_	_	B-VAR
is	_	_	O
$	_	_	O
250	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
grown	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
ice	_	_	O
cream	_	_	O
truck	_	_	O
sells	_	_	O
ice	_	_	B-VAR
cream	_	_	I-VAR
cones	_	_	I-VAR
and	_	_	O
ice	_	_	B-VAR
cream	_	_	I-VAR
cups	_	_	I-VAR
.	_	_	O
Each	_	_	O
ice	_	_	B-VAR
cream	_	_	I-VAR
cone	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
scoops	_	_	O
of	_	_	O
ice	_	_	O
cream	_	_	O
and	_	_	O
5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
toppings	_	_	O
.	_	_	O
Each	_	_	O
ice	_	_	B-VAR
cream	_	_	I-VAR
cup	_	_	I-VAR
requires	_	_	O
4	_	_	B-PARAM
scoops	_	_	O
of	_	_	O
ice	_	_	O
cream	_	_	O
and	_	_	O
6	_	_	B-PARAM
grams	_	_	O
of	_	_	O
toppings	_	_	O
.	_	_	O
The	_	_	O
truck	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
500	_	_	B-LIMIT
scoops	_	_	O
of	_	_	O
ice	_	_	O
cream	_	_	O
and	_	_	O
1000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
toppings	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
revenue	_	_	B-OBJ_NAME
per	_	_	O
ice	_	_	B-VAR
cream	_	_	I-VAR
cone	_	_	I-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
and	_	_	O
the	_	_	O
revenue	_	_	B-OBJ_NAME
per	_	_	O
ice	_	_	B-VAR
cream	_	_	I-VAR
cup	_	_	I-VAR
is	_	_	O
$	_	_	O
3.50	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
it	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
revenue	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
artist	_	_	O
uses	_	_	O
cotton	_	_	O
to	_	_	O
make	_	_	O
both	_	_	O
mini	_	_	B-VAR
bears	_	_	I-VAR
and	_	_	O
dogs	_	_	B-VAR
.	_	_	O
Each	_	_	O
mini	_	_	B-VAR
bear	_	_	I-VAR
requires	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
cotton	_	_	O
and	_	_	O
each	_	_	O
mini	_	_	B-VAR
dog	_	_	I-VAR
requires	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
cotton	_	_	O
.	_	_	O
The	_	_	O
artist	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
400	_	_	B-LIMIT
units	_	_	O
of	_	_	O
cotton	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
due	_	_	O
to	_	_	O
time	_	_	O
constraints	_	_	O
,	_	_	O
the	_	_	O
artist	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
40	_	_	B-LIMIT
animals	_	_	O
total	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
mini	_	_	B-VAR
bear	_	_	I-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
40	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
mini	_	_	B-VAR
dog	_	_	I-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
47	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
artist	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

In	_	_	O
an	_	_	O
arcade	_	_	O
shooter	_	_	O
,	_	_	O
each	_	_	O
duck	_	_	B-VAR
shot	_	_	I-VAR
is	_	_	O
5	_	_	B-PARAM
points	_	_	B-OBJ_NAME
and	_	_	O
each	_	_	O
goose	_	_	B-VAR
shot	_	_	I-VAR
is	_	_	O
6	_	_	B-PARAM
points	_	_	B-OBJ_NAME
.	_	_	O
You	_	_	O
must	_	_	O
shoot	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
ducks	_	_	B-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-LIMIT
geese	_	_	B-VAR
to	_	_	O
pass	_	_	O
the	_	_	O
level	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
you	_	_	O
can	_	_	O
shoot	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
12	_	_	B-LIMIT
ducks	_	_	B-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
7	_	_	B-LIMIT
geese	_	_	B-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
you	_	_	O
only	_	_	B-CONST_DIR
have	_	_	O
enough	_	_	O
bullets	_	_	O
to	_	_	O
shoot	_	_	O
15	_	_	B-LIMIT
animals	_	_	O
total	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
animal	_	_	O
should	_	_	O
you	_	_	O
shoot	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
your	_	_	O
points	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
berry	_	_	O
picker	_	_	O
must	_	_	O
pick	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3000	_	_	B-LIMIT
strawberries	_	_	O
and	_	_	O
15000	_	_	B-LIMIT
raspberries	_	_	O
.	_	_	O
He	_	_	O
visits	_	_	O
two	_	_	O
farms	_	_	O
.	_	_	O
For	_	_	O
each	_	_	O
hour	_	_	B-OBJ_NAME
at	_	_	O
farm	_	_	B-VAR
1	_	_	I-VAR
he	_	_	O
spends	_	_	O
,	_	_	O
he	_	_	O
can	_	_	O
pick	_	_	O
50	_	_	B-PARAM
strawberries	_	_	O
and	_	_	O
300	_	_	B-PARAM
raspberries	_	_	O
.	_	_	O
For	_	_	O
each	_	_	O
hour	_	_	B-OBJ_NAME
at	_	_	O
farm	_	_	B-VAR
2	_	_	I-VAR
he	_	_	O
spends	_	_	O
,	_	_	O
he	_	_	O
can	_	_	O
catch	_	_	O
70	_	_	B-PARAM
strawberries	_	_	O
and	_	_	O
200	_	_	B-PARAM
raspberries	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
hours	_	_	B-OBJ_NAME
should	_	_	O
he	_	_	O
spend	_	_	O
at	_	_	O
each	_	_	O
farm	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
time	_	_	I-OBJ_NAME
he	_	_	O
spends	_	_	O
at	_	_	O
both	_	_	O
farms	_	_	O
?	_	_	O

A	_	_	O
store	_	_	O
sells	_	_	O
ramen	_	_	O
in	_	_	O
large	_	_	B-VAR
and	_	_	O
small	_	_	B-VAR
packages	_	_	I-VAR
.	_	_	O
Each	_	_	O
large	_	_	B-VAR
package	_	_	I-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
3	_	_	B-PARAM
and	_	_	O
each	_	_	O
small	_	_	B-VAR
package	_	_	I-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
1	_	_	B-PARAM
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
2000	_	_	B-LIMIT
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
each	_	_	O
large	_	_	B-VAR
package	_	_	I-VAR
takes	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
shelf	_	_	O
space	_	_	O
while	_	_	O
each	_	_	O
small	_	_	B-VAR
package	_	_	I-VAR
takes	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
shelf	_	_	O
space	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
400	_	_	B-LIMIT
units	_	_	O
of	_	_	O
shelf	_	_	O
space	_	_	O
.	_	_	O
Also	_	_	O
the	_	_	O
store	_	_	O
wants	_	_	O
to	_	_	O
make	_	_	O
sure	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
70	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
all	_	_	O
stock	_	_	O
is	_	_	O
small	_	_	B-VAR
packages	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
large	_	_	B-VAR
package	_	_	I-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
small	_	_	B-VAR
package	_	_	I-VAR
is	_	_	O
$	_	_	O
0.50	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
store	_	_	O
keep	_	_	O
in	_	_	O
stock	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
candy	_	_	O
store	_	_	O
hand	_	_	O
makes	_	_	O
gummy	_	_	O
bears	_	_	O
.	_	_	O
Each	_	_	O
packet	_	_	O
of	_	_	O
fruit	_	_	B-VAR
gummy	_	_	I-VAR
bears	_	_	I-VAR
takes	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
make	_	_	O
and	_	_	O
each	_	_	O
packet	_	_	O
of	_	_	O
sour	_	_	B-VAR
gummy	_	_	I-VAR
bears	_	_	I-VAR
takes	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
make	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
2000	_	_	B-LIMIT
minutes	_	_	O
to	_	_	O
make	_	_	O
the	_	_	O
packets	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
they	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
120	_	_	B-LIMIT
fruit	_	_	B-VAR
gummy	_	_	I-VAR
bears	_	_	I-VAR
packets	_	_	O
and	_	_	O
70	_	_	B-LIMIT
sour	_	_	B-VAR
gummy	_	_	I-VAR
bears	_	_	I-VAR
packets	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
packet	_	_	O
of	_	_	O
fruit	_	_	B-VAR
gummy	_	_	I-VAR
bears	_	_	I-VAR
is	_	_	O
$	_	_	O
1	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
packet	_	_	O
of	_	_	O
sour	_	_	B-VAR
gummy	_	_	I-VAR
bears	_	_	I-VAR
is	_	_	O
$	_	_	O
1.25	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
small	_	_	O
grocery	_	_	O
weighs	_	_	O
and	_	_	O
packages	_	_	O
their	_	_	O
bulk	_	_	O
foods	_	_	O
.	_	_	O
Each	_	_	O
container	_	_	O
of	_	_	O
nuts	_	_	B-VAR
takes	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
weighing	_	_	O
and	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
packaging	_	_	O
.	_	_	O
Each	_	_	O
container	_	_	O
of	_	_	O
candy	_	_	B-VAR
takes	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
weighing	_	_	O
and	_	_	O
8	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
packaging	_	_	O
.	_	_	O
The	_	_	O
grocery	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
1000	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
weighing	_	_	O
and	_	_	O
1500	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
packaging	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
container	_	_	O
of	_	_	O
nuts	_	_	B-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
container	_	_	O
of	_	_	O
candy	_	_	B-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
grocery	_	_	O
prepare	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
electronics	_	_	O
store	_	_	O
sells	_	_	O
televisions	_	_	B-VAR
and	_	_	O
speakers	_	_	B-VAR
.	_	_	O
A	_	_	O
television	_	_	B-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
400	_	_	B-PARAM
and	_	_	O
a	_	_	O
speaker	_	_	B-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
200	_	_	B-PARAM
.	_	_	O
The	_	_	O
store	_	_	O
can	_	_	O
spend	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
25000	_	_	B-LIMIT
.	_	_	O
The	_	_	O
store	_	_	O
sells	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
televisions	_	_	B-VAR
but	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
75	_	_	B-LIMIT
televisions	_	_	B-VAR
.	_	_	O
Also	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
speakers	_	_	B-VAR
sold	_	_	O
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
a	_	_	O
half	_	_	B-PARAM
of	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
televisions	_	_	B-VAR
sold	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
television	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
400	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
speaker	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
250	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
store	_	_	O
buy	_	_	O
and	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
man	_	_	O
insists	_	_	O
he	_	_	O
can	_	_	O
meet	_	_	O
his	_	_	O
carbohydrate	_	_	O
and	_	_	O
protein	_	_	O
requirements	_	_	O
from	_	_	O
eating	_	_	O
beans	_	_	B-VAR
and	_	_	O
cereal	_	_	B-VAR
.	_	_	O
He	_	_	O
wants	_	_	O
to	_	_	O
get	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
300	_	_	B-LIMIT
g	_	_	O
of	_	_	O
carbohydrates	_	_	O
and	_	_	O
150	_	_	B-LIMIT
g	_	_	O
of	_	_	O
protein	_	_	O
.	_	_	O
Each	_	_	O
serving	_	_	O
of	_	_	O
beans	_	_	B-VAR
contains	_	_	O
50	_	_	B-PARAM
g	_	_	O
of	_	_	O
carbohydrates	_	_	O
and	_	_	O
20	_	_	B-PARAM
g	_	_	O
of	_	_	O
protein	_	_	O
while	_	_	O
each	_	_	O
serving	_	_	O
of	_	_	O
cereal	_	_	B-VAR
contains	_	_	O
30	_	_	B-PARAM
g	_	_	O
of	_	_	O
carbohydrates	_	_	O
and	_	_	O
5	_	_	B-PARAM
g	_	_	O
of	_	_	O
protein	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
serving	_	_	O
of	_	_	O
beans	_	_	B-VAR
is	_	_	O
$	_	_	O
2	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
serving	_	_	O
of	_	_	O
cereal	_	_	B-VAR
is	_	_	O
$	_	_	O
1	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
eat	_	_	O
to	_	_	O
meet	_	_	O
his	_	_	O
requirements	_	_	O
at	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
company	_	_	O
makes	_	_	O
surfboards	_	_	B-VAR
and	_	_	O
skateboards	_	_	B-VAR
.	_	_	O
Each	_	_	O
surfboard	_	_	B-VAR
requires	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
wood	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
paint	_	_	O
.	_	_	O
Each	_	_	O
skateboard	_	_	B-VAR
requires	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
wood	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
paint	_	_	O
.	_	_	O
At	_	_	O
the	_	_	O
company	_	_	O
,	_	_	O
there	_	_	O
are	_	_	O
700	_	_	B-LIMIT
units	_	_	O
of	_	_	O
wood	_	_	O
available	_	_	B-CONST_DIR
and	_	_	O
320	_	_	B-LIMIT
units	_	_	O
of	_	_	O
paint	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
surfboard	_	_	B-VAR
is	_	_	O
$	_	_	O
70	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
skateboard	_	_	B-VAR
is	_	_	O
$	_	_	O
45	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
woman	_	_	O
owns	_	_	O
two	_	_	O
cafes	_	_	O
.	_	_	O
Running	_	_	O
cafe	_	_	B-VAR
1	_	_	I-VAR
for	_	_	O
an	_	_	O
hour	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
400	_	_	B-PARAM
and	_	_	O
makes	_	_	O
12	_	_	B-PARAM
lattes	_	_	O
,	_	_	O
18	_	_	B-PARAM
americanos	_	_	O
,	_	_	O
and	_	_	O
16	_	_	B-PARAM
macchiatos	_	_	O
.	_	_	O
Running	_	_	O
cafe	_	_	B-VAR
2	_	_	I-VAR
for	_	_	O
an	_	_	O
hour	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
550	_	_	B-PARAM
and	_	_	O
makes	_	_	O
14	_	_	B-PARAM
lattes	_	_	O
,	_	_	O
20	_	_	B-PARAM
americanos	_	_	O
,	_	_	O
and	_	_	O
9	_	_	B-PARAM
macchiatos	_	_	O
.	_	_	O
To	_	_	O
meet	_	_	O
demand	_	_	O
,	_	_	O
she	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
90	_	_	B-LIMIT
lattes	_	_	O
,	_	_	O
80	_	_	B-LIMIT
americanos	_	_	O
,	_	_	O
and	_	_	O
40	_	_	B-LIMIT
macchiatos	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
hours	_	_	O
should	_	_	O
she	_	_	O
run	_	_	O
each	_	_	O
cafe	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
cereal	_	_	O
company	_	_	O
makes	_	_	O
nutritional	_	_	B-VAR
cereal	_	_	I-VAR
,	_	_	O
kids	_	_	B-VAR
'	_	_	I-VAR
cereal	_	_	I-VAR
,	_	_	O
and	_	_	O
sugary	_	_	B-VAR
cereal	_	_	I-VAR
.	_	_	O
Each	_	_	O
box	_	_	O
of	_	_	O
nutritional	_	_	B-VAR
cereal	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
oat	_	_	O
and	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
sugar	_	_	O
.	_	_	O
Each	_	_	O
kids	_	_	B-VAR
'	_	_	I-VAR
cereal	_	_	I-VAR
requires	_	_	O
1.5	_	_	B-PARAM
units	_	_	O
of	_	_	O
oat	_	_	O
and	_	_	O
1.5	_	_	B-PARAM
units	_	_	O
of	_	_	O
sugar	_	_	O
.	_	_	O
Each	_	_	O
sugary	_	_	B-VAR
cereal	_	_	I-VAR
requires	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
oat	_	_	O
and	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
sugar	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
oat	_	_	O
and	_	_	O
700	_	_	B-LIMIT
units	_	_	O
of	_	_	O
sugar	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
revenue	_	_	B-OBJ_NAME
per	_	_	O
box	_	_	O
of	_	_	O
nutritional	_	_	B-VAR
cereal	_	_	I-VAR
is	_	_	O
$	_	_	O
1	_	_	B-PARAM
,	_	_	O
the	_	_	O
revenue	_	_	B-OBJ_NAME
per	_	_	O
kids	_	_	B-VAR
'	_	_	I-VAR
cereal	_	_	I-VAR
is	_	_	O
$	_	_	O
1.50	_	_	B-PARAM
,	_	_	O
and	_	_	O
the	_	_	O
revenue	_	_	B-OBJ_NAME
per	_	_	O
sugary	_	_	B-VAR
cereal	_	_	I-VAR
is	_	_	O
$	_	_	O
2	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
revenue	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
doctor	_	_	O
prescribed	_	_	O
two	_	_	O
supplements	_	_	O
to	_	_	O
a	_	_	O
patient	_	_	O
.	_	_	O
Supplement	_	_	B-VAR
A	_	_	I-VAR
contains	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
calcium	_	_	O
,	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
A	_	_	O
,	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
B	_	_	O
per	_	_	O
supplement	_	_	O
.	_	_	O
Supplement	_	_	B-VAR
B	_	_	I-VAR
contains	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
calcium	_	_	O
,	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
vitamin	_	_	O
A	_	_	O
,	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
B	_	_	O
per	_	_	O
supplement	_	_	O
.	_	_	O
Supplement	_	_	B-VAR
A	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
3.50	_	_	B-PARAM
per	_	_	O
supplement	_	_	O
while	_	_	O
supplement	_	_	B-VAR
B	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
3.80	_	_	B-PARAM
per	_	_	O
supplement	_	_	O
.	_	_	O
The	_	_	O
patient	_	_	O
must	_	_	O
get	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
25	_	_	B-LIMIT
units	_	_	O
of	_	_	O
calcium	_	_	O
,	_	_	O
20	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamin	_	_	O
A	_	_	O
,	_	_	O
and	_	_	O
18	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamin	_	_	O
B.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
supplement	_	_	O
should	_	_	O
he	_	_	O
buy	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
cost	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
restaurant	_	_	O
makes	_	_	O
prepackaged	_	_	O
takeout	_	_	O
meals	_	_	O
.	_	_	O
The	_	_	O
breakfast	_	_	B-VAR
option	_	_	I-VAR
takes	_	_	O
7	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
prepare	_	_	O
and	_	_	O
2	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
package	_	_	O
.	_	_	O
The	_	_	O
lunch	_	_	B-VAR
option	_	_	I-VAR
takes	_	_	O
8	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
prepare	_	_	O
and	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
package	_	_	O
.	_	_	O
The	_	_	O
restaurant	_	_	O
has	_	_	O
700	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
preparations	_	_	O
and	_	_	O
500	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
packaging	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
breakfast	_	_	B-VAR
option	_	_	I-VAR
is	_	_	O
$	_	_	O
10	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
lunch	_	_	B-VAR
option	_	_	I-VAR
is	_	_	O
$	_	_	O
8	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
restaurant	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
grocery	_	_	O
store	_	_	O
wants	_	_	O
to	_	_	O
sell	_	_	O
their	_	_	O
bulk	_	_	O
quantities	_	_	O
of	_	_	O
gummy	_	_	O
bears	_	_	O
,	_	_	O
gummy	_	_	O
worms	_	_	O
,	_	_	O
and	_	_	O
sour	_	_	O
candies	_	_	O
by	_	_	O
mixing	_	_	O
them	_	_	O
into	_	_	O
special	_	_	O
combo	_	_	O
deals	_	_	O
.	_	_	O
They	_	_	O
have	_	_	B-CONST_DIR
1200	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
gummy	_	_	O
bears	_	_	O
,	_	_	O
1400	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
gummy	_	_	O
worms	_	_	O
,	_	_	O
and	_	_	O
900	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
sour	_	_	O
candies	_	_	O
.	_	_	O
Combo	_	_	B-VAR
1	_	_	I-VAR
contains	_	_	O
25	_	_	B-PARAM
grams	_	_	O
of	_	_	O
gummy	_	_	O
bears	_	_	O
,	_	_	O
20	_	_	B-PARAM
grams	_	_	O
of	_	_	O
gummy	_	_	O
worms	_	_	O
,	_	_	O
and	_	_	O
15	_	_	B-PARAM
grams	_	_	O
of	_	_	O
sour	_	_	O
candies	_	_	O
.	_	_	O
Combo	_	_	B-VAR
2	_	_	I-VAR
contains	_	_	O
12	_	_	B-PARAM
grams	_	_	O
of	_	_	O
gummy	_	_	O
bears	_	_	O
,	_	_	O
21	_	_	B-PARAM
grams	_	_	O
of	_	_	O
gummy	_	_	O
worms	_	_	O
,	_	_	O
and	_	_	O
24	_	_	B-PARAM
grams	_	_	O
of	_	_	O
sour	_	_	O
candies	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
combo	_	_	B-VAR
1	_	_	I-VAR
is	_	_	O
$	_	_	O
4	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
combo	_	_	B-VAR
2	_	_	I-VAR
is	_	_	O
$	_	_	O
4.50	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
store	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
museum	_	_	O
gift	_	_	O
shop	_	_	O
sells	_	_	O
gifts	_	_	O
in	_	_	O
two	_	_	O
packages	_	_	O
.	_	_	O
Package	_	_	B-VAR
1	_	_	I-VAR
contains	_	_	O
5	_	_	B-PARAM
souvenirs	_	_	O
and	_	_	O
10	_	_	B-PARAM
snacks	_	_	O
.	_	_	O
Package	_	_	B-VAR
2	_	_	I-VAR
contains	_	_	O
4	_	_	B-PARAM
souvenirs	_	_	O
and	_	_	O
15	_	_	B-PARAM
snacks	_	_	O
.	_	_	O
The	_	_	O
museum	_	_	O
has	_	_	B-CONST_DIR
1000	_	_	B-LIMIT
souvenirs	_	_	O
and	_	_	O
1400	_	_	B-LIMIT
snacks	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
package	_	_	B-VAR
1	_	_	I-VAR
is	_	_	O
$	_	_	O
10	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
package	_	_	B-VAR
2	_	_	I-VAR
is	_	_	O
$	_	_	O
12	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
package	_	_	O
should	_	_	O
they	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
cat	_	_	O
shelter	_	_	O
feeds	_	_	O
their	_	_	O
cats	_	_	O
using	_	_	O
cat	_	_	B-VAR
foods	_	_	I-VAR
and	_	_	O
canned	_	_	B-VAR
tuna	_	_	I-VAR
.	_	_	O
Each	_	_	O
packet	_	_	O
of	_	_	O
cat	_	_	B-VAR
food	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
12	_	_	B-PARAM
while	_	_	O
each	_	_	O
can	_	_	O
of	_	_	O
tuna	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
7	_	_	B-PARAM
.	_	_	O
Each	_	_	O
packet	_	_	O
of	_	_	O
cat	_	_	B-VAR
food	_	_	I-VAR
contains	_	_	O
5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
carbohydrates	_	_	O
,	_	_	O
15	_	_	B-PARAM
grams	_	_	O
of	_	_	O
vitamins	_	_	O
,	_	_	O
and	_	_	O
12	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
.	_	_	O
Each	_	_	O
can	_	_	O
of	_	_	O
tuna	_	_	B-VAR
contains	_	_	O
7	_	_	B-PARAM
grams	_	_	O
of	_	_	O
carbohydrates	_	_	O
,	_	_	O
12	_	_	B-PARAM
grams	_	_	O
of	_	_	O
vitamins	_	_	O
,	_	_	O
and	_	_	O
15	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
.	_	_	O
The	_	_	O
cat	_	_	O
shelter	_	_	O
needs	_	_	O
in	_	_	B-CONST_DIR
total	_	_	I-CONST_DIR
700	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
carbohydrates	_	_	O
,	_	_	O
1100	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
vitamins	_	_	O
,	_	_	O
and	_	_	O
900	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
protein	_	_	O
to	_	_	O
feed	_	_	O
their	_	_	O
cats	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
buy	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
man	_	_	O
takes	_	_	O
two	_	_	O
forms	_	_	O
of	_	_	O
vitamin	_	_	O
supplements	_	_	O
to	_	_	O
get	_	_	O
his	_	_	O
vitamin	_	_	O
B	_	_	O
and	_	_	O
vitamin	_	_	O
D	_	_	O
requirements	_	_	O
.	_	_	O
He	_	_	O
needs	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
14	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamin	_	_	O
B	_	_	O
and	_	_	O
24	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamin	_	_	O
D.	_	_	O
Per	_	_	O
serving	_	_	O
,	_	_	O
a	_	_	O
gummy	_	_	B-VAR
vitamin	_	_	I-VAR
contains	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
B	_	_	O
and	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
D.	_	_	O
Per	_	_	O
serving	_	_	O
,	_	_	O
a	_	_	O
powder	_	_	B-VAR
vitamin	_	_	I-VAR
contains	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
B	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
D.	_	_	O
If	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
serving	_	_	O
for	_	_	O
a	_	_	O
gummy	_	_	B-VAR
vitamin	_	_	I-VAR
is	_	_	O
$	_	_	O
1	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
serving	_	_	O
of	_	_	O
powder	_	_	B-VAR
vitamin	_	_	I-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
take	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
cost	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
Japanese	_	_	O
ramen	_	_	O
restaurant	_	_	O
sells	_	_	O
two	_	_	O
bowls	_	_	B-OBJ_NAME
of	_	_	O
ramen	_	_	O
.	_	_	O
Shio	_	_	B-VAR
ramen	_	_	I-VAR
requires	_	_	O
2	_	_	B-PARAM
eggs	_	_	O
and	_	_	O
1	_	_	B-PARAM
slice	_	_	O
of	_	_	O
pork	_	_	O
.	_	_	O
Shoyu	_	_	B-VAR
ramen	_	_	I-VAR
requires	_	_	O
1	_	_	B-PARAM
egg	_	_	O
and	_	_	O
2	_	_	B-PARAM
slices	_	_	O
of	_	_	O
pork	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
100	_	_	B-LIMIT
eggs	_	_	O
and	_	_	O
60	_	_	B-LIMIT
slices	_	_	O
of	_	_	O
pork	_	_	O
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
bowls	_	_	I-OBJ_NAME
of	_	_	O
either	_	_	O
type	_	_	O
that	_	_	O
can	_	_	O
be	_	_	O
made	_	_	O
.	_	_	O

A	_	_	O
factory	_	_	O
packages	_	_	O
glass	_	_	B-VAR
jars	_	_	I-VAR
and	_	_	O
plates	_	_	B-VAR
.	_	_	O
Glass	_	_	B-VAR
jars	_	_	I-VAR
take	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
worker	_	_	O
time	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
cardboard	_	_	O
.	_	_	O
Plates	_	_	B-VAR
take	_	_	O
12	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
worker	_	_	O
time	_	_	O
and	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
cardboard	_	_	O
.	_	_	O
The	_	_	O
factory	_	_	O
has	_	_	O
620	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
worker	_	_	O
time	_	_	O
available	_	_	B-CONST_DIR
and	_	_	O
120	_	_	B-LIMIT
units	_	_	O
of	_	_	O
cardboard	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
glass	_	_	B-VAR
jar	_	_	I-VAR
packaged	_	_	O
is	_	_	O
$	_	_	O
2	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
plate	_	_	B-VAR
packaged	_	_	O
is	_	_	O
$	_	_	O
2.50	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
package	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
processing	_	_	O
plant	_	_	O
cleans	_	_	O
and	_	_	O
shells	_	_	O
both	_	_	O
crabs	_	_	B-VAR
and	_	_	O
lobsters	_	_	B-VAR
.	_	_	O
Each	_	_	O
crab	_	_	B-VAR
takes	_	_	O
4	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
cleaning	_	_	O
and	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
shelling	_	_	O
.	_	_	O
Each	_	_	O
lobster	_	_	B-VAR
takes	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
cleaning	_	_	O
and	_	_	O
12	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
shelling	_	_	O
.	_	_	O
The	_	_	O
processing	_	_	O
plant	_	_	O
has	_	_	O
400	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
cleaning	_	_	O
and	_	_	O
900	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
shelling	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
crab	_	_	B-VAR
is	_	_	O
$	_	_	O
14	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
lobster	_	_	B-VAR
is	_	_	O
$	_	_	O
18	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
processing	_	_	O
plant	_	_	O
clean	_	_	O
and	_	_	O
shell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
salad	_	_	O
shop	_	_	O
makes	_	_	O
large	_	_	B-VAR
and	_	_	O
small	_	_	B-VAR
salads	_	_	I-VAR
.	_	_	O
A	_	_	O
large	_	_	B-VAR
salad	_	_	I-VAR
takes	_	_	O
45	_	_	B-PARAM
g	_	_	O
of	_	_	O
lettuce	_	_	O
and	_	_	O
10	_	_	B-PARAM
g	_	_	O
of	_	_	O
sauce	_	_	O
.	_	_	O
A	_	_	O
small	_	_	B-VAR
salad	_	_	I-VAR
takes	_	_	O
30	_	_	B-PARAM
g	_	_	O
of	_	_	O
lettuce	_	_	O
and	_	_	O
7	_	_	B-PARAM
g	_	_	O
of	_	_	O
sauce	_	_	O
.	_	_	O
The	_	_	O
shop	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
1500	_	_	B-LIMIT
g	_	_	O
of	_	_	O
lettuce	_	_	O
and	_	_	O
1200	_	_	B-LIMIT
g	_	_	O
of	_	_	O
sauce	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
large	_	_	B-VAR
salad	_	_	I-VAR
is	_	_	O
$	_	_	O
4	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
small	_	_	B-VAR
salad	_	_	I-VAR
is	_	_	O
$	_	_	O
2	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
company	_	_	O
sells	_	_	O
blankets	_	_	B-VAR
and	_	_	O
bedsheets	_	_	B-VAR
.	_	_	O
Each	_	_	O
blanket	_	_	B-VAR
takes	_	_	O
14	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
cut	_	_	O
and	_	_	O
12	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
hem	_	_	O
.	_	_	O
Each	_	_	O
bedsheet	_	_	B-VAR
takes	_	_	O
17	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
cut	_	_	O
and	_	_	O
14	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
hem	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
2000	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
cutting	_	_	O
and	_	_	O
1500	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
hemming	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
blanket	_	_	B-VAR
is	_	_	O
$	_	_	O
24	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
bedsheet	_	_	B-VAR
is	_	_	O
$	_	_	O
21	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
boy	_	_	O
buys	_	_	O
and	_	_	O
sells	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
hoodies	_	_	O
.	_	_	O
Zippered	_	_	B-VAR
hoodies	_	_	I-VAR
cost	_	_	O
him	_	_	O
$	_	_	O
20	_	_	B-PARAM
each	_	_	O
and	_	_	O
pullover	_	_	B-VAR
hoodies	_	_	I-VAR
cost	_	_	O
his	_	_	O
$	_	_	O
15	_	_	B-PARAM
each	_	_	O
.	_	_	O
He	_	_	O
can	_	_	O
spend	_	_	O
a	_	_	B-CONST_DIR
total	_	_	I-CONST_DIR
of	_	_	I-CONST_DIR
$	_	_	O
450	_	_	B-LIMIT
.	_	_	O
He	_	_	O
can	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
25	_	_	B-LIMIT
hoodies	_	_	O
total	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
zippered	_	_	B-VAR
hoodie	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
pullover	_	_	B-VAR
hoodie	_	_	I-VAR
is	_	_	O
$	_	_	O
4	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
buy	_	_	O
and	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

Angela	_	_	O
mixes	_	_	O
French	_	_	B-VAR
perfume	_	_	I-VAR
and	_	_	O
Spanish	_	_	B-VAR
perfume	_	_	I-VAR
together	_	_	O
to	_	_	O
create	_	_	O
a	_	_	O
new	_	_	O
mixture	_	_	O
.	_	_	O
The	_	_	O
mixture	_	_	O
must	_	_	O
contain	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
150	_	_	B-LIMIT
units	_	_	O
of	_	_	O
flower	_	_	O
scent	_	_	O
and	_	_	O
60	_	_	B-LIMIT
units	_	_	O
of	_	_	O
fruit	_	_	O
scent	_	_	O
.	_	_	O
Each	_	_	O
bottle	_	_	O
of	_	_	O
French	_	_	B-VAR
perfume	_	_	I-VAR
contains	_	_	O
50	_	_	B-PARAM
units	_	_	O
of	_	_	O
fruit	_	_	O
scent	_	_	O
and	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
flower	_	_	O
scent	_	_	O
.	_	_	O
Each	_	_	O
bottle	_	_	O
of	_	_	O
Spanish	_	_	B-VAR
perfume	_	_	I-VAR
contains	_	_	O
40	_	_	B-PARAM
units	_	_	O
of	_	_	O
fruit	_	_	O
scent	_	_	O
and	_	_	O
30	_	_	B-PARAM
units	_	_	O
of	_	_	O
flower	_	_	O
scent	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
bottle	_	_	O
of	_	_	O
French	_	_	B-VAR
perfume	_	_	I-VAR
is	_	_	O
$	_	_	O
50.00	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
bottle	_	_	O
of	_	_	O
Spanish	_	_	B-VAR
perfume	_	_	I-VAR
is	_	_	O
$	_	_	O
45.00	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
Angela	_	_	O
buy	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
wedding	_	_	O
cake	_	_	O
company	_	_	O
mixes	_	_	O
two	_	_	O
cake	_	_	O
mixes	_	_	O
to	_	_	O
get	_	_	O
a	_	_	O
perfect	_	_	O
consistency	_	_	O
.	_	_	O
Vanilla	_	_	B-VAR
cake	_	_	I-VAR
mix	_	_	I-VAR
contains	_	_	O
3	_	_	B-PARAM
%	_	_	I-PARAM
leavening	_	_	O
agent	_	_	O
and	_	_	O
55	_	_	B-PARAM
%	_	_	I-PARAM
flour	_	_	O
.	_	_	O
Chocolate	_	_	B-VAR
cake	_	_	I-VAR
mix	_	_	I-VAR
contains	_	_	O
2	_	_	B-PARAM
%	_	_	I-PARAM
leavening	_	_	O
agent	_	_	O
and	_	_	O
43	_	_	B-PARAM
%	_	_	I-PARAM
flour	_	_	O
.	_	_	O
The	_	_	O
final	_	_	O
mixture	_	_	O
needs	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
0.3	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
leavening	_	_	O
agent	_	_	O
and	_	_	O
10	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
flour	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
kg	_	_	O
of	_	_	O
vanilla	_	_	B-VAR
cake	_	_	I-VAR
mix	_	_	I-VAR
is	_	_	O
$	_	_	O
10	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
kg	_	_	O
of	_	_	O
chocolate	_	_	B-VAR
cake	_	_	I-VAR
mix	_	_	I-VAR
is	_	_	O
$	_	_	O
15	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
kg	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
wedding	_	_	O
cake	_	_	O
company	_	_	O
buy	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
man	_	_	O
wants	_	_	O
to	_	_	O
do	_	_	O
his	_	_	O
weekly	_	_	O
meal	_	_	O
prep	_	_	O
but	_	_	O
wants	_	_	O
to	_	_	O
minimize	_	_	O
his	_	_	O
fat	_	_	B-OBJ_NAME
intake	_	_	I-OBJ_NAME
.	_	_	O
He	_	_	O
eats	_	_	O
two	_	_	O
meals	_	_	O
.	_	_	O
Each	_	_	O
meal	_	_	O
of	_	_	O
chicken	_	_	B-VAR
salad	_	_	I-VAR
contains	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
carbs	_	_	O
,	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	B-OBJ_NAME
,	_	_	O
and	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
fiber	_	_	O
.	_	_	O
Each	_	_	O
meal	_	_	O
of	_	_	O
beef	_	_	B-VAR
tacos	_	_	I-VAR
contains	_	_	O
25	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
25	_	_	B-PARAM
units	_	_	O
of	_	_	O
carbs	_	_	O
,	_	_	O
25	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	B-OBJ_NAME
,	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
fiber	_	_	O
.	_	_	O
The	_	_	O
man	_	_	O
needs	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
120	_	_	B-LIMIT
units	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
150	_	_	B-LIMIT
units	_	_	O
of	_	_	O
carbs	_	_	O
.	_	_	O
However	_	_	O
he	_	_	O
wants	_	_	O
to	_	_	O
consume	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
25	_	_	B-LIMIT
units	_	_	O
of	_	_	O
fiber	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
meals	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
produce	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
fat	_	_	B-OBJ_NAME
intake	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
construction	_	_	O
worker	_	_	O
mixes	_	_	O
two	_	_	O
different	_	_	O
concrete	_	_	O
mixes	_	_	O
.	_	_	O
One	_	_	O
unit	_	_	O
of	_	_	O
mix	_	_	B-VAR
A	_	_	I-VAR
contains	_	_	O
5	_	_	B-PARAM
unit	_	_	O
of	_	_	O
cement	_	_	O
,	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
sand	_	_	O
,	_	_	O
and	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
gravel	_	_	O
.	_	_	O
One	_	_	O
unit	_	_	O
of	_	_	O
mix	_	_	B-VAR
B	_	_	I-VAR
contains	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
cement	_	_	O
,	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
sand	_	_	O
,	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
gravel	_	_	O
.	_	_	O
The	_	_	O
new	_	_	O
mixture	_	_	O
must	_	_	O
contain	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
70	_	_	B-LIMIT
units	_	_	O
of	_	_	O
cement	_	_	O
,	_	_	O
20	_	_	B-LIMIT
units	_	_	O
of	_	_	O
sand	_	_	O
,	_	_	O
and	_	_	O
15	_	_	B-LIMIT
units	_	_	O
of	_	_	O
gravel	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
unit	_	_	O
of	_	_	O
mix	_	_	B-VAR
A	_	_	I-VAR
is	_	_	O
$	_	_	O
1	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
unit	_	_	O
of	_	_	O
mix	_	_	B-VAR
B	_	_	I-VAR
is	_	_	O
$	_	_	O
1.25	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
mixed	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
cruise	_	_	O
ship	_	_	O
can	_	_	O
take	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
1500	_	_	B-LIMIT
people	_	_	O
.	_	_	O
A	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
500	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
long	_	_	B-VAR
-	_	_	I-VAR
term	_	_	I-VAR
cruise	_	_	I-VAR
ticket	_	_	O
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
150	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
week	_	_	B-VAR
-	_	_	I-VAR
long	_	_	I-VAR
cruise	_	_	I-VAR
ticket	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
35	_	_	B-LIMIT
long	_	_	B-VAR
-	_	_	I-VAR
term	_	_	I-VAR
cruise	_	_	I-VAR
tickets	_	_	O
available	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
4	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
many	_	_	O
people	_	_	O
prefer	_	_	O
to	_	_	O
buy	_	_	O
week	_	_	B-VAR
-	_	_	I-VAR
long	_	_	I-VAR
cruise	_	_	I-VAR
tickets	_	_	O
than	_	_	O
long	_	_	B-VAR
-	_	_	I-VAR
term	_	_	I-VAR
cruise	_	_	I-VAR
tickets	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
ticket	_	_	O
should	_	_	O
be	_	_	O
sold	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
store	_	_	O
sells	_	_	O
two	_	_	O
salad	_	_	O
bowls	_	_	O
.	_	_	O
The	_	_	O
individual	_	_	B-VAR
salad	_	_	I-VAR
contains	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
lettuce	_	_	O
,	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
tomatoes	_	_	O
,	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
sauce	_	_	O
.	_	_	O
The	_	_	O
family	_	_	B-VAR
-	_	_	I-VAR
sized	_	_	I-VAR
salad	_	_	I-VAR
contains	_	_	O
18	_	_	B-PARAM
units	_	_	O
of	_	_	O
lettuce	_	_	O
,	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
tomatoes	_	_	O
,	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
sauce	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
220	_	_	B-LIMIT
units	_	_	O
of	_	_	O
lettuce	_	_	O
,	_	_	O
150	_	_	B-LIMIT
units	_	_	O
of	_	_	O
tomatoes	_	_	O
,	_	_	O
and	_	_	O
140	_	_	B-LIMIT
units	_	_	O
of	_	_	O
sauce	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
individual	_	_	B-VAR
salad	_	_	I-VAR
is	_	_	O
$	_	_	O
4	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
family	_	_	B-VAR
-	_	_	I-VAR
sized	_	_	I-VAR
salad	_	_	I-VAR
is	_	_	O
$	_	_	O
7	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
taco	_	_	O
restaurant	_	_	O
sells	_	_	O
burritos	_	_	B-VAR
and	_	_	O
tacos	_	_	B-VAR
.	_	_	O
Each	_	_	O
burrito	_	_	B-VAR
contains	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
beef	_	_	O
and	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
toppings	_	_	O
.	_	_	O
Each	_	_	O
taco	_	_	B-VAR
contains	_	_	O
4.5	_	_	B-PARAM
units	_	_	O
of	_	_	O
beef	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
toppings	_	_	O
.	_	_	O
The	_	_	O
restaurant	_	_	O
has	_	_	O
500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
beef	_	_	O
available	_	_	B-CONST_DIR
and	_	_	O
400	_	_	B-LIMIT
units	_	_	O
of	_	_	O
toppings	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
burrito	_	_	B-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
taco	_	_	B-VAR
is	_	_	O
$	_	_	O
3.50	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
restaurant	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
grandmother	_	_	O
knits	_	_	O
blankets	_	_	B-VAR
and	_	_	O
sweaters	_	_	B-VAR
for	_	_	O
her	_	_	O
community	_	_	O
.	_	_	O
A	_	_	O
blanket	_	_	B-VAR
requires	_	_	O
30	_	_	B-PARAM
units	_	_	O
of	_	_	O
yarn	_	_	O
and	_	_	O
5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
knitting	_	_	O
.	_	_	O
A	_	_	O
sweater	_	_	B-VAR
requires	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
yarn	_	_	O
and	_	_	O
4	_	_	B-PARAM
hours	_	_	O
of	_	_	O
knitting	_	_	O
.	_	_	O
The	_	_	O
grandmother	_	_	O
has	_	_	O
200	_	_	B-LIMIT
units	_	_	O
of	_	_	O
yarn	_	_	O
available	_	_	B-CONST_DIR
and	_	_	O
40	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
knitting	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
blanket	_	_	B-VAR
is	_	_	O
$	_	_	O
5.50	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
sweater	_	_	B-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
she	_	_	O
knit	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
her	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
sign	_	_	O
company	_	_	O
makes	_	_	O
signs	_	_	O
by	_	_	O
hand	_	_	O
.	_	_	O
They	_	_	O
make	_	_	O
LED	_	_	B-VAR
signs	_	_	I-VAR
and	_	_	O
neon	_	_	B-VAR
signs	_	_	I-VAR
.	_	_	O
The	_	_	O
LED	_	_	B-VAR
signs	_	_	I-VAR
are	_	_	O
made	_	_	O
by	_	_	O
team	_	_	O
A	_	_	O
and	_	_	O
they	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
3	_	_	B-LIMIT
a	_	_	O
day	_	_	O
.	_	_	O
The	_	_	O
neon	_	_	B-VAR
signs	_	_	I-VAR
are	_	_	O
made	_	_	O
by	_	_	O
team	_	_	O
B	_	_	O
and	_	_	O
they	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
4	_	_	B-LIMIT
a	_	_	O
day	_	_	O
.	_	_	O
All	_	_	O
signs	_	_	O
have	_	_	O
to	_	_	O
be	_	_	O
quality	_	_	O
checked	_	_	O
by	_	_	O
a	_	_	O
senior	_	_	O
QC	_	_	O
inspector	_	_	O
and	_	_	O
he	_	_	O
can	_	_	O
check	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
7	_	_	B-LIMIT
signs	_	_	O
total	_	_	O
a	_	_	O
day	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
LED	_	_	B-VAR
sign	_	_	I-VAR
is	_	_	O
$	_	_	O
1500	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
neon	_	_	B-VAR
sign	_	_	I-VAR
is	_	_	O
$	_	_	O
1450	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
sign	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
ice	_	_	O
cream	_	_	O
shop	_	_	O
sells	_	_	O
regular	_	_	B-VAR
and	_	_	O
premium	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
.	_	_	O
They	_	_	O
make	_	_	O
x1	_	_	O
regular	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
1	_	_	B-PARAM
each	_	_	O
and	_	_	O
x2	_	_	O
premium	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
2.50	_	_	B-PARAM
each	_	_	O
(	_	_	O
x1	_	_	O
and	_	_	O
x2	_	_	O
are	_	_	O
unknown	_	_	O
and	_	_	O
greater	_	_	O
than	_	_	O
or	_	_	O
equal	_	_	O
to	_	_	O
0	_	_	O
)	_	_	O
.	_	_	O
The	_	_	O
demand	_	_	O
for	_	_	O
regular	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
40	_	_	B-LIMIT
and	_	_	O
the	_	_	O
demand	_	_	O
for	_	_	O
premium	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
25	_	_	B-LIMIT
.	_	_	O
In	_	_	O
addition	_	_	O
the	_	_	O
shop	_	_	O
can	_	_	O
only	_	_	B-CONST_DIR
make	_	_	O
60	_	_	B-LIMIT
ice	_	_	O
creams	_	_	O
total	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
hiker	_	_	O
eats	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
berry	_	_	O
mix	_	_	O
and	_	_	O
wants	_	_	O
to	_	_	O
make	_	_	O
sure	_	_	O
he	_	_	O
eats	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
150	_	_	B-LIMIT
g	_	_	O
of	_	_	O
blueberries	_	_	O
and	_	_	O
125	_	_	B-LIMIT
g	_	_	O
of	_	_	O
blackberries	_	_	O
.	_	_	O
Berry	_	_	B-VAR
mix	_	_	I-VAR
A	_	_	I-VAR
contains	_	_	O
30	_	_	B-PARAM
g	_	_	O
of	_	_	O
blueberries	_	_	O
and	_	_	O
45	_	_	B-PARAM
g	_	_	O
of	_	_	O
blackberries	_	_	O
per	_	_	O
bag	_	_	O
.	_	_	O
Berry	_	_	B-VAR
mix	_	_	I-VAR
B	_	_	I-VAR
contains	_	_	O
20	_	_	B-PARAM
g	_	_	O
of	_	_	O
blueberries	_	_	O
and	_	_	O
15	_	_	B-PARAM
g	_	_	O
of	_	_	O
blackberries	_	_	O
per	_	_	O
bag	_	_	O
.	_	_	O
If	_	_	O
berry	_	_	B-VAR
mix	_	_	I-VAR
A	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
5	_	_	B-PARAM
per	_	_	O
bag	_	_	O
and	_	_	O
berry	_	_	B-VAR
mix	_	_	I-VAR
B	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
3	_	_	B-PARAM
per	_	_	O
bag	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
bags	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
hiker	_	_	O
purchase	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
gardener	_	_	O
grows	_	_	O
lettuce	_	_	B-VAR
and	_	_	O
tomatoes	_	_	B-VAR
in	_	_	B-CONST_DIR
their	_	_	O
300	_	_	B-LIMIT
sqft	_	_	O
backyard	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
sqft	_	_	O
of	_	_	O
lettuce	_	_	B-VAR
is	_	_	O
$	_	_	O
2	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
sqft	_	_	O
of	_	_	O
tomatoes	_	_	B-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
bug	_	_	O
spray	_	_	O
must	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
grow	_	_	O
both	_	_	O
lettuce	_	_	B-VAR
and	_	_	O
tomatoes	_	_	B-VAR
.	_	_	O
Per	_	_	O
sqft	_	_	O
of	_	_	O
lettuce	_	_	B-VAR
,	_	_	O
5	_	_	B-PARAM
mL	_	_	O
of	_	_	O
bug	_	_	O
spray	_	_	O
are	_	_	O
needed	_	_	O
.	_	_	O
Per	_	_	O
sqft	_	_	O
of	_	_	O
tomatoes	_	_	B-VAR
,	_	_	O
7	_	_	B-PARAM
mL	_	_	O
of	_	_	O
bug	_	_	O
spray	_	_	O
are	_	_	O
needed	_	_	O
.	_	_	O
The	_	_	O
gardener	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
255	_	_	B-LIMIT
mL	_	_	O
of	_	_	O
bug	_	_	O
spray	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
sqft	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
gardener	_	_	O
grow	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
company	_	_	O
makes	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
cars	_	_	O
,	_	_	O
a	_	_	O
SUV	_	_	B-VAR
and	_	_	O
a	_	_	O
sedan	_	_	B-VAR
.	_	_	O
The	_	_	O
SUV	_	_	B-VAR
takes	_	_	O
200	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
manufacturing	_	_	O
line	_	_	O
and	_	_	O
120	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
testing	_	_	O
.	_	_	O
The	_	_	O
sedan	_	_	B-VAR
takes	_	_	O
150	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
manufacturing	_	_	O
line	_	_	O
and	_	_	O
100	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
testing	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
20000	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
on	_	_	O
the	_	_	O
manufacturing	_	_	O
line	_	_	O
and	_	_	O
10000	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
testing	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
SUV	_	_	B-VAR
is	_	_	O
$	_	_	O
10000	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
sedan	_	_	B-VAR
is	_	_	O
$	_	_	O
9000	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
pizza	_	_	O
shop	_	_	O
specializes	_	_	O
in	_	_	O
pizza	_	_	O
and	_	_	O
they	_	_	O
make	_	_	O
two	_	_	O
types	_	_	O
.	_	_	O
Pizza	_	_	B-VAR
A	_	_	I-VAR
requires	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
mozzarella	_	_	O
cheese	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
American	_	_	O
cheese	_	_	O
.	_	_	O
Pizza	_	_	B-VAR
B	_	_	I-VAR
requires	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
mozzarella	_	_	O
cheese	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
American	_	_	O
cheese	_	_	O
.	_	_	O
The	_	_	O
shop	_	_	O
has	_	_	O
600	_	_	B-LIMIT
units	_	_	O
and	_	_	O
500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
mozzarella	_	_	O
and	_	_	O
American	_	_	O
cheese	_	_	O
available	_	_	B-CONST_DIR
,	_	_	O
respectively	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
pizza	_	_	B-VAR
A	_	_	I-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
pizza	_	_	B-VAR
B	_	_	I-VAR
is	_	_	O
$	_	_	O
4	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
shop	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

John	_	_	O
mixes	_	_	O
two	_	_	O
brands	_	_	O
of	_	_	O
cereal	_	_	O
to	_	_	O
ensure	_	_	O
he	_	_	O
gets	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
400	_	_	B-LIMIT
units	_	_	O
of	_	_	O
iron	_	_	O
and	_	_	O
450	_	_	B-LIMIT
units	_	_	O
of	_	_	O
fiber	_	_	O
.	_	_	O
A	_	_	O
serving	_	_	O
of	_	_	O
cereal	_	_	B-VAR
A	_	_	I-VAR
contains	_	_	O
25	_	_	B-PARAM
units	_	_	O
of	_	_	O
iron	_	_	O
and	_	_	O
30	_	_	B-PARAM
units	_	_	O
of	_	_	O
fiber	_	_	O
.	_	_	O
A	_	_	O
serving	_	_	O
of	_	_	O
cereal	_	_	B-VAR
B	_	_	I-VAR
contains	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
iron	_	_	O
and	_	_	O
40	_	_	B-PARAM
units	_	_	O
of	_	_	O
fiber	_	_	O
.	_	_	O
If	_	_	O
cereal	_	_	B-VAR
A	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
0.45	_	_	B-PARAM
per	_	_	O
serving	_	_	O
and	_	_	O
cereal	_	_	B-VAR
B	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
0.55	_	_	B-PARAM
per	_	_	O
serving	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
servings	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
John	_	_	O
buy	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
fish	_	_	O
food	_	_	O
company	_	_	O
makes	_	_	O
small	_	_	B-VAR
and	_	_	O
bulk	_	_	B-VAR
size	_	_	I-VAR
containers	_	_	O
of	_	_	O
fish	_	_	O
food	_	_	O
.	_	_	O
To	_	_	O
make	_	_	O
a	_	_	O
small	_	_	B-VAR
container	_	_	I-VAR
of	_	_	O
fish	_	_	O
food	_	_	O
,	_	_	O
it	_	_	O
takes	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
fish	_	_	O
food	_	_	O
and	_	_	O
2	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
fill	_	_	O
.	_	_	O
To	_	_	O
make	_	_	O
a	_	_	O
bulk	_	_	B-VAR
size	_	_	I-VAR
container	_	_	O
of	_	_	O
fish	_	_	O
food	_	_	O
,	_	_	O
it	_	_	O
takes	_	_	O
30	_	_	B-PARAM
units	_	_	O
of	_	_	O
fish	_	_	O
food	_	_	O
and	_	_	O
7	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
fill	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
200	_	_	B-LIMIT
units	_	_	O
of	_	_	O
fish	_	_	O
food	_	_	O
available	_	_	B-CONST_DIR
and	_	_	O
120	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
filling	_	_	O
time	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
small	_	_	B-VAR
container	_	_	I-VAR
of	_	_	O
fish	_	_	O
food	_	_	O
is	_	_	O
$	_	_	O
2	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
bulk	_	_	B-VAR
size	_	_	I-VAR
container	_	_	I-VAR
of	_	_	O
fish	_	_	O
food	_	_	O
is	_	_	O
$	_	_	O
7	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

You	_	_	O
have	_	_	B-CONST_DIR
$	_	_	O
20000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
four	_	_	O
different	_	_	O
companies	_	_	O
who	_	_	O
specialize	_	_	O
in	_	_	O
specific	_	_	O
products	_	_	O
.	_	_	O
There	_	_	O
is	_	_	O
a	_	_	O
electric	_	_	B-VAR
vehicle	_	_	I-VAR
company	_	_	I-VAR
,	_	_	O
a	_	_	O
microprocessor	_	_	B-VAR
company	_	_	I-VAR
,	_	_	O
a	_	_	O
business	_	_	B-VAR
analytics	_	_	I-VAR
software	_	_	I-VAR
company	_	_	I-VAR
,	_	_	O
and	_	_	O
a	_	_	O
construction	_	_	B-VAR
supply	_	_	I-VAR
company	_	_	I-VAR
.	_	_	O
The	_	_	O
return	_	_	B-OBJ_NAME
on	_	_	O
investment	_	_	O
for	_	_	O
each	_	_	O
is	_	_	O
as	_	_	O
follows	_	_	O
:	_	_	O
electric	_	_	B-VAR
vehicle	_	_	I-VAR
company	_	_	I-VAR
,	_	_	O
4	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
microprocessor	_	_	B-VAR
company	_	_	I-VAR
,	_	_	O
2.5	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
business	_	_	B-VAR
analytics	_	_	I-VAR
software	_	_	I-VAR
company	_	_	I-VAR
,	_	_	O
5	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
construction	_	_	B-VAR
supply	_	_	I-VAR
company	_	_	I-VAR
3	_	_	B-PARAM
%	_	_	I-PARAM
.	_	_	O
You	_	_	O
have	_	_	O
self	_	_	O
imposed	_	_	O
some	_	_	O
restrictions	_	_	O
on	_	_	O
your	_	_	O
investment	_	_	O
.	_	_	O
For	_	_	O
instance	_	_	O
,	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
construction	_	_	B-VAR
supply	_	_	I-VAR
company	_	_	I-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
electric	_	_	B-VAR
vehicle	_	_	I-VAR
company	_	_	I-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
microprocessor	_	_	B-VAR
company	_	_	I-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
business	_	_	B-VAR
analytics	_	_	I-VAR
software	_	_	I-VAR
company	_	_	I-VAR
.	_	_	O
Finally	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
20	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
your	_	_	O
total	_	_	O
investment	_	_	O
can	_	_	O
be	_	_	O
in	_	_	O
the	_	_	O
construction	_	_	B-VAR
supply	_	_	I-VAR
company	_	_	I-VAR
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
your	_	_	O
returns	_	_	B-OBJ_NAME
.	_	_	O

You	_	_	O
are	_	_	O
put	_	_	O
on	_	_	O
a	_	_	O
special	_	_	O
diet	_	_	O
where	_	_	O
you	_	_	O
can	_	_	O
drink	_	_	O
two	_	_	O
juices	_	_	O
.	_	_	O
Prune	_	_	B-VAR
juice	_	_	I-VAR
contains	_	_	O
10	_	_	B-PARAM
grams	_	_	O
of	_	_	O
vitamin	_	_	O
A	_	_	O
,	_	_	O
12	_	_	B-PARAM
grams	_	_	O
of	_	_	O
vitamin	_	_	O
B	_	_	O
,	_	_	O
5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
fiber	_	_	O
,	_	_	O
and	_	_	O
15	_	_	B-PARAM
grams	_	_	O
of	_	_	O
sugar	_	_	B-OBJ_NAME
per	_	_	O
cup	_	_	O
.	_	_	O
Apple	_	_	B-VAR
juice	_	_	I-VAR
contains	_	_	O
12	_	_	B-PARAM
grams	_	_	O
of	_	_	O
vitamin	_	_	O
A	_	_	O
,	_	_	O
15	_	_	B-PARAM
grams	_	_	O
of	_	_	O
vitamin	_	_	O
B	_	_	O
,	_	_	O
3	_	_	B-PARAM
grams	_	_	O
of	_	_	O
fiber	_	_	O
,	_	_	O
and	_	_	O
17	_	_	B-PARAM
grams	_	_	O
of	_	_	O
sugar	_	_	B-OBJ_NAME
per	_	_	O
cup	_	_	O
.	_	_	O
You	_	_	O
must	_	_	O
consume	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
105	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
vitamin	_	_	O
A	_	_	O
and	_	_	O
120	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
vitamin	_	_	O
B.	_	_	O
However	_	_	O
you	_	_	O
can	_	_	O
consume	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
80	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
fiber	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
cups	_	_	O
of	_	_	O
each	_	_	O
juice	_	_	O
should	_	_	O
you	_	_	O
drink	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
sugar	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
tropical	_	_	O
farmer	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
200	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
to	_	_	O
grow	_	_	O
pineapples	_	_	B-VAR
and	_	_	O
bananas	_	_	B-VAR
.	_	_	O
He	_	_	O
likes	_	_	O
bananas	_	_	B-VAR
,	_	_	O
but	_	_	O
because	_	_	O
they	_	_	O
require	_	_	O
so	_	_	O
much	_	_	O
more	_	_	O
work	_	_	O
,	_	_	O
he	_	_	O
can	_	_	O
grow	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
4	_	_	B-PARAM
times	_	_	I-PARAM
the	_	_	O
amount	_	_	O
of	_	_	O
bananas	_	_	B-VAR
as	_	_	O
pineapples	_	_	B-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
he	_	_	O
must	_	_	O
grow	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
40	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
pineapples	_	_	B-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
60	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
bananas	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
pineapples	_	_	B-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acres	_	_	O
of	_	_	O
bananas	_	_	B-VAR
is	_	_	O
$	_	_	O
150	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acre	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
grow	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
cheese	_	_	O
factory	_	_	O
mixes	_	_	O
two	_	_	O
cheese	_	_	O
mixes	_	_	O
to	_	_	O
create	_	_	O
a	_	_	O
final	_	_	O
product	_	_	O
.	_	_	O
Pizza	_	_	B-VAR
mix	_	_	I-VAR
contains	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
mozzarella	_	_	O
,	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
cheddar	_	_	O
,	_	_	O
and	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
salt	_	_	O
.	_	_	O
Mac	_	_	B-VAR
and	_	_	I-VAR
cheese	_	_	I-VAR
mix	_	_	O
contains	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
mozzarella	_	_	O
,	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
cheddar	_	_	O
,	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
salt	_	_	O
.	_	_	O
The	_	_	O
minimum	_	_	B-CONST_DIR
requirements	_	_	O
of	_	_	O
the	_	_	O
new	_	_	O
product	_	_	O
are	_	_	O
30	_	_	B-LIMIT
units	_	_	O
of	_	_	O
mozzarella	_	_	O
,	_	_	O
25	_	_	B-LIMIT
units	_	_	O
of	_	_	O
cheddar	_	_	O
,	_	_	O
and	_	_	O
5	_	_	B-LIMIT
units	_	_	O
of	_	_	O
salt	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
pizza	_	_	B-VAR
mix	_	_	I-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
mac	_	_	B-VAR
and	_	_	I-VAR
cheese	_	_	I-VAR
mix	_	_	O
is	_	_	O
$	_	_	O
3.25	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
toy	_	_	O
shop	_	_	O
makes	_	_	O
plush	_	_	B-VAR
toys	_	_	I-VAR
and	_	_	O
action	_	_	B-VAR
figures	_	_	I-VAR
.	_	_	O
Each	_	_	O
plush	_	_	B-VAR
toy	_	_	I-VAR
takes	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
assembly	_	_	O
and	_	_	O
4	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
packaging	_	_	O
.	_	_	O
Each	_	_	O
action	_	_	B-VAR
figure	_	_	I-VAR
takes	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
assembly	_	_	O
and	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
packaging	_	_	O
.	_	_	O
The	_	_	O
shop	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
1200	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
assembly	_	_	O
and	_	_	O
900	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
packaging	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
plush	_	_	B-VAR
toy	_	_	I-VAR
is	_	_	O
$	_	_	O
4	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
action	_	_	B-VAR
figure	_	_	I-VAR
is	_	_	O
$	_	_	O
4.50	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
construction	_	_	O
company	_	_	O
makes	_	_	O
bulldozers	_	_	B-VAR
and	_	_	O
forklifts	_	_	B-VAR
.	_	_	O
Each	_	_	O
bulldozer	_	_	B-VAR
takes	_	_	O
3	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
assembly	_	_	O
line	_	_	O
and	_	_	O
2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
QC	_	_	O
time	_	_	O
.	_	_	O
Each	_	_	O
forklift	_	_	B-VAR
takes	_	_	O
2	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
assembly	_	_	O
line	_	_	O
and	_	_	O
1.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
QC	_	_	O
time	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
600	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
assembly	_	_	O
line	_	_	O
time	_	_	O
available	_	_	B-CONST_DIR
and	_	_	O
400	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
QC	_	_	O
time	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
bulldozer	_	_	B-VAR
is	_	_	O
$	_	_	O
7000	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
forklift	_	_	B-VAR
is	_	_	O
$	_	_	O
6000	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
construction	_	_	O
company	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

You	_	_	O
have	_	_	O
$	_	_	O
50000	_	_	B-LIMIT
available	_	_	B-CONST_DIR
to	_	_	O
invest	_	_	O
in	_	_	O
either	_	_	O
the	_	_	O
solar	_	_	B-VAR
energy	_	_	I-VAR
industry	_	_	I-VAR
or	_	_	O
the	_	_	O
wind	_	_	B-VAR
energy	_	_	I-VAR
industry	_	_	I-VAR
.	_	_	O
Money	_	_	O
placed	_	_	O
in	_	_	O
the	_	_	O
solar	_	_	B-VAR
energy	_	_	I-VAR
industry	_	_	I-VAR
yields	_	_	O
a	_	_	O
return	_	_	B-OBJ_NAME
of	_	_	O
6	_	_	B-PARAM
%	_	_	I-PARAM
while	_	_	O
money	_	_	O
placed	_	_	O
in	_	_	O
the	_	_	O
wind	_	_	B-VAR
energy	_	_	I-VAR
industry	_	_	I-VAR
yields	_	_	O
a	_	_	O
return	_	_	B-OBJ_NAME
of	_	_	O
5	_	_	B-PARAM
%	_	_	I-PARAM
.	_	_	O
With	_	_	O
high	_	_	O
expectations	_	_	O
of	_	_	O
the	_	_	O
wind	_	_	B-VAR
energy	_	_	I-VAR
industry	_	_	O
,	_	_	O
you	_	_	O
decide	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
70	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
your	_	_	O
investment	_	_	O
be	_	_	O
placed	_	_	O
in	_	_	O
the	_	_	O
wind	_	_	B-VAR
energy	_	_	I-VAR
industry	_	_	I-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
20	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
your	_	_	O
investment	_	_	O
can	_	_	O
be	_	_	O
in	_	_	O
the	_	_	O
solar	_	_	B-VAR
energy	_	_	I-VAR
industry	_	_	I-VAR
.	_	_	O
How	_	_	O
much	_	_	O
should	_	_	O
you	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
your	_	_	O
return	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
toy	_	_	O
company	_	_	O
makes	_	_	O
bear	_	_	B-VAR
plush	_	_	I-VAR
toys	_	_	I-VAR
and	_	_	O
dog	_	_	B-VAR
plush	_	_	I-VAR
toys	_	_	O
.	_	_	O
Each	_	_	O
bear	_	_	B-VAR
takes	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
make	_	_	O
and	_	_	O
each	_	_	O
dog	_	_	B-VAR
takes	_	_	O
12	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
make	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
1000	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
to	_	_	O
make	_	_	O
both	_	_	O
plush	_	_	O
toys	_	_	O
.	_	_	O
Due	_	_	O
to	_	_	O
the	_	_	O
popularity	_	_	O
of	_	_	O
bears	_	_	B-VAR
,	_	_	O
the	_	_	O
company	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
two	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
many	_	_	O
bears	_	_	B-VAR
as	_	_	O
dogs	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
bear	_	_	B-VAR
is	_	_	O
$	_	_	O
4	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
dog	_	_	B-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Fred	_	_	O
can	_	_	O
invest	_	_	O
up	_	_	B-CONST_DIR
to	_	_	I-CONST_DIR
$	_	_	O
5000	_	_	B-LIMIT
in	_	_	O
the	_	_	O
farming	_	_	O
industry	_	_	O
.	_	_	O
Each	_	_	O
dollar	_	_	O
invested	_	_	O
in	_	_	O
a	_	_	O
fertilizer	_	_	B-VAR
company	_	_	I-VAR
yields	_	_	O
a	_	_	O
$	_	_	O
0.14	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
.	_	_	O
Each	_	_	O
dollar	_	_	O
invested	_	_	O
in	_	_	O
a	_	_	O
pesticide	_	_	B-VAR
company	_	_	I-VAR
yields	_	_	O
a	_	_	O
$	_	_	O
0.15	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
.	_	_	O
He	_	_	O
wants	_	_	O
to	_	_	O
invest	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
%	_	_	I-LIMIT
in	_	_	O
the	_	_	O
fertilizer	_	_	B-VAR
company	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
$	_	_	O
1000	_	_	B-LIMIT
in	_	_	O
the	_	_	O
pesticide	_	_	B-VAR
company	_	_	I-VAR
.	_	_	O
How	_	_	O
much	_	_	O
money	_	_	O
should	_	_	O
he	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

There	_	_	O
is	_	_	O
only	_	_	O
3000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
black	_	_	O
tea	_	_	O
available	_	_	B-CONST_DIR
to	_	_	O
make	_	_	O
earl	_	_	B-VAR
grey	_	_	I-VAR
and	_	_	O
English	_	_	B-VAR
breakfast	_	_	I-VAR
teabags	_	_	I-VAR
.	_	_	O
Each	_	_	O
earl	_	_	B-VAR
grey	_	_	I-VAR
teabag	_	_	I-VAR
requires	_	_	O
25	_	_	B-PARAM
grams	_	_	O
of	_	_	O
black	_	_	O
tea	_	_	O
while	_	_	O
each	_	_	O
English	_	_	B-VAR
breakfast	_	_	I-VAR
teabag	_	_	I-VAR
requires	_	_	O
20	_	_	B-PARAM
grams	_	_	O
of	_	_	O
black	_	_	O
tea	_	_	O
.	_	_	O
Due	_	_	O
to	_	_	O
demand	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
4	_	_	B-PARAM
times	_	_	I-PARAM
the	_	_	O
amount	_	_	O
of	_	_	O
earl	_	_	B-VAR
grey	_	_	I-VAR
teabags	_	_	I-VAR
are	_	_	O
needed	_	_	O
than	_	_	O
English	_	_	B-VAR
breakfast	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
English	_	_	B-VAR
breakfast	_	_	I-VAR
teabags	_	_	I-VAR
need	_	_	O
to	_	_	O
be	_	_	O
made	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
earl	_	_	B-VAR
grey	_	_	I-VAR
teabag	_	_	O
is	_	_	O
$	_	_	O
0.30	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
English	_	_	B-VAR
breakfast	_	_	I-VAR
teabag	_	_	I-VAR
is	_	_	O
$	_	_	O
0.25	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
sports	_	_	O
warehouse	_	_	O
stocks	_	_	O
rafts	_	_	B-VAR
and	_	_	O
kayaks	_	_	B-VAR
.	_	_	O
Each	_	_	O
raft	_	_	B-VAR
takes	_	_	O
10	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
of	_	_	O
space	_	_	O
while	_	_	O
each	_	_	O
kayak	_	_	B-VAR
takes	_	_	O
12	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
of	_	_	O
space	_	_	O
.	_	_	O
The	_	_	O
warehouse	_	_	O
has	_	_	O
400	_	_	B-LIMIT
sq	_	_	O
ft	_	_	O
of	_	_	O
space	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
The	_	_	O
warehouse	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
10000	_	_	B-LIMIT
with	_	_	O
each	_	_	O
raft	_	_	B-VAR
costing	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
each	_	_	O
kayak	_	_	B-VAR
costing	_	_	O
$	_	_	O
250	_	_	B-PARAM
.	_	_	O
With	_	_	O
rafting	_	_	O
being	_	_	O
much	_	_	O
more	_	_	O
popular	_	_	O
in	_	_	O
the	_	_	O
area	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
55	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
all	_	_	O
items	_	_	O
in	_	_	O
stock	_	_	O
must	_	_	O
be	_	_	O
rafts	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
raft	_	_	B-VAR
is	_	_	O
$	_	_	O
45	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
kayak	_	_	B-VAR
is	_	_	O
$	_	_	O
55	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
bought	_	_	O
and	_	_	O
sold	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
computer	_	_	O
store	_	_	O
can	_	_	O
spend	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
20,000	_	_	B-LIMIT
on	_	_	O
computers	_	_	O
.	_	_	O
Each	_	_	O
laptop	_	_	B-VAR
costs	_	_	O
$	_	_	O
500	_	_	B-PARAM
and	_	_	O
each	_	_	O
desktop	_	_	B-VAR
costs	_	_	O
$	_	_	O
400	_	_	B-PARAM
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
laptop	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
210	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
desktop	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
160	_	_	B-PARAM
.	_	_	O
The	_	_	O
store	_	_	O
owner	_	_	O
estimates	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
laptops	_	_	B-VAR
but	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
35	_	_	B-LIMIT
are	_	_	O
sold	_	_	O
each	_	_	O
month	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
desktops	_	_	B-VAR
sold	_	_	O
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
a	_	_	O
third	_	_	B-PARAM
of	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
laptops	_	_	B-VAR
sold	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
store	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
businessman	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
20000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
two	_	_	O
factories	_	_	O
,	_	_	O
a	_	_	O
shoe	_	_	B-VAR
factory	_	_	I-VAR
and	_	_	O
a	_	_	O
hat	_	_	B-VAR
factory	_	_	I-VAR
.	_	_	O
Because	_	_	O
the	_	_	O
shoe	_	_	B-VAR
factory	_	_	I-VAR
has	_	_	O
more	_	_	O
experience	_	_	O
,	_	_	O
he	_	_	O
has	_	_	O
decided	_	_	O
to	_	_	O
invest	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
4	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
much	_	_	O
money	_	_	O
in	_	_	O
the	_	_	O
shoe	_	_	B-VAR
factory	_	_	I-VAR
than	_	_	O
in	_	_	O
the	_	_	O
hat	_	_	B-VAR
factory	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
shoe	_	_	B-VAR
factory	_	_	I-VAR
can	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
15000	_	_	B-LIMIT
.	_	_	O
If	_	_	O
investments	_	_	O
in	_	_	O
the	_	_	O
shoe	_	_	B-VAR
factory	_	_	I-VAR
earn	_	_	B-OBJ_NAME
7	_	_	B-PARAM
%	_	_	I-PARAM
and	_	_	O
investments	_	_	O
in	_	_	O
the	_	_	O
hat	_	_	B-VAR
factory	_	_	I-VAR
earn	_	_	B-OBJ_NAME
6	_	_	B-PARAM
%	_	_	I-PARAM
,	_	_	O
how	_	_	O
much	_	_	O
money	_	_	O
should	_	_	O
he	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
earnings	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
flight	_	_	O
has	_	_	B-CONST_DIR
150	_	_	B-LIMIT
tickets	_	_	O
.	_	_	O
A	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
150	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
first	_	_	B-VAR
-	_	_	I-VAR
class	_	_	I-VAR
ticket	_	_	O
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
350	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
economy	_	_	B-VAR
-	_	_	I-VAR
class	_	_	I-VAR
ticket	_	_	O
.	_	_	O
The	_	_	O
flight	_	_	O
reserves	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
tickets	_	_	O
to	_	_	O
be	_	_	O
first	_	_	B-VAR
-	_	_	I-VAR
class	_	_	I-VAR
but	_	_	O
because	_	_	O
the	_	_	O
journey	_	_	O
is	_	_	O
short	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
many	_	_	O
people	_	_	O
prefer	_	_	O
to	_	_	O
save	_	_	O
money	_	_	O
and	_	_	O
travel	_	_	O
by	_	_	O
economy	_	_	B-VAR
-	_	_	I-VAR
class	_	_	I-VAR
than	_	_	O
first	_	_	B-VAR
-	_	_	I-VAR
class	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
ticket	_	_	O
type	_	_	O
should	_	_	O
be	_	_	O
sold	_	_	O
to	_	_	O
passengers	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
company	_	_	O
has	_	_	O
to	_	_	O
send	_	_	O
out	_	_	O
their	_	_	O
products	_	_	B-OBJ_NAME
overseas	_	_	O
.	_	_	O
They	_	_	O
can	_	_	O
send	_	_	O
the	_	_	O
products	_	_	B-OBJ_NAME
using	_	_	O
a	_	_	O
shipping	_	_	B-VAR
container	_	_	I-VAR
which	_	_	O
can	_	_	O
take	_	_	O
1000	_	_	B-PARAM
products	_	_	B-OBJ_NAME
each	_	_	O
or	_	_	O
by	_	_	O
using	_	_	O
cargo	_	_	B-VAR
planes	_	_	I-VAR
which	_	_	O
can	_	_	O
take	_	_	O
800	_	_	B-PARAM
products	_	_	B-OBJ_NAME
each	_	_	O
.	_	_	O
The	_	_	O
cost	_	_	O
per	_	_	O
shipping	_	_	B-VAR
container	_	_	I-VAR
sent	_	_	O
is	_	_	O
$	_	_	O
5000	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	O
per	_	_	O
cargo	_	_	B-VAR
plane	_	_	I-VAR
sent	_	_	O
is	_	_	O
$	_	_	O
6000	_	_	B-PARAM
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
due	_	_	O
to	_	_	O
shipping	_	_	O
delays	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
shipping	_	_	B-VAR
containers	_	_	I-VAR
sent	_	_	O
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
cargo	_	_	B-VAR
planes	_	_	I-VAR
sent	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
store	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
20000	_	_	B-LIMIT
,	_	_	O
how	_	_	O
should	_	_	O
they	_	_	O
spend	_	_	O
their	_	_	O
money	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
products	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
sent	_	_	O
?	_	_	O

A	_	_	O
restaurant	_	_	O
has	_	_	O
new	_	_	B-VAR
cooks	_	_	I-VAR
earning	_	_	B-OBJ_NAME
$	_	_	O
500	_	_	B-PARAM
a	_	_	O
week	_	_	O
and	_	_	O
senior	_	_	B-VAR
cooks	_	_	I-VAR
earning	_	_	B-OBJ_NAME
$	_	_	O
1000	_	_	B-PARAM
a	_	_	O
week	_	_	O
.	_	_	O
The	_	_	O
weekly	_	_	O
wage	_	_	B-OBJ_NAME
bill	_	_	I-OBJ_NAME
must	_	_	O
be	_	_	O
kept	_	_	O
below	_	_	B-CONST_DIR
$	_	_	O
50000	_	_	B-LIMIT
.	_	_	O
To	_	_	O
meet	_	_	O
customer	_	_	O
demand	_	_	O
,	_	_	O
they	_	_	O
require	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
30	_	_	B-LIMIT
total	_	_	O
cooks	_	_	O
of	_	_	O
whom	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
must	_	_	O
be	_	_	O
senior	_	_	B-VAR
cooks	_	_	I-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
senior	_	_	B-VAR
cooks	_	_	I-VAR
should	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
a	_	_	O
third	_	_	B-PARAM
the	_	_	O
number	_	_	O
of	_	_	O
new	_	_	B-VAR
cooks	_	_	I-VAR
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	B-OBJ_NAME
wage	_	_	I-OBJ_NAME
bill	_	_	I-OBJ_NAME
.	_	_	O

A	_	_	O
man	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
500000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
four	_	_	O
industries	_	_	O
.	_	_	O
He	_	_	O
can	_	_	O
invest	_	_	O
in	_	_	O
the	_	_	O
pharmaceutical	_	_	B-VAR
industry	_	_	I-VAR
,	_	_	O
renewable	_	_	B-VAR
energy	_	_	I-VAR
industry	_	_	I-VAR
,	_	_	O
entertainment	_	_	B-VAR
industry	_	_	I-VAR
,	_	_	O
and	_	_	O
construction	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
The	_	_	O
return	_	_	B-OBJ_NAME
on	_	_	O
investment	_	_	O
for	_	_	O
each	_	_	O
of	_	_	O
the	_	_	O
industries	_	_	O
is	_	_	O
as	_	_	O
follows	_	_	O
:	_	_	O
pharmaceutical	_	_	B-VAR
,	_	_	O
5	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
renewable	_	_	B-VAR
energy	_	_	I-VAR
,	_	_	O
3	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
entertainment	_	_	B-VAR
,	_	_	O
4	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
and	_	_	O
construction	_	_	B-VAR
4.5	_	_	B-PARAM
%	_	_	I-PARAM
.	_	_	O
To	_	_	O
be	_	_	O
safe	_	_	O
,	_	_	O
he	_	_	O
wants	_	_	O
to	_	_	O
make	_	_	O
sure	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
construction	_	_	B-VAR
industry	_	_	I-VAR
does	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
pharmaceutical	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
Also	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
renewable	_	_	B-VAR
energy	_	_	I-VAR
industry	_	_	I-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
entertainment	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
Lastly	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
20	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
investment	_	_	O
can	_	_	O
be	_	_	O
in	_	_	O
the	_	_	O
construction	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
How	_	_	O
much	_	_	O
should	_	_	O
he	_	_	O
invested	_	_	O
in	_	_	O
each	_	_	O
industry	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
returns	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
farmer	_	_	O
has	_	_	B-CONST_DIR
40	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
to	_	_	O
grow	_	_	O
corn	_	_	B-VAR
and	_	_	O
wheat	_	_	B-VAR
.	_	_	O
He	_	_	O
must	_	_	O
grow	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
6	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
corn	_	_	B-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
12	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
wheat	_	_	B-VAR
.	_	_	O
Although	_	_	O
corn	_	_	B-VAR
is	_	_	O
easier	_	_	O
to	_	_	O
grow	_	_	O
,	_	_	O
he	_	_	O
can	_	_	O
only	_	_	O
grow	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
2	_	_	B-PARAM
times	_	_	I-PARAM
the	_	_	O
amount	_	_	O
of	_	_	O
corn	_	_	B-VAR
as	_	_	O
wheat	_	_	B-VAR
in	_	_	O
case	_	_	O
insects	_	_	O
ruin	_	_	O
his	_	_	O
corn	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
corn	_	_	B-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
wheat	_	_	B-VAR
is	_	_	O
$	_	_	O
300	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
grow	_	_	O
to	_	_	O
make	_	_	O
maximum	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

In	_	_	O
a	_	_	O
warm	_	_	O
region	_	_	O
,	_	_	O
a	_	_	O
hostel	_	_	O
offers	_	_	O
heated	_	_	B-VAR
rooms	_	_	I-VAR
and	_	_	O
unheated	_	_	B-VAR
rooms	_	_	I-VAR
.	_	_	O
The	_	_	O
hostel	_	_	O
has	_	_	B-CONST_DIR
40	_	_	B-LIMIT
rooms	_	_	O
available	_	_	O
.	_	_	O
The	_	_	O
hostel	_	_	O
reserves	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
15	_	_	B-LIMIT
rooms	_	_	O
to	_	_	O
be	_	_	O
heated	_	_	B-VAR
.	_	_	O
However	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
4	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
many	_	_	O
people	_	_	O
prefer	_	_	O
unheated	_	_	B-VAR
rooms	_	_	I-VAR
to	_	_	O
heated	_	_	B-VAR
rooms	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
heated	_	_	B-VAR
room	_	_	I-VAR
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
unheated	_	_	B-VAR
room	_	_	I-VAR
is	_	_	O
$	_	_	O
35	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
room	_	_	O
type	_	_	O
should	_	_	O
be	_	_	O
sold	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
pizza	_	_	O
shop	_	_	O
sells	_	_	O
pepperoni	_	_	B-VAR
and	_	_	O
Hawaiian	_	_	B-VAR
pizzas	_	_	I-VAR
.	_	_	O
They	_	_	O
must	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
35	_	_	B-LIMIT
pepperoni	_	_	B-VAR
pizzas	_	_	I-VAR
but	_	_	O
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
sell	_	_	I-CONST_DIR
more	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
40	_	_	B-LIMIT
.	_	_	O
They	_	_	O
must	_	_	O
also	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
40	_	_	B-LIMIT
Hawaiian	_	_	B-VAR
pizzas	_	_	I-VAR
but	_	_	O
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
sell	_	_	I-CONST_DIR
more	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
70	_	_	B-LIMIT
.	_	_	O
In	_	_	O
total	_	_	O
,	_	_	O
they	_	_	O
only	_	_	B-CONST_DIR
have	_	_	O
enough	_	_	O
supplies	_	_	O
to	_	_	O
sell	_	_	O
90	_	_	B-LIMIT
pizzas	_	_	O
total	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
pepperoni	_	_	B-VAR
pizza	_	_	I-VAR
is	_	_	O
$	_	_	O
4	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
Hawaiian	_	_	B-VAR
pizza	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

In	_	_	O
an	_	_	O
exam	_	_	O
,	_	_	O
you	_	_	O
can	_	_	O
solve	_	_	O
easy	_	_	B-VAR
questions	_	_	I-VAR
worth	_	_	O
4	_	_	B-PARAM
points	_	_	B-OBJ_NAME
each	_	_	O
or	_	_	O
hard	_	_	B-VAR
questions	_	_	I-VAR
worth	_	_	O
10	_	_	B-PARAM
points	_	_	B-OBJ_NAME
each	_	_	O
.	_	_	O
You	_	_	O
have	_	_	O
to	_	_	O
solve	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
4	_	_	B-LIMIT
easy	_	_	B-VAR
questions	_	_	I-VAR
and	_	_	O
2	_	_	B-LIMIT
hard	_	_	B-VAR
question	_	_	I-VAR
to	_	_	O
pass	_	_	O
.	_	_	O
Due	_	_	O
to	_	_	O
time	_	_	O
restrictions	_	_	O
,	_	_	O
you	_	_	O
can	_	_	O
solve	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
12	_	_	B-LIMIT
easy	_	_	B-VAR
questions	_	_	I-VAR
and	_	_	O
4	_	_	B-LIMIT
hard	_	_	B-VAR
questions	_	_	I-VAR
.	_	_	O
In	_	_	O
total	_	_	O
,	_	_	O
you	_	_	O
can	_	_	O
only	_	_	O
solve	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
9	_	_	B-LIMIT
questions	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
question	_	_	O
type	_	_	O
should	_	_	O
you	_	_	O
solve	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
your	_	_	O
points	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
furniture	_	_	O
store	_	_	O
makes	_	_	O
desks	_	_	B-VAR
and	_	_	O
chairs	_	_	B-VAR
.	_	_	O
Two	_	_	O
different	_	_	O
manufacturers	_	_	O
make	_	_	O
each	_	_	O
item	_	_	O
.	_	_	O
Manufacturer	_	_	O
X	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
22	_	_	B-LIMIT
desks	_	_	B-VAR
a	_	_	O
day	_	_	O
.	_	_	O
Manufacturer	_	_	O
Y	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
28	_	_	B-LIMIT
chairs	_	_	B-VAR
a	_	_	O
day	_	_	O
.	_	_	O
Both	_	_	O
have	_	_	O
to	_	_	O
be	_	_	O
quality	_	_	O
checked	_	_	O
by	_	_	O
another	_	_	O
company	_	_	O
,	_	_	O
and	_	_	O
this	_	_	O
company	_	_	O
can	_	_	O
quality	_	_	O
check	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
40	_	_	B-LIMIT
items	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
desk	_	_	B-VAR
is	_	_	O
$	_	_	O
140	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
chair	_	_	B-VAR
is	_	_	O
$	_	_	O
120	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Kim	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
40000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
two	_	_	O
technology	_	_	O
industries	_	_	O
.	_	_	O
She	_	_	O
decides	_	_	O
to	_	_	O
invest	_	_	O
in	_	_	O
the	_	_	O
LED	_	_	B-VAR
display	_	_	I-VAR
industry	_	_	I-VAR
and	_	_	O
microprocessor	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
Money	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
LED	_	_	B-VAR
display	_	_	I-VAR
industry	_	_	I-VAR
yields	_	_	O
a	_	_	O
return	_	_	B-OBJ_NAME
of	_	_	O
4	_	_	B-PARAM
%	_	_	I-PARAM
while	_	_	O
money	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
microprocessor	_	_	B-VAR
industry	_	_	I-VAR
yields	_	_	O
a	_	_	O
return	_	_	B-OBJ_NAME
of	_	_	O
5.5	_	_	B-PARAM
%	_	_	I-PARAM
.	_	_	O
She	_	_	O
has	_	_	O
been	_	_	O
advised	_	_	O
to	_	_	O
invest	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
money	_	_	O
in	_	_	O
the	_	_	O
LED	_	_	B-VAR
display	_	_	I-VAR
industry	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
65	_	_	B-LIMIT
%	_	_	I-LIMIT
in	_	_	O
the	_	_	O
microprocessor	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
How	_	_	O
much	_	_	O
should	_	_	O
she	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
her	_	_	O
return	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
artisan	_	_	O
kitchen	_	_	O
company	_	_	O
sells	_	_	O
handmade	_	_	O
wooden	_	_	O
plates	_	_	B-VAR
and	_	_	O
forks	_	_	B-VAR
.	_	_	O
Each	_	_	O
plate	_	_	B-VAR
takes	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
woodworker	_	_	O
time	_	_	O
and	_	_	O
each	_	_	O
fork	_	_	B-VAR
takes	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
woodworker	_	_	O
time	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
5000	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
woodworker	_	_	O
time	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
Since	_	_	O
forks	_	_	B-VAR
are	_	_	O
most	_	_	O
popular	_	_	O
,	_	_	O
the	_	_	O
store	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-LIMIT
the	_	_	O
number	_	_	O
of	_	_	O
forks	_	_	B-VAR
as	_	_	O
plates	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
plate	_	_	B-VAR
is	_	_	O
$	_	_	O
10	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
fork	_	_	B-VAR
is	_	_	O
$	_	_	O
8	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
woman	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
6000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
energy	_	_	O
companies	_	_	O
.	_	_	O
She	_	_	O
can	_	_	O
invest	_	_	O
in	_	_	O
a	_	_	O
solar	_	_	B-VAR
energy	_	_	I-VAR
company	_	_	I-VAR
and	_	_	O
a	_	_	O
wind	_	_	B-VAR
energy	_	_	I-VAR
company	_	_	I-VAR
.	_	_	O
Each	_	_	O
dollar	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
solar	_	_	B-VAR
energy	_	_	I-VAR
company	_	_	I-VAR
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
0.10	_	_	B-PARAM
while	_	_	O
each	_	_	O
dollar	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
wind	_	_	B-VAR
energy	_	_	I-VAR
company	_	_	I-VAR
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
0.09	_	_	B-PARAM
.	_	_	O
She	_	_	O
wants	_	_	O
to	_	_	O
invest	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
45	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
her	_	_	O
investment	_	_	O
into	_	_	O
the	_	_	O
solar	_	_	B-VAR
energy	_	_	I-VAR
company	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
$	_	_	O
3000	_	_	B-LIMIT
in	_	_	O
the	_	_	O
wind	_	_	B-VAR
energy	_	_	I-VAR
company	_	_	I-VAR
.	_	_	O
How	_	_	O
much	_	_	O
money	_	_	O
should	_	_	O
she	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
her	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
leatherworker	_	_	O
has	_	_	B-CONST_DIR
2000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
leather	_	_	O
to	_	_	O
make	_	_	O
wallets	_	_	B-VAR
and	_	_	O
purses	_	_	B-VAR
.	_	_	O
Each	_	_	O
wallet	_	_	B-VAR
needs	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
leather	_	_	O
and	_	_	O
each	_	_	O
purse	_	_	B-VAR
needs	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
leather	_	_	O
.	_	_	O
Due	_	_	O
to	_	_	O
popularity	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
four	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
many	_	_	O
purses	_	_	B-VAR
are	_	_	O
needed	_	_	O
than	_	_	O
wallets	_	_	B-VAR
and	_	_	O
there	_	_	O
needs	_	_	O
to	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
wallets	_	_	B-VAR
made	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
wallet	_	_	B-VAR
is	_	_	O
$	_	_	O
40	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
purse	_	_	B-VAR
is	_	_	O
$	_	_	O
85	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
art	_	_	O
gallery	_	_	O
sells	_	_	O
paintings	_	_	B-VAR
and	_	_	O
photo	_	_	B-VAR
prints	_	_	I-VAR
.	_	_	O
A	_	_	O
painting	_	_	B-VAR
takes	_	_	O
7	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
of	_	_	O
wall	_	_	O
space	_	_	O
while	_	_	O
a	_	_	O
photo	_	_	B-VAR
print	_	_	I-VAR
takes	_	_	O
4	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
of	_	_	O
wall	_	_	O
space	_	_	O
.	_	_	O
The	_	_	O
gallery	_	_	O
has	_	_	B-CONST_DIR
200	_	_	B-LIMIT
sq	_	_	O
ft	_	_	O
of	_	_	O
wall	_	_	O
space	_	_	O
available	_	_	O
.	_	_	O
A	_	_	O
painting	_	_	B-VAR
costs	_	_	O
the	_	_	O
gallery	_	_	O
$	_	_	O
400	_	_	B-PARAM
and	_	_	O
a	_	_	O
photo	_	_	B-VAR
print	_	_	I-VAR
costs	_	_	O
the	_	_	O
gallery	_	_	O
$	_	_	O
200	_	_	B-PARAM
.	_	_	O
The	_	_	O
gallery	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
7000	_	_	B-LIMIT
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
items	_	_	O
in	_	_	O
stock	_	_	O
must	_	_	O
be	_	_	O
photo	_	_	B-VAR
prints	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
painting	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
330	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
photo	_	_	B-VAR
print	_	_	I-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
170	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
gallery	_	_	O
stock	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
makeup	_	_	O
store	_	_	O
sells	_	_	O
perfume	_	_	B-VAR
and	_	_	O
mascara	_	_	B-VAR
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
20,000	_	_	B-LIMIT
.	_	_	O
Each	_	_	O
bottle	_	_	O
of	_	_	O
perfume	_	_	B-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
each	_	_	O
bottle	_	_	O
of	_	_	O
mascara	_	_	B-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
40	_	_	B-PARAM
.	_	_	O
Each	_	_	O
bottle	_	_	O
of	_	_	O
perfume	_	_	B-VAR
is	_	_	O
then	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
20	_	_	B-PARAM
while	_	_	O
each	_	_	O
bottle	_	_	O
of	_	_	O
mascara	_	_	B-VAR
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
15	_	_	B-PARAM
.	_	_	O
The	_	_	O
owner	_	_	O
estimates	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
but	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
40	_	_	B-LIMIT
bottles	_	_	O
of	_	_	O
perfume	_	_	B-VAR
will	_	_	O
be	_	_	O
sold	_	_	O
.	_	_	O
The	_	_	O
number	_	_	O
of	_	_	O
mascara	_	_	B-VAR
sold	_	_	O
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
a	_	_	O
third	_	_	B-PARAM
the	_	_	O
number	_	_	O
of	_	_	O
perfume	_	_	B-VAR
sold	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
bottles	_	_	O
of	_	_	O
perfume	_	_	B-VAR
and	_	_	O
mascara	_	_	B-VAR
should	_	_	O
the	_	_	O
store	_	_	O
buy	_	_	O
and	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
company	_	_	O
is	_	_	O
looking	_	_	O
to	_	_	O
purchase	_	_	O
ads	_	_	O
to	_	_	O
place	_	_	O
in	_	_	O
three	_	_	O
video	_	_	O
categories	_	_	O
:	_	_	O
DIY	_	_	B-VAR
videos	_	_	I-VAR
,	_	_	O
shopping	_	_	B-VAR
videos	_	_	I-VAR
,	_	_	O
and	_	_	O
unboxing	_	_	B-VAR
videos	_	_	I-VAR
.	_	_	O
The	_	_	O
cost	_	_	O
of	_	_	O
placing	_	_	O
an	_	_	O
ad	_	_	O
in	_	_	O
each	_	_	O
video	_	_	O
and	_	_	O
the	_	_	O
expected	_	_	O
viewership	_	_	B-OBJ_NAME
is	_	_	O
given	_	_	O
as	_	_	O
follows	_	_	O
.	_	_	O
Each	_	_	O
ad	_	_	O
placed	_	_	O
in	_	_	O
a	_	_	O
DIY	_	_	B-VAR
video	_	_	I-VAR
costs	_	_	O
$	_	_	O
5000	_	_	B-PARAM
and	_	_	O
reaches	_	_	O
10000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
Each	_	_	O
ad	_	_	O
placed	_	_	O
in	_	_	O
a	_	_	O
shopping	_	_	B-VAR
video	_	_	I-VAR
costs	_	_	O
$	_	_	O
3200	_	_	B-PARAM
and	_	_	O
reaches	_	_	O
4000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
Finally	_	_	O
,	_	_	O
each	_	_	O
ad	_	_	O
placed	_	_	O
in	_	_	O
an	_	_	O
unboxing	_	_	B-VAR
video	_	_	I-VAR
costs	_	_	O
$	_	_	O
4000	_	_	B-PARAM
and	_	_	O
reaches	_	_	O
9000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
There	_	_	O
are	_	_	O
few	_	_	O
DIY	_	_	B-VAR
videos	_	_	I-VAR
,	_	_	O
hence	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
ads	_	_	O
placed	_	_	O
on	_	_	O
DIY	_	_	B-VAR
videos	_	_	I-VAR
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
5	_	_	B-LIMIT
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
half	_	_	B-LIMIT
the	_	_	O
number	_	_	O
of	_	_	O
ads	_	_	O
should	_	_	O
be	_	_	O
at	_	_	O
unboxing	_	_	B-VAR
videos	_	_	I-VAR
,	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
ads	_	_	O
should	_	_	O
be	_	_	O
in	_	_	O
shopping	_	_	B-VAR
videos	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
company	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
120000	_	_	B-LIMIT
,	_	_	O
how	_	_	O
many	_	_	O
ads	_	_	O
should	_	_	O
they	_	_	O
place	_	_	O
in	_	_	O
each	_	_	O
category	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
viewership	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
record	_	_	O
company	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
400000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
two	_	_	O
artists	_	_	O
,	_	_	O
a	_	_	O
pop	_	_	B-VAR
artist	_	_	I-VAR
and	_	_	O
a	_	_	O
rapper	_	_	B-VAR
.	_	_	O
They	_	_	O
have	_	_	O
decided	_	_	O
to	_	_	O
invest	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
much	_	_	O
money	_	_	O
in	_	_	O
the	_	_	O
pop	_	_	B-VAR
artist	_	_	I-VAR
than	_	_	O
in	_	_	O
the	_	_	O
rapper	_	_	B-VAR
.	_	_	O
However	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
pop	_	_	B-VAR
artist	_	_	I-VAR
can	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
250000	_	_	B-LIMIT
.	_	_	O
If	_	_	O
the	_	_	O
money	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
rapper	_	_	B-VAR
earns	_	_	B-OBJ_NAME
5	_	_	B-PARAM
%	_	_	I-PARAM
and	_	_	O
the	_	_	O
money	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
pop	_	_	B-VAR
artist	_	_	I-VAR
earns	_	_	B-OBJ_NAME
3	_	_	B-PARAM
%	_	_	I-PARAM
.	_	_	O
How	_	_	O
much	_	_	O
money	_	_	O
should	_	_	O
they	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
their	_	_	O
earnings	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
movie	_	_	O
theatre	_	_	O
sells	_	_	O
regular	_	_	B-VAR
passes	_	_	I-VAR
and	_	_	O
premium	_	_	B-VAR
passes	_	_	I-VAR
,	_	_	O
which	_	_	O
give	_	_	O
better	_	_	O
seating	_	_	O
.	_	_	O
The	_	_	O
movie	_	_	O
theatre	_	_	O
can	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
500	_	_	B-LIMIT
passes	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
regular	_	_	B-VAR
pass	_	_	I-VAR
is	_	_	O
$	_	_	O
40	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
premium	_	_	B-VAR
pass	_	_	I-VAR
is	_	_	O
$	_	_	O
90	_	_	B-PARAM
.	_	_	O
The	_	_	O
theatre	_	_	O
reserves	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
passes	_	_	O
to	_	_	O
be	_	_	O
premium	_	_	B-VAR
but	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
many	_	_	O
people	_	_	O
prefer	_	_	O
to	_	_	O
buy	_	_	O
regular	_	_	B-VAR
passes	_	_	I-VAR
than	_	_	O
premium	_	_	B-VAR
passes	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
passes	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
the	_	_	O
movie	_	_	O
theatre	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
farm	_	_	O
has	_	_	O
to	_	_	O
deliver	_	_	O
its	_	_	O
milk	_	_	O
.	_	_	O
They	_	_	O
can	_	_	O
either	_	_	O
be	_	_	O
transported	_	_	O
by	_	_	O
rail	_	_	B-VAR
or	_	_	O
by	_	_	O
truck	_	_	B-VAR
.	_	_	O
Each	_	_	O
rail	_	_	B-VAR
shipment	_	_	I-VAR
can	_	_	O
take	_	_	O
400	_	_	B-PARAM
litres	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
milk	_	_	I-OBJ_NAME
while	_	_	O
each	_	_	O
truck	_	_	B-VAR
shipment	_	_	I-VAR
can	_	_	O
take	_	_	O
200	_	_	B-PARAM
litres	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
milk	_	_	I-OBJ_NAME
.	_	_	O
The	_	_	O
cost	_	_	O
per	_	_	O
rail	_	_	B-VAR
shipment	_	_	I-VAR
is	_	_	O
$	_	_	O
100	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	O
per	_	_	O
truck	_	_	B-VAR
shipment	_	_	I-VAR
is	_	_	O
$	_	_	O
85	_	_	B-PARAM
.	_	_	O
The	_	_	O
farm	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
3000	_	_	B-LIMIT
and	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
rail	_	_	B-VAR
shipments	_	_	I-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
truck	_	_	B-VAR
shipments	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
shipment	_	_	O
should	_	_	O
be	_	_	O
taken	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
litres	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
milk	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
transported	_	_	O
?	_	_	O

A	_	_	O
gardening	_	_	O
company	_	_	O
employs	_	_	O
newcomers	_	_	B-VAR
earning	_	_	B-OBJ_NAME
$	_	_	O
400	_	_	B-PARAM
a	_	_	O
week	_	_	O
and	_	_	O
full	_	_	B-VAR
-	_	_	I-VAR
time	_	_	I-VAR
employees	_	_	I-VAR
earning	_	_	B-OBJ_NAME
$	_	_	O
700	_	_	B-PARAM
a	_	_	O
week	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
needs	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
gardeners	_	_	O
of	_	_	O
whom	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
40	_	_	B-LIMIT
must	_	_	O
be	_	_	O
full	_	_	B-VAR
-	_	_	I-VAR
time	_	_	I-VAR
employees	_	_	I-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
to	_	_	O
make	_	_	O
sure	_	_	O
there	_	_	O
is	_	_	O
supervision	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
full	_	_	B-VAR
-	_	_	I-VAR
time	_	_	I-VAR
employees	_	_	I-VAR
should	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
half	_	_	B-PARAM
the	_	_	O
number	_	_	O
of	_	_	O
newcomers	_	_	B-VAR
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	B-OBJ_NAME
wage	_	_	I-OBJ_NAME
bill	_	_	I-OBJ_NAME
.	_	_	O

An	_	_	O
investor	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
200000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
four	_	_	O
subsets	_	_	O
of	_	_	O
the	_	_	O
music	_	_	O
industry	_	_	O
:	_	_	O
the	_	_	O
pop	_	_	B-VAR
industry	_	_	I-VAR
,	_	_	O
the	_	_	O
rap	_	_	B-VAR
industry	_	_	I-VAR
,	_	_	O
the	_	_	O
country	_	_	B-VAR
industry	_	_	I-VAR
,	_	_	O
and	_	_	O
the	_	_	O
indie	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
The	_	_	O
rate	_	_	O
of	_	_	O
return	_	_	B-OBJ_NAME
for	_	_	O
each	_	_	O
investment	_	_	O
is	_	_	O
as	_	_	O
follows	_	_	O
:	_	_	O
pop	_	_	B-VAR
industry	_	_	I-VAR
,	_	_	O
5	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
rap	_	_	B-VAR
industry	_	_	I-VAR
,	_	_	O
4	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
country	_	_	B-VAR
industry	_	_	I-VAR
,	_	_	O
3	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
and	_	_	O
indie	_	_	B-VAR
industry	_	_	I-VAR
,	_	_	O
3.5	_	_	B-PARAM
%	_	_	I-PARAM
.	_	_	O
Here	_	_	O
are	_	_	O
some	_	_	O
restrictions	_	_	O
on	_	_	O
the	_	_	O
investments	_	_	O
.	_	_	O
The	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
indie	_	_	B-VAR
industry	_	_	I-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
pop	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
The	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
rap	_	_	B-VAR
industry	_	_	I-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
country	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
Finally	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
20	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
total	_	_	O
amount	_	_	O
can	_	_	O
be	_	_	O
in	_	_	O
the	_	_	O
indie	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
How	_	_	O
much	_	_	O
should	_	_	O
the	_	_	O
investor	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
industry	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
return	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
farmer	_	_	O
has	_	_	B-CONST_DIR
400	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
on	_	_	O
which	_	_	O
he	_	_	O
plants	_	_	O
apple	_	_	B-VAR
and	_	_	O
peach	_	_	B-VAR
trees	_	_	I-VAR
.	_	_	O
He	_	_	O
must	_	_	O
plant	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
60	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
apple	_	_	B-VAR
trees	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
40	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
peach	_	_	B-VAR
trees	_	_	I-VAR
.	_	_	O
He	_	_	O
prefers	_	_	O
to	_	_	O
plant	_	_	O
peach	_	_	B-VAR
trees	_	_	I-VAR
but	_	_	O
can	_	_	O
plant	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	I-PARAM
the	_	_	O
amount	_	_	O
of	_	_	O
peach	_	_	B-VAR
trees	_	_	I-VAR
as	_	_	O
apple	_	_	B-VAR
trees	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
apple	_	_	B-VAR
trees	_	_	I-VAR
is	_	_	O
$	_	_	O
900	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
peach	_	_	B-VAR
trees	_	_	I-VAR
is	_	_	O
$	_	_	O
1100	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
plant	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
travel	_	_	O
company	_	_	O
can	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
300	_	_	B-LIMIT
tickets	_	_	O
to	_	_	O
LA	_	_	O
.	_	_	O
They	_	_	O
offer	_	_	O
guided	_	_	B-VAR
tour	_	_	I-VAR
packages	_	_	I-VAR
as	_	_	O
well	_	_	O
as	_	_	O
regular	_	_	B-VAR
tickets	_	_	I-VAR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
guided	_	_	B-VAR
tour	_	_	I-VAR
package	_	_	I-VAR
is	_	_	O
$	_	_	O
500	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
regular	_	_	B-VAR
ticket	_	_	I-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
.	_	_	O
The	_	_	O
travel	_	_	O
company	_	_	O
reserves	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
guided	_	_	B-VAR
tour	_	_	I-VAR
packages	_	_	I-VAR
,	_	_	O
but	_	_	O
since	_	_	O
most	_	_	O
people	_	_	O
like	_	_	O
to	_	_	O
go	_	_	O
at	_	_	O
their	_	_	O
own	_	_	O
pace	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
2	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
many	_	_	O
people	_	_	O
prefer	_	_	O
to	_	_	O
buy	_	_	O
regular	_	_	B-VAR
tickets	_	_	I-VAR
than	_	_	O
guided	_	_	B-VAR
tour	_	_	I-VAR
packages	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
ticket	_	_	O
type	_	_	O
should	_	_	O
be	_	_	O
sold	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
glass	_	_	O
company	_	_	O
makes	_	_	O
sliding	_	_	B-VAR
doors	_	_	I-VAR
and	_	_	O
windows	_	_	B-VAR
.	_	_	O
They	_	_	O
have	_	_	O
orders	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
120	_	_	B-LIMIT
sliding	_	_	B-VAR
doors	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
110	_	_	B-LIMIT
windows	_	_	B-VAR
per	_	_	O
day	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
due	_	_	O
to	_	_	O
supply	_	_	O
constraints	_	_	O
,	_	_	O
the	_	_	O
company	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
210	_	_	B-LIMIT
sliding	_	_	B-VAR
doors	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
170	_	_	B-LIMIT
windows	_	_	B-VAR
per	_	_	O
day	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
they	_	_	O
have	_	_	O
a	_	_	O
contract	_	_	O
to	_	_	O
ship	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
250	_	_	B-LIMIT
products	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
sliding	_	_	B-VAR
door	_	_	I-VAR
is	_	_	O
$	_	_	O
30	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
window	_	_	B-VAR
is	_	_	O
$	_	_	O
25	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
pie	_	_	O
shop	_	_	O
sells	_	_	O
apple	_	_	B-VAR
and	_	_	O
peach	_	_	B-VAR
pies	_	_	I-VAR
.	_	_	O
In	_	_	O
a	_	_	O
day	_	_	O
,	_	_	O
they	_	_	O
must	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
15	_	_	B-LIMIT
apple	_	_	B-VAR
pies	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
12	_	_	B-LIMIT
peach	_	_	B-VAR
pies	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
they	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
20	_	_	B-LIMIT
apple	_	_	B-VAR
pies	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
18	_	_	B-LIMIT
peach	_	_	B-VAR
pies	_	_	I-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
they	_	_	O
only	_	_	B-CONST_DIR
have	_	_	O
enough	_	_	O
pie	_	_	O
crusts	_	_	O
to	_	_	O
make	_	_	O
30	_	_	B-LIMIT
pies	_	_	O
total	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
apple	_	_	B-VAR
pie	_	_	I-VAR
is	_	_	O
$	_	_	O
7	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
peach	_	_	B-VAR
pie	_	_	I-VAR
is	_	_	O
$	_	_	O
8	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

You	_	_	O
are	_	_	O
playing	_	_	O
a	_	_	O
game	_	_	O
where	_	_	O
you	_	_	O
can	_	_	O
catch	_	_	O
fish	_	_	B-VAR
or	_	_	O
birds	_	_	B-VAR
.	_	_	O
Each	_	_	O
fish	_	_	B-VAR
caught	_	_	O
is	_	_	O
4	_	_	B-PARAM
points	_	_	B-OBJ_NAME
and	_	_	O
each	_	_	O
bird	_	_	B-VAR
caught	_	_	O
is	_	_	O
6	_	_	B-PARAM
points	_	_	B-OBJ_NAME
.	_	_	O
You	_	_	O
have	_	_	O
to	_	_	O
catch	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
6	_	_	B-LIMIT
fishes	_	_	B-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
2	_	_	B-LIMIT
birds	_	_	B-VAR
to	_	_	O
progress	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
you	_	_	O
only	_	_	O
have	_	_	O
time	_	_	O
to	_	_	O
catch	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
9	_	_	B-LIMIT
fishes	_	_	B-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
4	_	_	B-LIMIT
birds	_	_	B-VAR
.	_	_	O
In	_	_	O
total	_	_	O
,	_	_	O
you	_	_	O
can	_	_	O
catch	_	_	O
no	_	_	B-CONST_DIR
more	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
12	_	_	B-LIMIT
animals	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
animal	_	_	O
should	_	_	O
you	_	_	O
catch	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
your	_	_	O
points	_	_	B-OBJ_NAME
?	_	_	O

XYZ	_	_	O
Automobile	_	_	O
sells	_	_	O
SUV	_	_	B-VAR
cars	_	_	I-VAR
and	_	_	O
minivans	_	_	B-VAR
.	_	_	O
Two	_	_	O
different	_	_	O
factories	_	_	O
produce	_	_	O
these	_	_	O
cars	_	_	O
.	_	_	O
The	_	_	O
SUV	_	_	B-VAR
car	_	_	I-VAR
factory	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
5	_	_	B-LIMIT
SUV	_	_	B-VAR
cars	_	_	I-VAR
per	_	_	O
day	_	_	O
while	_	_	O
the	_	_	O
minivan	_	_	B-VAR
car	_	_	I-VAR
factory	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
3	_	_	B-LIMIT
minivans	_	_	B-VAR
per	_	_	O
day	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
outsources	_	_	O
the	_	_	O
finishing	_	_	O
touches	_	_	O
to	_	_	O
a	_	_	O
third	_	_	O
party	_	_	O
,	_	_	O
which	_	_	O
can	_	_	O
process	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
5	_	_	B-LIMIT
vehicle	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
SUV	_	_	B-VAR
car	_	_	I-VAR
is	_	_	O
$	_	_	O
7500	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
minivan	_	_	B-VAR
is	_	_	O
$	_	_	O
4000	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
vehicle	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
electronics	_	_	O
company	_	_	O
produces	_	_	O
entry	_	_	B-VAR
-	_	_	I-VAR
level	_	_	I-VAR
devices	_	_	I-VAR
and	_	_	O
premium	_	_	B-VAR
devices	_	_	I-VAR
.	_	_	O
The	_	_	O
company	_	_	O
makes	_	_	O
a	_	_	O
$	_	_	O
300	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
for	_	_	O
each	_	_	O
entry	_	_	B-VAR
-	_	_	I-VAR
level	_	_	I-VAR
device	_	_	I-VAR
sold	_	_	O
and	_	_	O
a	_	_	O
$	_	_	O
200	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
for	_	_	O
each	_	_	O
premium	_	_	B-VAR
device	_	_	I-VAR
sold	_	_	O
.	_	_	O
Note	_	_	O
that	_	_	O
the	_	_	O
daily	_	_	O
demand	_	_	O
for	_	_	O
entry	_	_	B-VAR
-	_	_	I-VAR
level	_	_	I-VAR
devices	_	_	I-VAR
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
20	_	_	B-LIMIT
and	_	_	O
the	_	_	O
daily	_	_	O
demand	_	_	O
for	_	_	O
premium	_	_	B-VAR
devices	_	_	I-VAR
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
15	_	_	B-LIMIT
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
the	_	_	O
company	_	_	O
can	_	_	O
only	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
devices	_	_	O
total	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
devices	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Andy	_	_	O
has	_	_	B-CONST_DIR
decided	_	_	O
to	_	_	O
put	_	_	O
$	_	_	O
10	_	_	B-LIMIT
million	_	_	O
of	_	_	O
his	_	_	O
wealth	_	_	O
in	_	_	O
a	_	_	O
trust	_	_	O
fund	_	_	O
for	_	_	O
his	_	_	O
children	_	_	O
.	_	_	O
His	_	_	O
financial	_	_	O
advisor	_	_	O
has	_	_	O
evaluated	_	_	O
that	_	_	O
the	_	_	O
money	_	_	O
should	_	_	O
be	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
energy	_	_	B-VAR
sector	_	_	I-VAR
or	_	_	O
in	_	_	O
the	_	_	O
travel	_	_	B-VAR
sector	_	_	I-VAR
.	_	_	O
Money	_	_	O
placed	_	_	O
in	_	_	O
the	_	_	O
energy	_	_	B-VAR
sector	_	_	I-VAR
is	_	_	O
likely	_	_	O
to	_	_	O
give	_	_	O
a	_	_	O
32	_	_	B-PARAM
%	_	_	I-PARAM
total	_	_	O
return	_	_	B-OBJ_NAME
while	_	_	O
money	_	_	O
placed	_	_	O
in	_	_	O
the	_	_	O
travel	_	_	B-VAR
sector	_	_	I-VAR
yields	_	_	O
a	_	_	O
20	_	_	B-PARAM
%	_	_	I-PARAM
total	_	_	O
return	_	_	B-OBJ_NAME
.	_	_	O
Andy	_	_	O
wants	_	_	O
to	_	_	O
place	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
25	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
investment	_	_	O
in	_	_	O
the	_	_	O
energy	_	_	B-VAR
sector	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
50	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
investment	_	_	O
in	_	_	O
the	_	_	O
travel	_	_	B-VAR
sector	_	_	I-VAR
.	_	_	O
How	_	_	O
much	_	_	O
money	_	_	O
should	_	_	O
be	_	_	O
placed	_	_	O
in	_	_	O
each	_	_	O
sector	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
return	_	_	B-OBJ_NAME
on	_	_	O
investment	_	_	O
?	_	_	O

Party	_	_	O
Supplies	_	_	O
Ltd	_	_	O
plans	_	_	O
to	_	_	O
sell	_	_	O
superhero	_	_	B-VAR
costumes	_	_	I-VAR
and	_	_	O
fantasy	_	_	B-VAR
costumes	_	_	I-VAR
for	_	_	O
Halloween	_	_	O
.	_	_	O
It	_	_	O
takes	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
superhero	_	_	B-VAR
costume	_	_	I-VAR
and	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
fantasy	_	_	B-VAR
costume	_	_	I-VAR
.	_	_	O
Based	_	_	O
on	_	_	O
market	_	_	O
research	_	_	O
,	_	_	O
the	_	_	O
company	_	_	O
should	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
many	_	_	O
fantasy	_	_	B-VAR
costumes	_	_	I-VAR
as	_	_	O
superhero	_	_	B-VAR
costumes	_	_	I-VAR
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
about	_	_	O
3000	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
to	_	_	O
make	_	_	O
the	_	_	O
costumes	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
superhero	_	_	B-VAR
costume	_	_	I-VAR
is	_	_	O
$	_	_	O
24	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
fantasy	_	_	B-VAR
costume	_	_	I-VAR
is	_	_	O
$	_	_	O
32	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
its	_	_	O
total	_	_	B-OBJ_NAME
profit	_	_	I-OBJ_NAME
?	_	_	O

Marty	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
20000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
the	_	_	O
fishing	_	_	B-VAR
and	_	_	O
transportation	_	_	B-VAR
industries	_	_	I-VAR
.	_	_	O
The	_	_	O
fishing	_	_	B-VAR
industry	_	_	I-VAR
yields	_	_	O
a	_	_	O
$	_	_	O
0.3	_	_	B-PARAM
return	_	_	B-OBJ_NAME
per	_	_	O
dollar	_	_	O
invested	_	_	O
whereas	_	_	O
the	_	_	O
transportation	_	_	B-VAR
industry	_	_	I-VAR
yields	_	_	O
a	_	_	O
$	_	_	O
0.15	_	_	B-PARAM
return	_	_	B-OBJ_NAME
per	_	_	O
dollar	_	_	O
invested	_	_	O
.	_	_	O
At	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
40	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
money	_	_	O
has	_	_	O
to	_	_	O
be	_	_	O
used	_	_	O
in	_	_	O
fishing	_	_	B-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
$	_	_	O
5000	_	_	B-LIMIT
has	_	_	O
to	_	_	O
be	_	_	O
invested	_	_	O
in	_	_	O
transportation	_	_	B-VAR
.	_	_	O
How	_	_	O
much	_	_	O
should	_	_	O
he	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
return	_	_	B-OBJ_NAME
?	_	_	O

Amazing	_	_	O
Decor	_	_	O
buys	_	_	O
and	_	_	O
sells	_	_	O
both	_	_	O
furniture	_	_	B-VAR
and	_	_	O
carpet	_	_	B-VAR
.	_	_	O
Each	_	_	O
furniture	_	_	B-VAR
takes	_	_	O
12	_	_	B-PARAM
square	_	_	O
feet	_	_	O
of	_	_	O
space	_	_	O
while	_	_	O
each	_	_	O
carpet	_	_	B-VAR
takes	_	_	O
7	_	_	B-PARAM
square	_	_	O
feet	_	_	O
of	_	_	O
space	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
1200	_	_	B-LIMIT
square	_	_	O
feet	_	_	O
of	_	_	O
space	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
Buying	_	_	O
a	_	_	O
furniture	_	_	B-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
300	_	_	B-PARAM
and	_	_	O
buying	_	_	O
a	_	_	O
carpet	_	_	B-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
80	_	_	B-PARAM
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
30000	_	_	B-PARAM
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
items	_	_	O
in	_	_	O
stock	_	_	O
have	_	_	O
to	_	_	O
be	_	_	O
furniture	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
furniture	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
40	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
carpet	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
30	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
buy	_	_	O
and	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
e	_	_	O
-	_	_	O
commerce	_	_	O
company	_	_	O
sells	_	_	O
face	_	_	B-VAR
masks	_	_	I-VAR
and	_	_	O
hand	_	_	B-VAR
sanitizers	_	_	I-VAR
.	_	_	O
He	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
1000	_	_	B-LIMIT
and	_	_	O
each	_	_	O
face	_	_	B-VAR
mask	_	_	I-VAR
costs	_	_	O
$	_	_	O
1.5	_	_	B-PARAM
whereas	_	_	O
each	_	_	O
hand	_	_	B-VAR
sanitizer	_	_	I-VAR
costs	_	_	O
$	_	_	O
3	_	_	B-PARAM
.	_	_	O
Each	_	_	O
mask	_	_	B-VAR
is	_	_	O
then	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
1	_	_	B-PARAM
while	_	_	O
each	_	_	O
sanitizer	_	_	B-VAR
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
1.5	_	_	B-PARAM
.	_	_	O
The	_	_	O
owner	_	_	O
estimates	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
80	_	_	B-LIMIT
but	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
500	_	_	B-LIMIT
face	_	_	B-VAR
masks	_	_	I-VAR
are	_	_	O
sold	_	_	O
each	_	_	O
day	_	_	O
.	_	_	O
He	_	_	O
also	_	_	O
estimates	_	_	O
that	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
hand	_	_	B-VAR
sanitizers	_	_	I-VAR
sold	_	_	O
will	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
half	_	_	B-PARAM
the	_	_	O
number	_	_	O
of	_	_	O
face	_	_	B-VAR
masks	_	_	I-VAR
sold	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
item	_	_	O
should	_	_	O
he	_	_	O
have	_	_	O
in	_	_	O
stock	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
daily	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

Maximus	_	_	O
Ltd	_	_	O
wants	_	_	O
to	_	_	O
launch	_	_	O
a	_	_	O
campaign	_	_	O
to	_	_	O
advertise	_	_	O
their	_	_	O
new	_	_	O
Max	_	_	O
product	_	_	O
.	_	_	O
They	_	_	O
can	_	_	O
buy	_	_	O
ads	_	_	O
on	_	_	O
billboards	_	_	B-VAR
,	_	_	O
podcasts	_	_	B-VAR
,	_	_	O
and	_	_	O
merchandises	_	_	B-VAR
.	_	_	O
The	_	_	O
cost	_	_	O
for	_	_	O
an	_	_	O
ad	_	_	O
on	_	_	O
each	_	_	O
as	_	_	O
well	_	_	O
as	_	_	O
the	_	_	O
expected	_	_	O
viewership	_	_	O
is	_	_	O
given	_	_	O
.	_	_	O
On	_	_	O
billboards	_	_	B-VAR
an	_	_	O
ad	_	_	O
costs	_	_	O
$	_	_	O
750	_	_	B-PARAM
and	_	_	O
reaches	_	_	O
40000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
On	_	_	O
podcasts	_	_	B-VAR
an	_	_	O
ad	_	_	O
costs	_	_	O
$	_	_	O
1000	_	_	B-PARAM
and	_	_	O
reaches	_	_	O
10000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
On	_	_	O
merchandises	_	_	B-VAR
an	_	_	O
ad	_	_	O
costs	_	_	O
$	_	_	O
300	_	_	B-PARAM
and	_	_	O
reaches	_	_	O
2000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
billboard	_	_	B-VAR
provider	_	_	O
limits	_	_	B-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
ads	_	_	O
from	_	_	O
the	_	_	O
same	_	_	O
company	_	_	O
to	_	_	O
3	_	_	B-LIMIT
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
40	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
total	_	_	O
number	_	_	O
of	_	_	O
ads	_	_	O
can	_	_	O
occur	_	_	O
on	_	_	O
merchandises	_	_	B-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
25	_	_	B-LIMIT
%	_	_	I-LIMIT
should	_	_	O
occur	_	_	O
on	_	_	O
podcasts	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
company	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
20000	_	_	B-LIMIT
,	_	_	O
how	_	_	O
many	_	_	O
ads	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
they	_	_	O
purchase	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
viewership	_	_	B-OBJ_NAME
.	_	_	O

Marty	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
10000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
both	_	_	O
the	_	_	O
wood	_	_	B-VAR
and	_	_	O
bamboo	_	_	B-VAR
industries	_	_	I-VAR
.	_	_	O
He	_	_	O
has	_	_	O
decided	_	_	O
that	_	_	O
the	_	_	O
investment	_	_	O
in	_	_	O
the	_	_	O
wood	_	_	B-VAR
industry	_	_	I-VAR
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
four	_	_	B-PARAM
times	_	_	O
as	_	_	O
much	_	_	O
as	_	_	O
that	_	_	O
in	_	_	O
the	_	_	O
bamboo	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
he	_	_	O
has	_	_	O
restricted	_	_	O
to	_	_	O
invest	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
7000	_	_	B-LIMIT
in	_	_	O
the	_	_	O
wood	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
If	_	_	O
investments	_	_	O
in	_	_	O
the	_	_	O
wood	_	_	B-VAR
industry	_	_	I-VAR
earn	_	_	O
7	_	_	B-PARAM
%	_	_	I-PARAM
return	_	_	B-OBJ_NAME
and	_	_	O
investments	_	_	O
in	_	_	O
the	_	_	O
bamboo	_	_	B-VAR
industry	_	_	I-VAR
earn	_	_	O
a	_	_	O
3	_	_	B-PARAM
%	_	_	I-PARAM
return	_	_	B-OBJ_NAME
,	_	_	O
how	_	_	O
much	_	_	O
should	_	_	O
he	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
average	_	_	O
return	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
West	_	_	O
Coast	_	_	O
train	_	_	O
company	_	_	O
has	_	_	O
a	_	_	O
total	_	_	B-CONST_DIR
of	_	_	O
300	_	_	B-LIMIT
seats	_	_	O
,	_	_	O
first	_	_	B-VAR
-	_	_	I-VAR
class	_	_	I-VAR
seats	_	_	I-VAR
and	_	_	O
regular	_	_	B-VAR
seats	_	_	I-VAR
.	_	_	O
A	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
1200	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
first	_	_	B-VAR
-	_	_	I-VAR
class	_	_	I-VAR
seat	_	_	I-VAR
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
700	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
regular	_	_	B-VAR
seat	_	_	I-VAR
.	_	_	O
The	_	_	O
train	_	_	O
company	_	_	O
reserves	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
seats	_	_	O
to	_	_	O
be	_	_	O
first	_	_	B-VAR
-	_	_	I-VAR
class	_	_	I-VAR
but	_	_	O
because	_	_	O
of	_	_	O
the	_	_	O
pandemic	_	_	O
is	_	_	O
finally	_	_	O
over	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
many	_	_	O
people	_	_	O
now	_	_	O
prefer	_	_	O
regular	_	_	B-VAR
seats	_	_	I-VAR
to	_	_	O
first	_	_	B-VAR
-	_	_	I-VAR
class	_	_	I-VAR
seats	_	_	I-VAR
to	_	_	O
save	_	_	O
on	_	_	O
travel	_	_	O
costs	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
tickets	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
its	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
litchi	_	_	O
farm	_	_	O
is	_	_	O
trying	_	_	O
to	_	_	O
send	_	_	O
their	_	_	O
litchis	_	_	O
to	_	_	O
the	_	_	O
city	_	_	O
.	_	_	O
They	_	_	O
decide	_	_	O
to	_	_	O
ship	_	_	O
them	_	_	O
either	_	_	O
by	_	_	O
boat	_	_	B-VAR
or	_	_	O
by	_	_	O
cargo	_	_	B-VAR
plane	_	_	I-VAR
.	_	_	O
Each	_	_	O
boat	_	_	B-VAR
trip	_	_	I-VAR
costs	_	_	O
$	_	_	O
5000	_	_	B-PARAM
and	_	_	O
can	_	_	O
take	_	_	O
500	_	_	B-PARAM
boxes	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
litchis	_	_	I-OBJ_NAME
while	_	_	O
each	_	_	O
cargo	_	_	B-VAR
plane	_	_	I-VAR
trip	_	_	I-VAR
costs	_	_	O
$	_	_	O
3000	_	_	B-PARAM
and	_	_	O
can	_	_	O
take	_	_	O
200	_	_	B-PARAM
boxes	_	_	B-OBJ_NAME
.	_	_	O
In	_	_	O
order	_	_	O
to	_	_	O
transport	_	_	O
all	_	_	O
the	_	_	O
produce	_	_	O
on	_	_	O
time	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
boat	_	_	B-VAR
trips	_	_	I-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
cargo	_	_	B-VAR
plane	_	_	I-VAR
trips	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
farm	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
200000	_	_	B-LIMIT
,	_	_	O
decide	_	_	O
how	_	_	O
many	_	_	O
to	_	_	O
ship	_	_	O
by	_	_	O
boat	_	_	B-VAR
or	_	_	O
by	_	_	B-VAR
plane	_	_	I-VAR
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
boxes	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
litchis	_	_	I-OBJ_NAME
the	_	_	O
farm	_	_	O
can	_	_	O
deliver	_	_	O
to	_	_	O
their	_	_	O
customers	_	_	O
.	_	_	O

A	_	_	O
startup	_	_	O
plans	_	_	O
to	_	_	O
hire	_	_	O
computer	_	_	B-VAR
engineers	_	_	I-VAR
earning	_	_	B-OBJ_NAME
$	_	_	O
1000	_	_	B-PARAM
a	_	_	O
week	_	_	O
and	_	_	O
software	_	_	B-VAR
engineers	_	_	I-VAR
earning	_	_	B-OBJ_NAME
$	_	_	O
800	_	_	B-PARAM
a	_	_	O
week	_	_	O
.	_	_	O
The	_	_	O
startup	_	_	O
requires	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
a	_	_	O
total	_	_	O
of	_	_	O
50	_	_	B-LIMIT
engineers	_	_	O
,	_	_	O
of	_	_	O
whom	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
must	_	_	O
be	_	_	O
computer	_	_	B-VAR
engineers	_	_	I-VAR
.	_	_	O
To	_	_	O
make	_	_	O
sure	_	_	O
the	_	_	O
startup	_	_	O
can	_	_	O
release	_	_	O
their	_	_	O
first	_	_	O
product	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
software	_	_	B-VAR
engineers	_	_	I-VAR
should	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-PARAM
of	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
computer	_	_	B-VAR
engineers	_	_	I-VAR
.	_	_	O
Help	_	_	O
the	_	_	O
startup	_	_	O
find	_	_	O
the	_	_	O
right	_	_	O
number	_	_	O
of	_	_	O
engineers	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
labor	_	_	O
cost	_	_	B-OBJ_NAME
.	_	_	O

An	_	_	O
essential	_	_	O
oil	_	_	O
producer	_	_	O
has	_	_	O
100	_	_	B-LIMIT
acres	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
growing	_	_	O
ylang	_	_	B-VAR
ylang	_	_	I-VAR
and	_	_	O
vanilla	_	_	B-VAR
.	_	_	O
The	_	_	O
producer	_	_	O
must	_	_	O
grow	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
ylang	_	_	B-VAR
ylang	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
vanilla	_	_	B-VAR
.	_	_	O
Even	_	_	O
though	_	_	O
ylang	_	_	B-VAR
ylang	_	_	I-VAR
oil	_	_	O
extract	_	_	O
sells	_	_	O
better	_	_	O
,	_	_	O
the	_	_	O
producer	_	_	O
can	_	_	O
grow	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
twice	_	_	B-PARAM
the	_	_	O
amount	_	_	O
of	_	_	O
ylang	_	_	B-VAR
ylang	_	_	I-VAR
as	_	_	O
vanilla	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
ylang	_	_	B-VAR
ylang	_	_	I-VAR
is	_	_	O
$	_	_	O
150	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
vanilla	_	_	B-VAR
is	_	_	O
$	_	_	O
100	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
grown	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
amusement	_	_	O
company	_	_	O
offers	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
tickets	_	_	O
.	_	_	O
There	_	_	O
is	_	_	O
a	_	_	O
all	_	_	B-VAR
-	_	_	I-VAR
inclusive	_	_	I-VAR
ticket	_	_	I-VAR
which	_	_	O
offers	_	_	O
unlimited	_	_	O
rides	_	_	O
to	_	_	O
all	_	_	O
attractions	_	_	O
,	_	_	O
and	_	_	O
a	_	_	O
regular	_	_	B-VAR
ticket	_	_	I-VAR
that	_	_	O
gives	_	_	O
one	_	_	O
ride	_	_	O
to	_	_	O
a	_	_	O
a	_	_	O
limited	_	_	O
number	_	_	O
of	_	_	O
attractions	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
sells	_	_	O
500	_	_	B-LIMIT
tickets	_	_	O
in	_	_	O
a	_	_	O
day	_	_	O
due	_	_	O
to	_	_	O
capacity	_	_	B-CONST_DIR
constraint	_	_	O
.	_	_	O
They	_	_	O
reserve	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
of	_	_	O
them	_	_	O
to	_	_	O
be	_	_	O
all	_	_	B-VAR
-	_	_	I-VAR
inclusive	_	_	I-VAR
tickets	_	_	I-VAR
.	_	_	O
Since	_	_	O
most	_	_	O
people	_	_	O
just	_	_	O
want	_	_	O
to	_	_	O
try	_	_	O
an	_	_	O
attraction	_	_	O
only	_	_	O
once	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
many	_	_	O
people	_	_	O
prefer	_	_	O
regular	_	_	B-VAR
tickets	_	_	I-VAR
than	_	_	O
all	_	_	B-VAR
-	_	_	I-VAR
inclusive	_	_	I-VAR
tickets	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
all	_	_	B-VAR
-	_	_	I-VAR
inclusive	_	_	I-VAR
ticket	_	_	I-VAR
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
regular	_	_	B-VAR
ticker	_	_	I-VAR
is	_	_	O
$	_	_	O
20	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
sold	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
bakery	_	_	O
shop	_	_	O
makes	_	_	O
strawberry	_	_	B-VAR
and	_	_	O
caramel	_	_	B-VAR
brownies	_	_	I-VAR
.	_	_	O
Every	_	_	O
day	_	_	O
,	_	_	O
there	_	_	O
are	_	_	O
repeat	_	_	O
customers	_	_	O
that	_	_	O
order	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
strawberry	_	_	B-VAR
brownies	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
75	_	_	B-LIMIT
caramel	_	_	B-VAR
brownies	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
the	_	_	O
bakery	_	_	O
shop	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
strawberry	_	_	B-VAR
brownies	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
150	_	_	B-LIMIT
caramel	_	_	B-VAR
brownies	_	_	I-VAR
.	_	_	O
Based	_	_	O
on	_	_	O
past	_	_	O
sales	_	_	O
,	_	_	O
the	_	_	O
shop	_	_	O
makes	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-PARAM
as	_	_	O
many	_	_	O
strawberry	_	_	B-VAR
brownies	_	_	I-VAR
as	_	_	O
caramel	_	_	B-VAR
brownies	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
price	_	_	B-OBJ_NAME
of	_	_	O
a	_	_	O
strawberry	_	_	B-VAR
brownie	_	_	I-VAR
is	_	_	O
$	_	_	O
1.5	_	_	B-PARAM
and	_	_	O
the	_	_	O
price	_	_	B-OBJ_NAME
of	_	_	O
a	_	_	O
caramel	_	_	B-VAR
brownie	_	_	I-VAR
is	_	_	O
$	_	_	O
2	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
revenue	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
food	_	_	O
truck	_	_	O
sells	_	_	O
burritos	_	_	B-VAR
and	_	_	O
tacitos	_	_	B-VAR
.	_	_	O
To	_	_	O
stay	_	_	O
in	_	_	O
business	_	_	O
,	_	_	O
they	_	_	O
must	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
orders	_	_	O
of	_	_	O
burritos	_	_	B-VAR
but	_	_	O
they	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
orders	_	_	O
of	_	_	O
burritos	_	_	B-VAR
.	_	_	O
Also	_	_	O
,	_	_	O
they	_	_	O
must	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
orders	_	_	O
of	_	_	O
tacitos	_	_	B-VAR
but	_	_	O
they	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
150	_	_	B-LIMIT
orders	_	_	O
of	_	_	O
tacitos	_	_	B-VAR
.	_	_	O
Due	_	_	O
to	_	_	O
the	_	_	O
lack	_	_	O
of	_	_	O
help	_	_	O
,	_	_	O
the	_	_	O
food	_	_	O
truck	_	_	O
can	_	_	O
only	_	_	O
sell	_	_	O
250	_	_	B-LIMIT
orders	_	_	O
in	_	_	O
total	_	_	B-CONST_DIR
.	_	_	O
If	_	_	O
the	_	_	O
price	_	_	B-OBJ_NAME
per	_	_	O
order	_	_	O
of	_	_	O
burritos	_	_	B-VAR
is	_	_	O
$	_	_	O
17	_	_	B-PARAM
and	_	_	O
the	_	_	O
price	_	_	B-OBJ_NAME
per	_	_	O
order	_	_	O
of	_	_	O
tacitos	_	_	B-VAR
is	_	_	O
$	_	_	O
12	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
orders	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
revenue	_	_	B-OBJ_NAME
?	_	_	O

In	_	_	O
a	_	_	O
basketball	_	_	O
game	_	_	O
,	_	_	O
your	_	_	O
team	_	_	O
can	_	_	O
shoot	_	_	O
long	_	_	B-VAR
shots	_	_	I-VAR
or	_	_	O
mid	_	_	B-VAR
-	_	_	I-VAR
range	_	_	I-VAR
shots	_	_	I-VAR
.	_	_	O
Each	_	_	O
long	_	_	B-VAR
shot	_	_	I-VAR
is	_	_	O
worth	_	_	O
3	_	_	B-PARAM
points	_	_	O
and	_	_	O
each	_	_	O
mid	_	_	B-VAR
-	_	_	I-VAR
range	_	_	I-VAR
shot	_	_	I-VAR
is	_	_	O
worth	_	_	O
2	_	_	B-PARAM
points	_	_	O
.	_	_	O
To	_	_	O
win	_	_	O
against	_	_	O
the	_	_	O
next	_	_	O
team	_	_	O
,	_	_	O
your	_	_	O
team	_	_	O
must	_	_	O
score	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
95	_	_	B-LIMIT
points	_	_	O
.	_	_	O
Based	_	_	O
on	_	_	O
previous	_	_	O
games	_	_	O
,	_	_	O
your	_	_	O
team	_	_	O
always	_	_	O
makes	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
long	_	_	B-VAR
shots	_	_	I-VAR
in	_	_	O
a	_	_	O
game	_	_	O
.	_	_	O
The	_	_	O
stats	_	_	O
also	_	_	O
show	_	_	O
that	_	_	O
your	_	_	O
team	_	_	O
efficiency	_	_	B-OBJ_NAME
is	_	_	O
25	_	_	B-PARAM
%	_	_	I-PARAM
for	_	_	O
long	_	_	B-VAR
shots	_	_	I-VAR
and	_	_	O
40	_	_	B-PARAM
%	_	_	I-PARAM
for	_	_	O
mid	_	_	B-VAR
-	_	_	I-VAR
range	_	_	I-VAR
shots	_	_	I-VAR
.	_	_	O
Determine	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
long	_	_	B-VAR
shots	_	_	I-VAR
and	_	_	O
mid	_	_	B-VAR
-	_	_	I-VAR
range	_	_	I-VAR
shots	_	_	I-VAR
that	_	_	O
your	_	_	O
team	_	_	O
should	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
its	_	_	O
efficiency	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
jewelry	_	_	O
company	_	_	O
produces	_	_	O
and	_	_	O
sells	_	_	O
bracelets	_	_	B-VAR
and	_	_	O
rings	_	_	B-VAR
.	_	_	O
The	_	_	O
bracelets	_	_	B-VAR
are	_	_	O
hand	_	_	O
-	_	_	O
crafted	_	_	O
by	_	_	O
a	_	_	O
team	_	_	O
who	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
4	_	_	B-LIMIT
bracelets	_	_	B-VAR
per	_	_	O
day	_	_	O
.	_	_	O
The	_	_	O
rings	_	_	B-VAR
are	_	_	O
made	_	_	O
by	_	_	O
another	_	_	O
team	_	_	O
who	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
7	_	_	B-LIMIT
rings	_	_	B-VAR
per	_	_	O
day	_	_	O
.	_	_	O
All	_	_	O
rings	_	_	B-VAR
have	_	_	O
to	_	_	O
be	_	_	O
approved	_	_	O
by	_	_	O
a	_	_	O
master	_	_	O
jeweler	_	_	O
and	_	_	O
he	_	_	O
can	_	_	O
check	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
jewels	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
bracelet	_	_	B-VAR
is	_	_	O
$	_	_	O
700	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
ring	_	_	B-VAR
is	_	_	O
$	_	_	O
300	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
jewelry	_	_	O
company	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
investment	_	_	O
bank	_	_	O
has	_	_	O
$	_	_	O
800000	_	_	B-LIMIT
available	_	_	B-CONST_DIR
to	_	_	O
invest	_	_	O
in	_	_	O
a	_	_	O
24	_	_	O
-	_	_	O
month	_	_	O
commitment	_	_	O
.	_	_	O
It	_	_	O
can	_	_	O
either	_	_	O
invest	_	_	O
in	_	_	O
the	_	_	O
pharmaceutical	_	_	B-VAR
industry	_	_	I-VAR
which	_	_	O
yields	_	_	O
a	_	_	O
5.5	_	_	B-PARAM
%	_	_	I-PARAM
return	_	_	B-OBJ_NAME
or	_	_	O
in	_	_	O
the	_	_	O
fast	_	_	B-VAR
food	_	_	I-VAR
industry	_	_	I-VAR
which	_	_	O
yields	_	_	O
a	_	_	O
12	_	_	B-PARAM
%	_	_	I-PARAM
return	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
bank	_	_	O
requires	_	_	O
that	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
55	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
investment	_	_	O
must	_	_	O
be	_	_	O
placed	_	_	O
in	_	_	O
the	_	_	O
pharmaceutical	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
Due	_	_	O
to	_	_	O
recent	_	_	O
issues	_	_	O
in	_	_	O
fast	_	_	B-VAR
food	_	_	I-VAR
,	_	_	O
the	_	_	O
bank	_	_	O
has	_	_	O
decided	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
40	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
its	_	_	O
investment	_	_	O
be	_	_	O
placed	_	_	O
in	_	_	O
the	_	_	O
fast	_	_	B-VAR
food	_	_	I-VAR
industry	_	_	I-VAR
.	_	_	O
How	_	_	O
much	_	_	O
should	_	_	O
the	_	_	O
bank	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
area	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
its	_	_	O
return	_	_	B-OBJ_NAME
on	_	_	O
investments	_	_	O
?	_	_	O

The	_	_	O
city	_	_	O
council	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
up	_	_	O
to	_	_	O
$	_	_	O
5500	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
infrastructure	_	_	O
.	_	_	O
They	_	_	O
can	_	_	O
invest	_	_	O
their	_	_	O
money	_	_	O
in	_	_	O
clean	_	_	B-VAR
water	_	_	I-VAR
and	_	_	O
electricity	_	_	B-VAR
.	_	_	O
Each	_	_	O
dollar	_	_	O
invested	_	_	O
in	_	_	O
clean	_	_	B-VAR
water	_	_	I-VAR
yields	_	_	O
a	_	_	O
$	_	_	O
1.9	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
.	_	_	O
Each	_	_	O
dollar	_	_	O
invested	_	_	O
in	_	_	O
electricity	_	_	B-VAR
yields	_	_	O
a	_	_	O
$	_	_	O
2.3	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
.	_	_	O
No	_	_	B-CONST_DIR
less	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
$	_	_	O
1000	_	_	B-LIMIT
must	_	_	O
be	_	_	O
in	_	_	O
clean	_	_	B-VAR
water	_	_	I-VAR
and	_	_	O
no	_	_	B-CONST_DIR
less	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
30	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
all	_	_	O
money	_	_	O
invested	_	_	O
must	_	_	O
be	_	_	O
in	_	_	O
electricity	_	_	B-VAR
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
that	_	_	O
can	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
total	_	_	O
profit	_	_	B-OBJ_NAME
.	_	_	O

Zeta	_	_	O
Furniture	_	_	O
stocks	_	_	O
and	_	_	O
sells	_	_	O
bookcases	_	_	B-VAR
and	_	_	O
computer	_	_	B-VAR
desks	_	_	I-VAR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
bookcase	_	_	B-VAR
is	_	_	O
$	_	_	O
500	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
computer	_	_	B-VAR
desk	_	_	I-VAR
is	_	_	O
$	_	_	O
80	_	_	B-PARAM
.	_	_	O
There	_	_	O
are	_	_	O
1000	_	_	B-LIMIT
sq	_	_	O
ft	_	_	O
of	_	_	O
space	_	_	O
available	_	_	B-CONST_DIR
and	_	_	O
a	_	_	O
bookcase	_	_	B-VAR
requires	_	_	O
12	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
of	_	_	O
floor	_	_	O
space	_	_	O
while	_	_	O
a	_	_	O
computer	_	_	B-VAR
desk	_	_	I-VAR
requires	_	_	O
5	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
.	_	_	O
Because	_	_	O
computer	_	_	B-VAR
desks	_	_	I-VAR
sell	_	_	O
in	_	_	O
larger	_	_	O
quantities	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
65	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
all	_	_	O
furniture	_	_	O
in	_	_	O
the	_	_	O
store	_	_	O
must	_	_	O
be	_	_	O
computer	_	_	B-VAR
desks	_	_	I-VAR
.	_	_	O
In	_	_	O
terms	_	_	O
of	_	_	O
capital	_	_	O
,	_	_	O
a	_	_	O
bookcase	_	_	B-VAR
ties	_	_	O
up	_	_	O
$	_	_	O
1200	_	_	B-PARAM
in	_	_	O
capital	_	_	O
and	_	_	O
a	_	_	O
computer	_	_	B-VAR
desk	_	_	I-VAR
ties	_	_	O
up	_	_	O
$	_	_	O
200	_	_	B-PARAM
in	_	_	O
capital	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
wants	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
22000	_	_	B-LIMIT
worth	_	_	O
of	_	_	O
capital	_	_	O
tied	_	_	O
up	_	_	O
at	_	_	O
any	_	_	O
time	_	_	O
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
.	_	_	O

Iota	_	_	O
Game	_	_	O
spends	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
50000	_	_	B-LIMIT
on	_	_	O
controllers	_	_	B-VAR
and	_	_	O
speakers	_	_	B-VAR
each	_	_	O
month	_	_	O
.	_	_	O
A	_	_	O
controller	_	_	B-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
150	_	_	B-PARAM
and	_	_	O
a	_	_	O
speaker	_	_	B-VAR
costs	_	_	O
$	_	_	O
100	_	_	B-PARAM
.	_	_	O
Each	_	_	O
controller	_	_	B-VAR
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
70	_	_	B-PARAM
while	_	_	O
each	_	_	O
speaker	_	_	B-VAR
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
20	_	_	B-PARAM
.	_	_	O
The	_	_	O
store	_	_	O
estimates	_	_	O
that	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
15	_	_	B-LIMIT
but	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
60	_	_	B-LIMIT
controllers	_	_	B-VAR
are	_	_	O
sold	_	_	O
each	_	_	O
month	_	_	O
.	_	_	O
They	_	_	O
also	_	_	O
estimate	_	_	O
that	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
speakers	_	_	B-VAR
sold	_	_	O
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
four	_	_	B-PARAM
times	_	_	I-PARAM
the	_	_	O
number	_	_	O
of	_	_	O
controllers	_	_	B-VAR
sold	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
,	_	_	O
controllers	_	_	B-VAR
and	_	_	O
speakers	_	_	B-VAR
,	_	_	O
should	_	_	O
be	_	_	O
sold	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
food	_	_	O
truck	_	_	O
wants	_	_	O
to	_	_	O
make	_	_	O
bean	_	_	B-VAR
burritos	_	_	I-VAR
and	_	_	O
beef	_	_	B-VAR
burritos	_	_	I-VAR
using	_	_	B-CONST_DIR
5000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
lettuce	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
bean	_	_	B-VAR
burrito	_	_	I-VAR
is	_	_	O
$	_	_	O
6.5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
beef	_	_	B-VAR
burrito	_	_	I-VAR
is	_	_	O
$	_	_	O
9	_	_	B-PARAM
.	_	_	O
The	_	_	O
bean	_	_	B-VAR
burrito	_	_	I-VAR
contains	_	_	O
25	_	_	B-PARAM
grams	_	_	O
of	_	_	O
lettuce	_	_	O
and	_	_	O
the	_	_	O
beef	_	_	B-VAR
burrito	_	_	I-VAR
contains	_	_	O
18	_	_	B-PARAM
grams	_	_	O
of	_	_	O
lettuce	_	_	O
.	_	_	O
The	_	_	O
beef	_	_	B-VAR
burrito	_	_	I-VAR
is	_	_	O
much	_	_	O
more	_	_	O
popular	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
four	_	_	B-PARAM
times	_	_	I-PARAM
the	_	_	O
amount	_	_	O
of	_	_	O
beef	_	_	B-VAR
burritos	_	_	I-VAR
need	_	_	O
to	_	_	O
be	_	_	O
made	_	_	O
than	_	_	O
the	_	_	O
bean	_	_	B-VAR
burritos	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
5	_	_	B-LIMIT
bean	_	_	B-VAR
burritos	_	_	I-VAR
need	_	_	O
to	_	_	O
be	_	_	O
made	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
burrito	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Thomas	_	_	O
wants	_	_	O
to	_	_	O
invest	_	_	O
in	_	_	O
the	_	_	O
renewable	_	_	B-VAR
energy	_	_	I-VAR
and	_	_	O
education	_	_	B-VAR
industries	_	_	O
.	_	_	O
He	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
50000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
.	_	_	O
He	_	_	O
has	_	_	O
decided	_	_	O
that	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
renewable	_	_	B-VAR
energy	_	_	I-VAR
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
four	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
much	_	_	O
as	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
education	_	_	B-VAR
.	_	_	O
But	_	_	O
the	_	_	O
money	_	_	O
invested	_	_	O
in	_	_	O
renewable	_	_	B-VAR
energy	_	_	I-VAR
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
40000	_	_	B-LIMIT
.	_	_	O
If	_	_	O
investments	_	_	O
in	_	_	O
renewable	_	_	B-VAR
energy	_	_	I-VAR
earn	_	_	B-OBJ_NAME
5.9	_	_	B-PARAM
%	_	_	I-PARAM
and	_	_	O
investments	_	_	O
in	_	_	O
education	_	_	B-VAR
earn	_	_	B-OBJ_NAME
7.1	_	_	B-PARAM
%	_	_	I-PARAM
,	_	_	O
how	_	_	O
much	_	_	O
should	_	_	O
Thomas	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
high	_	_	O
-	_	_	O
speed	_	_	O
train	_	_	O
can	_	_	O
carry	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
400	_	_	B-LIMIT
passengers	_	_	O
.	_	_	O
They	_	_	O
offer	_	_	O
general	_	_	B-VAR
class	_	_	I-VAR
tickets	_	_	O
as	_	_	O
well	_	_	O
as	_	_	O
sleeper	_	_	B-VAR
class	_	_	I-VAR
tickets	_	_	O
.	_	_	O
The	_	_	O
train	_	_	O
reserves	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
sleeper	_	_	B-VAR
class	_	_	I-VAR
tickets	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1.5	_	_	B-LIMIT
times	_	_	I-LIMIT
as	_	_	O
many	_	_	O
passengers	_	_	O
prefer	_	_	O
to	_	_	O
buy	_	_	O
general	_	_	B-VAR
class	_	_	I-VAR
tickets	_	_	O
than	_	_	O
sleeper	_	_	B-VAR
class	_	_	I-VAR
tickets	_	_	O
.	_	_	O
A	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
200	_	_	B-PARAM
is	_	_	O
made	_	_	O
per	_	_	O
sleeper	_	_	B-VAR
class	_	_	I-VAR
ticket	_	_	O
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
80	_	_	B-PARAM
is	_	_	O
made	_	_	O
per	_	_	O
general	_	_	B-VAR
class	_	_	I-VAR
ticket	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
ticket	_	_	O
should	_	_	O
be	_	_	O
sold	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O
What	_	_	O
is	_	_	O
that	_	_	O
profit	_	_	O
?	_	_	O

Theta	_	_	O
Fishing	_	_	O
wants	_	_	O
to	_	_	O
transport	_	_	O
their	_	_	O
catch	_	_	O
.	_	_	O
They	_	_	O
can	_	_	O
either	_	_	O
use	_	_	O
freight	_	_	B-VAR
trains	_	_	I-VAR
or	_	_	O
cargo	_	_	B-VAR
ships	_	_	I-VAR
.	_	_	O
Freight	_	_	B-VAR
trains	_	_	I-VAR
can	_	_	O
take	_	_	O
2000	_	_	B-PARAM
fish	_	_	B-OBJ_NAME
per	_	_	O
trip	_	_	O
while	_	_	O
cargo	_	_	B-VAR
ships	_	_	I-VAR
can	_	_	O
take	_	_	O
7000	_	_	B-PARAM
fish	_	_	B-OBJ_NAME
per	_	_	O
trip	_	_	O
.	_	_	O
The	_	_	O
cost	_	_	O
per	_	_	O
trip	_	_	O
for	_	_	O
freight	_	_	B-VAR
trains	_	_	I-VAR
is	_	_	O
$	_	_	O
100	_	_	B-PARAM
while	_	_	O
the	_	_	O
cost	_	_	O
per	_	_	O
trip	_	_	O
for	_	_	O
cargo	_	_	B-VAR
ships	_	_	I-VAR
is	_	_	O
$	_	_	O
180	_	_	B-PARAM
.	_	_	O
The	_	_	O
budget	_	_	O
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
1500	_	_	B-LIMIT
and	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
freight	_	_	B-VAR
train	_	_	I-VAR
trips	_	_	O
must	_	_	O
be	_	_	O
less	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
cargo	_	_	B-VAR
ship	_	_	I-VAR
trips	_	_	O
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
fish	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
transported	_	_	O
.	_	_	O

Elias	_	_	O
Investments	_	_	O
is	_	_	O
attempting	_	_	O
to	_	_	O
determine	_	_	O
where	_	_	O
its	_	_	O
assets	_	_	O
should	_	_	O
be	_	_	O
invested	_	_	O
during	_	_	O
the	_	_	O
current	_	_	O
year	_	_	O
.	_	_	O
At	_	_	O
present	_	_	O
,	_	_	O
$	_	_	O
2,500,000	_	_	B-LIMIT
is	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
investment	_	_	O
in	_	_	O
gold	_	_	B-VAR
,	_	_	O
silver	_	_	B-VAR
,	_	_	O
platinum	_	_	B-VAR
,	_	_	O
and	_	_	O
diamond	_	_	B-VAR
.	_	_	O
The	_	_	O
annual	_	_	O
rate	_	_	O
of	_	_	O
return	_	_	B-OBJ_NAME
on	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
investment	_	_	O
is	_	_	O
known	_	_	O
to	_	_	O
be	_	_	O
:	_	_	O
gold	_	_	B-VAR
,	_	_	O
5	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
silver	_	_	B-VAR
,	_	_	O
3.2	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
platinum	_	_	B-VAR
,	_	_	O
7	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
diamond	_	_	B-VAR
,	_	_	O
10	_	_	B-PARAM
%	_	_	I-PARAM
.	_	_	O
To	_	_	O
ensure	_	_	O
that	_	_	O
the	_	_	O
company	_	_	O
's	_	_	O
portfolio	_	_	O
is	_	_	O
not	_	_	O
too	_	_	O
risky	_	_	O
,	_	_	O
the	_	_	O
investment	_	_	O
manager	_	_	O
has	_	_	O
placed	_	_	O
the	_	_	O
following	_	_	O
three	_	_	O
restrictions	_	_	O
:	_	_	O
a	_	_	O
The	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
diamond	_	_	B-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
gold	_	_	B-VAR
.	_	_	O
b	_	_	O
At	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
35	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
total	_	_	O
amount	_	_	O
invested	_	_	O
may	_	_	O
be	_	_	O
in	_	_	O
diamond	_	_	B-VAR
.	_	_	O
c	_	_	O
The	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
silver	_	_	B-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
platinum	_	_	B-VAR
.	_	_	O
The	_	_	O
company	_	_	O
’s	_	_	O
objective	_	_	O
is	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
annual	_	_	O
return	_	_	B-OBJ_NAME
on	_	_	O
its	_	_	O
investment	_	_	O
portfolio	_	_	O
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
that	_	_	O
will	_	_	O
enable	_	_	O
the	_	_	O
company	_	_	O
to	_	_	O
meet	_	_	O
this	_	_	O
goal	_	_	O
.	_	_	O

Eli	_	_	O
has	_	_	O
100	_	_	B-LIMIT
acres	_	_	O
available	_	_	B-CONST_DIR
to	_	_	O
grow	_	_	O
beans	_	_	B-VAR
and	_	_	O
pumpkins	_	_	B-VAR
.	_	_	O
He	_	_	O
must	_	_	O
grow	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
5	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
beans	_	_	B-VAR
and	_	_	O
10	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
pumpkins	_	_	B-VAR
.	_	_	O
Pumpkins	_	_	B-VAR
sell	_	_	O
better	_	_	O
so	_	_	O
he	_	_	O
prefers	_	_	O
to	_	_	O
plant	_	_	O
more	_	_	B-CONST_DIR
pumpkins	_	_	B-VAR
than	_	_	O
beans	_	_	B-VAR
.	_	_	O
However	_	_	O
,	_	_	O
due	_	_	O
to	_	_	O
labor	_	_	O
constraints	_	_	O
,	_	_	O
he	_	_	O
can	_	_	O
only	_	_	O
plant	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	I-PARAM
the	_	_	O
quantity	_	_	O
of	_	_	O
pumpkins	_	_	B-VAR
as	_	_	O
beans	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
beans	_	_	B-VAR
is	_	_	O
$	_	_	O
100	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
pumpkins	_	_	B-VAR
is	_	_	O
$	_	_	O
110	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
Eli	_	_	O
plant	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
luxury	_	_	O
hotel	_	_	O
has	_	_	B-CONST_DIR
500	_	_	B-LIMIT
rooms	_	_	O
.	_	_	O
A	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
100	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
regular	_	_	B-VAR
room	_	_	I-VAR
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
500	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
premium	_	_	B-VAR
room	_	_	I-VAR
.	_	_	O
The	_	_	O
hotel	_	_	O
reserves	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
rooms	_	_	O
for	_	_	O
regular	_	_	B-VAR
rooms	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
twice	_	_	B-PARAM
as	_	_	O
many	_	_	O
customers	_	_	O
prefer	_	_	O
to	_	_	O
stay	_	_	O
in	_	_	O
a	_	_	O
premium	_	_	B-VAR
room	_	_	I-VAR
than	_	_	O
stay	_	_	O
in	_	_	O
a	_	_	O
regular	_	_	B-VAR
room	_	_	I-VAR
.	_	_	O
Determine	_	_	O
how	_	_	O
many	_	_	O
rooms	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
be	_	_	O
sold	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
profit	_	_	B-OBJ_NAME
for	_	_	O
the	_	_	O
hotel	_	_	O
.	_	_	O

A	_	_	O
furniture	_	_	O
company	_	_	O
makes	_	_	O
regular	_	_	B-VAR
refrigerators	_	_	I-VAR
and	_	_	O
energy	_	_	B-VAR
-	_	_	I-VAR
efficient	_	_	I-VAR
refrigerators	_	_	I-VAR
.	_	_	O
There	_	_	O
is	_	_	O
an	_	_	O
expected	_	_	O
demand	_	_	O
of	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
25	_	_	B-LIMIT
regular	_	_	B-VAR
refrigerators	_	_	I-VAR
and	_	_	O
40	_	_	B-LIMIT
energy	_	_	B-VAR
-	_	_	I-VAR
efficient	_	_	I-VAR
refrigerators	_	_	I-VAR
each	_	_	O
day	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
due	_	_	O
to	_	_	O
the	_	_	O
size	_	_	O
of	_	_	O
their	_	_	O
factory	_	_	O
,	_	_	O
they	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
regular	_	_	B-VAR
refrigerators	_	_	I-VAR
and	_	_	O
70	_	_	B-LIMIT
energy	_	_	B-VAR
-	_	_	I-VAR
efficient	_	_	I-VAR
refrigerators	_	_	I-VAR
per	_	_	O
day	_	_	O
.	_	_	O
To	_	_	O
satisfy	_	_	O
a	_	_	O
contract	_	_	O
,	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
90	_	_	B-LIMIT
refrigerators	_	_	O
must	_	_	O
be	_	_	O
made	_	_	O
each	_	_	O
day	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
regular	_	_	B-VAR
refrigerator	_	_	I-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
energy	_	_	B-VAR
-	_	_	I-VAR
efficient	_	_	I-VAR
refrigerator	_	_	I-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
80	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
refrigerators	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
fast	_	_	O
-	_	_	O
food	_	_	O
restaurant	_	_	O
sells	_	_	O
burgers	_	_	B-VAR
and	_	_	O
sandwiches	_	_	B-VAR
.	_	_	O
To	_	_	O
stay	_	_	O
in	_	_	O
business	_	_	O
,	_	_	O
they	_	_	O
must	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
burgers	_	_	B-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
80	_	_	B-LIMIT
sandwiches	_	_	B-VAR
.	_	_	O
However	_	_	O
,	_	_	O
they	_	_	O
only	_	_	O
have	_	_	O
enough	_	_	O
supplies	_	_	O
to	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
120	_	_	B-LIMIT
burgers	_	_	B-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
sandwiches	_	_	B-VAR
.	_	_	O
Given	_	_	O
their	_	_	O
tight	_	_	O
schedule	_	_	O
,	_	_	O
they	_	_	O
can	_	_	O
only	_	_	O
cook	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
200	_	_	B-LIMIT
items	_	_	O
total	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
burger	_	_	B-VAR
is	_	_	O
$	_	_	O
4.5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
sandwich	_	_	B-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
item	_	_	O
should	_	_	O
they	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Tom	_	_	O
is	_	_	O
playing	_	_	O
a	_	_	O
first	_	_	O
-	_	_	O
person	_	_	O
shooter	_	_	O
game	_	_	O
where	_	_	O
a	_	_	O
slow	_	_	B-VAR
shot	_	_	I-VAR
is	_	_	O
worth	_	_	O
3	_	_	B-PARAM
points	_	_	B-OBJ_NAME
and	_	_	O
a	_	_	O
quick	_	_	B-VAR
shot	_	_	I-VAR
is	_	_	O
worth	_	_	O
6	_	_	B-PARAM
points	_	_	B-OBJ_NAME
.	_	_	O
In	_	_	O
total	_	_	O
,	_	_	O
Tom	_	_	O
can	_	_	O
take	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
20	_	_	B-LIMIT
shots	_	_	O
.	_	_	O
He	_	_	O
must	_	_	O
take	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
8	_	_	B-LIMIT
slow	_	_	B-VAR
shots	_	_	I-VAR
and	_	_	O
5	_	_	B-LIMIT
quick	_	_	B-VAR
shots	_	_	I-VAR
,	_	_	O
but	_	_	O
due	_	_	O
to	_	_	O
time	_	_	O
restrictions	_	_	O
,	_	_	O
he	_	_	O
can	_	_	O
take	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
12	_	_	B-LIMIT
slow	_	_	B-VAR
shots	_	_	I-VAR
or	_	_	O
12	_	_	B-LIMIT
quick	_	_	B-VAR
shots	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
shot	_	_	O
must	_	_	O
Tom	_	_	O
take	_	_	O
,	_	_	O
assuming	_	_	O
all	_	_	O
his	_	_	O
shots	_	_	O
get	_	_	O
points	_	_	B-OBJ_NAME
,	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
score	_	_	B-OBJ_NAME
?	_	_	O

Beta	_	_	O
Audio	_	_	O
makes	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
speakers	_	_	O
:	_	_	O
regular	_	_	B-VAR
speakers	_	_	I-VAR
and	_	_	O
portable	_	_	B-VAR
speakers	_	_	I-VAR
.	_	_	O
Two	_	_	O
different	_	_	O
teams	_	_	O
make	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
speaker	_	_	O
.	_	_	O
Team	_	_	O
A	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
120	_	_	B-LIMIT
regular	_	_	B-VAR
speakers	_	_	I-VAR
per	_	_	O
day	_	_	O
and	_	_	O
Team	_	_	O
B	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
200	_	_	B-LIMIT
portable	_	_	B-VAR
speakers	_	_	I-VAR
per	_	_	O
day	_	_	O
.	_	_	O
Both	_	_	O
teams	_	_	O
require	_	_	O
the	_	_	O
use	_	_	O
of	_	_	O
a	_	_	O
shared	_	_	O
testing	_	_	O
machine	_	_	O
,	_	_	O
and	_	_	O
this	_	_	O
machine	_	_	O
can	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
300	_	_	B-LIMIT
total	_	_	O
speakers	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
regular	_	_	B-VAR
speaker	_	_	I-VAR
is	_	_	O
$	_	_	O
40	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
portable	_	_	B-VAR
speaker	_	_	I-VAR
is	_	_	O
$	_	_	O
60	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
speaker	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
bubble	_	_	O
tea	_	_	O
store	_	_	O
sells	_	_	O
two	_	_	O
products	_	_	O
:	_	_	O
almond	_	_	B-VAR
bubble	_	_	I-VAR
tea	_	_	I-VAR
and	_	_	O
ginger	_	_	B-VAR
bubble	_	_	I-VAR
tea	_	_	I-VAR
.	_	_	O
The	_	_	O
store	_	_	O
makes	_	_	O
x1	_	_	O
bottles	_	_	O
of	_	_	O
almond	_	_	B-VAR
bubble	_	_	I-VAR
tea	_	_	I-VAR
a	_	_	O
day	_	_	O
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
5	_	_	B-PARAM
each	_	_	O
and	_	_	O
x2	_	_	O
bottles	_	_	O
of	_	_	O
ginger	_	_	B-VAR
bubble	_	_	I-VAR
tea	_	_	I-VAR
a	_	_	O
day	_	_	O
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
9	_	_	B-PARAM
each	_	_	O
.	_	_	O
(	_	_	O
x1	_	_	O
and	_	_	O
x2	_	_	O
are	_	_	O
unknowns	_	_	O
and	_	_	O
they	_	_	O
both	_	_	O
must	_	_	O
be	_	_	O
greater	_	_	O
than	_	_	O
or	_	_	O
equal	_	_	O
to	_	_	O
0	_	_	O
)	_	_	O
.	_	_	O
Currently	_	_	O
,	_	_	O
the	_	_	O
demand	_	_	O
is	_	_	O
limited	_	_	O
to	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
120	_	_	B-LIMIT
bottles	_	_	O
of	_	_	O
almond	_	_	B-VAR
bubble	_	_	I-VAR
tea	_	_	I-VAR
per	_	_	O
day	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
200	_	_	B-LIMIT
bottles	_	_	O
of	_	_	O
ginger	_	_	B-VAR
bubble	_	_	I-VAR
tea	_	_	I-VAR
per	_	_	O
day	_	_	O
.	_	_	O
Also	_	_	O
,	_	_	O
the	_	_	O
store	_	_	O
can	_	_	O
make	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
300	_	_	B-LIMIT
bottles	_	_	O
of	_	_	O
bubble	_	_	O
tea	_	_	O
(	_	_	O
ignoring	_	_	O
the	_	_	O
type	_	_	O
)	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
bubble	_	_	O
tea	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
city	_	_	O
has	_	_	O
$	_	_	O
200000	_	_	B-LIMIT
available	_	_	B-CONST_DIR
to	_	_	O
invest	_	_	O
in	_	_	O
a	_	_	O
9	_	_	O
-	_	_	O
month	_	_	O
commitment	_	_	O
.	_	_	O
They	_	_	O
have	_	_	O
decided	_	_	O
to	_	_	O
invest	_	_	O
in	_	_	O
both	_	_	O
the	_	_	O
film	_	_	B-VAR
and	_	_	O
healthcare	_	_	B-VAR
industries	_	_	I-VAR
.	_	_	O
After	_	_	O
consulting	_	_	O
an	_	_	O
advisor	_	_	O
,	_	_	O
the	_	_	O
city	_	_	O
has	_	_	O
decided	_	_	O
to	_	_	O
invest	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
25	_	_	B-LIMIT
%	_	_	I-LIMIT
in	_	_	O
the	_	_	O
film	_	_	B-VAR
industry	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
60	_	_	B-LIMIT
%	_	_	I-LIMIT
in	_	_	O
the	_	_	O
healthcare	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
The	_	_	O
money	_	_	O
placed	_	_	O
in	_	_	O
the	_	_	O
film	_	_	B-VAR
industry	_	_	I-VAR
yields	_	_	O
an	_	_	O
8	_	_	B-PARAM
%	_	_	I-PARAM
return	_	_	B-OBJ_NAME
and	_	_	O
the	_	_	O
money	_	_	O
placed	_	_	O
in	_	_	O
the	_	_	O
healthcare	_	_	B-VAR
industry	_	_	I-VAR
yields	_	_	O
a	_	_	O
10	_	_	B-PARAM
%	_	_	I-PARAM
return	_	_	B-OBJ_NAME
.	_	_	O
How	_	_	O
much	_	_	O
should	_	_	O
the	_	_	O
city	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
industry	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
its	_	_	O
return	_	_	B-OBJ_NAME
on	_	_	O
investment	_	_	O
over	_	_	O
this	_	_	O
period	_	_	O
of	_	_	O
time	_	_	O
?	_	_	O

Luca	_	_	O
would	_	_	O
like	_	_	O
to	_	_	O
invest	_	_	O
up	_	_	B-CONST_DIR
to	_	_	I-CONST_DIR
$	_	_	O
20000	_	_	B-LIMIT
in	_	_	O
the	_	_	O
fishing	_	_	B-VAR
and	_	_	O
education	_	_	B-VAR
industries	_	_	I-VAR
.	_	_	O
Each	_	_	O
dollar	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
fishing	_	_	B-VAR
industry	_	_	I-VAR
yields	_	_	O
a	_	_	O
$	_	_	O
1.30	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
and	_	_	O
each	_	_	O
dollar	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
education	_	_	B-VAR
industry	_	_	I-VAR
yields	_	_	O
a	_	_	O
$	_	_	O
2.10	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
.	_	_	O
A	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
5000	_	_	B-LIMIT
must	_	_	O
be	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
education	_	_	B-VAR
industry	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
all	_	_	O
money	_	_	O
invested	_	_	O
must	_	_	O
be	_	_	O
in	_	_	O
the	_	_	O
fishing	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
that	_	_	O
can	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
Luca	_	_	O
's	_	_	O
profit	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
restaurant	_	_	O
has	_	_	B-CONST_DIR
5000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
pork	_	_	O
meat	_	_	O
to	_	_	O
make	_	_	O
both	_	_	O
burritos	_	_	B-VAR
and	_	_	O
sandwiches	_	_	B-VAR
.	_	_	O
Each	_	_	O
burrito	_	_	B-VAR
requires	_	_	O
25	_	_	B-PARAM
grams	_	_	O
of	_	_	O
pork	_	_	O
meat	_	_	O
while	_	_	O
each	_	_	O
sandwich	_	_	B-VAR
requires	_	_	O
15	_	_	B-PARAM
grams	_	_	O
of	_	_	O
pork	_	_	O
meat	_	_	O
.	_	_	O
Past	_	_	O
sales	_	_	O
have	_	_	O
indicated	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
four	_	_	B-PARAM
times	_	_	I-PARAM
the	_	_	O
number	_	_	O
of	_	_	O
sandwiches	_	_	B-VAR
are	_	_	O
needed	_	_	O
than	_	_	O
burritos	_	_	B-VAR
.	_	_	O
There	_	_	O
also	_	_	O
needs	_	_	O
to	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
6	_	_	B-LIMIT
burritos	_	_	B-VAR
made	_	_	O
.	_	_	O
Each	_	_	O
burrito	_	_	B-VAR
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
2.5	_	_	B-PARAM
and	_	_	O
each	_	_	O
sandwich	_	_	B-VAR
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
7	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
item	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Theta	_	_	O
Electronics	_	_	O
must	_	_	O
determine	_	_	O
how	_	_	O
many	_	_	O
keyboards	_	_	B-VAR
and	_	_	O
PC	_	_	B-VAR
controllers	_	_	I-VAR
to	_	_	O
keep	_	_	O
in	_	_	O
stock	_	_	O
.	_	_	O
A	_	_	O
keyboard	_	_	B-VAR
requires	_	_	O
12	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
of	_	_	O
floor	_	_	O
space	_	_	O
,	_	_	O
whereas	_	_	O
a	_	_	O
PC	_	_	B-VAR
controller	_	_	I-VAR
requires	_	_	O
4	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	B-CONST_DIR
200	_	_	B-LIMIT
sq	_	_	O
ft	_	_	O
of	_	_	O
floor	_	_	O
space	_	_	O
available	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
keyboard	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
20	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
PC	_	_	B-VAR
controller	_	_	I-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
10	_	_	B-PARAM
.	_	_	O
The	_	_	O
store	_	_	O
stocks	_	_	O
only	_	_	O
keyboards	_	_	B-VAR
and	_	_	O
PC	_	_	B-VAR
controllers	_	_	I-VAR
.	_	_	O
Past	_	_	O
sales	_	_	O
dictate	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
35	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
all	_	_	O
items	_	_	O
in	_	_	O
stock	_	_	O
be	_	_	O
PC	_	_	B-VAR
controllers	_	_	I-VAR
.	_	_	O
Finally	_	_	O
,	_	_	O
a	_	_	O
keyboard	_	_	B-VAR
ties	_	_	O
up	_	_	O
$	_	_	O
200	_	_	B-PARAM
in	_	_	O
capital	_	_	O
,	_	_	O
and	_	_	O
a	_	_	O
PC	_	_	B-VAR
controller	_	_	I-VAR
,	_	_	O
$	_	_	O
150	_	_	B-PARAM
.	_	_	O
The	_	_	O
store	_	_	O
wants	_	_	O
to	_	_	O
have	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
5,000	_	_	B-LIMIT
worth	_	_	O
of	_	_	O
capital	_	_	O
tied	_	_	O
up	_	_	O
at	_	_	O
any	_	_	O
time	_	_	O
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
that	_	_	O
can	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
.	_	_	O

Cooper	_	_	O
is	_	_	O
a	_	_	O
store	_	_	O
owner	_	_	O
and	_	_	O
he	_	_	O
can	_	_	O
spend	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
1000	_	_	B-LIMIT
on	_	_	O
potatoes	_	_	B-VAR
and	_	_	O
pumpkins	_	_	B-VAR
.	_	_	O
A	_	_	O
potato	_	_	B-VAR
costs	_	_	O
Cooper	_	_	O
$	_	_	O
0.50	_	_	B-PARAM
and	_	_	O
a	_	_	O
pumpkin	_	_	B-VAR
costs	_	_	O
Cooper	_	_	O
$	_	_	O
0.90	_	_	B-PARAM
.	_	_	O
Each	_	_	O
potato	_	_	B-VAR
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
1.5	_	_	B-PARAM
and	_	_	O
each	_	_	O
pumpkin	_	_	B-VAR
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
2.8	_	_	B-PARAM
.	_	_	O
Cooper	_	_	O
estimates	_	_	O
that	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
pumpkins	_	_	B-VAR
sold	_	_	O
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
a	_	_	O
third	_	_	B-PARAM
of	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
potatoes	_	_	B-VAR
sold	_	_	O
.	_	_	O
He	_	_	O
also	_	_	O
estimates	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
250	_	_	B-LIMIT
potatoes	_	_	B-VAR
but	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
800	_	_	B-LIMIT
potatoes	_	_	B-VAR
are	_	_	O
sold	_	_	O
each	_	_	O
month	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
,	_	_	O
potatoes	_	_	B-VAR
and	_	_	O
pumpkins	_	_	B-VAR
,	_	_	O
should	_	_	O
be	_	_	O
sold	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

Iota	_	_	O
Food	_	_	O
wants	_	_	O
to	_	_	O
advertise	_	_	O
the	_	_	O
release	_	_	O
of	_	_	O
their	_	_	O
new	_	_	O
product	_	_	O
using	_	_	O
ads	_	_	O
in	_	_	O
three	_	_	O
areas	_	_	O
:	_	_	O
grocery	_	_	B-VAR
stores	_	_	I-VAR
,	_	_	O
train	_	_	B-VAR
stations	_	_	I-VAR
,	_	_	O
and	_	_	O
water	_	_	B-VAR
parks	_	_	I-VAR
.	_	_	O
They	_	_	O
have	_	_	O
a	_	_	O
weekly	_	_	O
advertising	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
50000	_	_	B-LIMIT
.	_	_	O
The	_	_	O
cost	_	_	O
of	_	_	O
an	_	_	O
ad	_	_	O
in	_	_	O
each	_	_	O
area	_	_	O
and	_	_	O
their	_	_	O
audience	_	_	O
reach	_	_	O
is	_	_	O
given	_	_	O
.	_	_	O
An	_	_	O
ad	_	_	O
in	_	_	O
a	_	_	O
grocery	_	_	B-VAR
store	_	_	I-VAR
costs	_	_	O
$	_	_	O
300	_	_	B-PARAM
and	_	_	O
reaches	_	_	O
10000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
An	_	_	O
ad	_	_	O
at	_	_	O
a	_	_	O
train	_	_	B-VAR
station	_	_	I-VAR
costs	_	_	O
$	_	_	O
500	_	_	B-PARAM
and	_	_	O
reaches	_	_	O
20000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
An	_	_	O
ad	_	_	O
in	_	_	O
a	_	_	O
water	_	_	B-VAR
park	_	_	I-VAR
costs	_	_	O
$	_	_	O
1000	_	_	B-PARAM
and	_	_	O
reaches	_	_	O
50000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
city	_	_	O
limits	_	_	B-CONST_DIR
the	_	_	I-CONST_DIR
number	_	_	I-CONST_DIR
of	_	_	O
ads	_	_	O
at	_	_	O
a	_	_	O
train	_	_	B-VAR
station	_	_	I-VAR
from	_	_	O
a	_	_	O
single	_	_	O
company	_	_	O
to	_	_	O
15	_	_	B-LIMIT
.	_	_	O
In	_	_	O
order	_	_	O
to	_	_	O
maintain	_	_	O
balance	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
a	_	_	O
third	_	_	B-LIMIT
of	_	_	O
the	_	_	O
total	_	_	O
number	_	_	O
of	_	_	O
ads	_	_	O
should	_	_	O
be	_	_	O
in	_	_	O
water	_	_	B-VAR
parks	_	_	I-VAR
and	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
10	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
ads	_	_	O
should	_	_	O
be	_	_	O
in	_	_	O
grocery	_	_	B-VAR
stores	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
ads	_	_	O
should	_	_	O
be	_	_	O
run	_	_	O
in	_	_	O
each	_	_	O
of	_	_	O
the	_	_	O
three	_	_	O
areas	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
viewership	_	_	B-OBJ_NAME
?	_	_	O

Ella	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
15000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
the	_	_	O
healthcare	_	_	B-VAR
and	_	_	O
fashion	_	_	B-VAR
industries	_	_	I-VAR
.	_	_	O
The	_	_	O
money	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
healthcare	_	_	B-VAR
industry	_	_	I-VAR
earns	_	_	B-OBJ_NAME
12	_	_	B-PARAM
%	_	_	I-PARAM
while	_	_	O
the	_	_	O
money	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
fashion	_	_	B-VAR
industry	_	_	I-VAR
earns	_	_	B-OBJ_NAME
9.5	_	_	B-PARAM
%	_	_	I-PARAM
.	_	_	O
She	_	_	O
has	_	_	O
decided	_	_	O
that	_	_	O
the	_	_	O
money	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
healthcare	_	_	B-VAR
industry	_	_	I-VAR
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
two	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
much	_	_	O
as	_	_	O
the	_	_	O
money	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
fashion	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
the	_	_	O
money	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
healthcare	_	_	B-VAR
industry	_	_	I-VAR
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
12000	_	_	B-LIMIT
.	_	_	O
How	_	_	O
much	_	_	O
should	_	_	O
she	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
industry	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
passenger	_	_	O
train	_	_	O
carries	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
500	_	_	B-LIMIT
passengers	_	_	O
.	_	_	O
A	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
75	_	_	B-PARAM
is	_	_	O
made	_	_	O
for	_	_	O
each	_	_	O
first	_	_	B-VAR
class	_	_	I-VAR
seat	_	_	O
with	_	_	O
a	_	_	O
pillow	_	_	O
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
50	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
second	_	_	B-VAR
class	_	_	I-VAR
seat	_	_	O
.	_	_	O
The	_	_	O
train	_	_	O
reserves	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
seats	_	_	O
for	_	_	O
the	_	_	O
first	_	_	B-VAR
class	_	_	I-VAR
seats	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-PARAM
as	_	_	O
many	_	_	O
passengers	_	_	O
prefer	_	_	O
to	_	_	O
save	_	_	O
money	_	_	O
and	_	_	O
travel	_	_	O
by	_	_	O
second	_	_	B-VAR
class	_	_	I-VAR
than	_	_	O
by	_	_	O
first	_	_	B-VAR
class	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
seats	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
be	_	_	O
sold	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Robert	_	_	O
is	_	_	O
a	_	_	O
pumpkin	_	_	B-OBJ_NAME
seller	_	_	O
and	_	_	O
he	_	_	O
has	_	_	O
to	_	_	O
transport	_	_	O
pumpkins	_	_	B-OBJ_NAME
using	_	_	O
either	_	_	O
trucks	_	_	B-VAR
or	_	_	O
vans	_	_	B-VAR
.	_	_	O
The	_	_	O
truck	_	_	B-VAR
can	_	_	O
take	_	_	O
40	_	_	B-PARAM
pumpkins	_	_	B-OBJ_NAME
each	_	_	O
and	_	_	O
cost	_	_	O
$	_	_	O
15	_	_	B-PARAM
per	_	_	O
trip	_	_	O
.	_	_	O
The	_	_	O
van	_	_	B-VAR
can	_	_	O
take	_	_	O
25	_	_	B-PARAM
pumpkins	_	_	B-OBJ_NAME
each	_	_	O
and	_	_	O
cost	_	_	O
$	_	_	O
10	_	_	B-PARAM
per	_	_	O
trip	_	_	O
.	_	_	O
Robert	_	_	O
has	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
300	_	_	B-LIMIT
to	_	_	O
spend	_	_	O
on	_	_	O
transporting	_	_	O
the	_	_	O
pumpkins	_	_	B-OBJ_NAME
.	_	_	O
Due	_	_	O
to	_	_	O
pollution	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
trucks	_	_	B-VAR
must	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
vans	_	_	B-VAR
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
pumpkins	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
transported	_	_	O
.	_	_	O

A	_	_	O
furniture	_	_	O
company	_	_	O
employs	_	_	O
designers	_	_	B-VAR
earning	_	_	B-OBJ_NAME
$	_	_	O
1,500	_	_	B-PARAM
per	_	_	O
week	_	_	O
and	_	_	O
assemblers	_	_	B-VAR
earning	_	_	B-OBJ_NAME
$	_	_	O
1,000	_	_	B-PARAM
per	_	_	O
week	_	_	O
.	_	_	O
It	_	_	O
is	_	_	O
required	_	_	O
to	_	_	O
keep	_	_	O
the	_	_	O
weekly	_	_	B-OBJ_NAME
wage	_	_	I-OBJ_NAME
bill	_	_	I-OBJ_NAME
below	_	_	B-CONST_DIR
$	_	_	O
50,000	_	_	B-LIMIT
.	_	_	O
The	_	_	O
company	_	_	O
requires	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
20	_	_	B-LIMIT
staff	_	_	O
,	_	_	O
of	_	_	O
whom	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
must	_	_	O
be	_	_	O
assemblers	_	_	B-VAR
.	_	_	O
Union	_	_	O
regulations	_	_	O
require	_	_	O
that	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
designers	_	_	B-VAR
should	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
one	_	_	B-PARAM
third	_	_	I-PARAM
the	_	_	O
number	_	_	O
of	_	_	O
assemblers	_	_	B-VAR
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	B-OBJ_NAME
wage	_	_	I-OBJ_NAME
bill	_	_	I-OBJ_NAME
.	_	_	O

Charles	_	_	O
has	_	_	O
$	_	_	O
100000	_	_	B-LIMIT
available	_	_	B-CONST_DIR
and	_	_	O
has	_	_	O
decided	_	_	O
to	_	_	O
invest	_	_	O
in	_	_	O
the	_	_	O
fishing	_	_	B-VAR
,	_	_	O
education	_	_	B-VAR
,	_	_	O
clothing	_	_	B-VAR
,	_	_	O
and	_	_	O
pharmaceutical	_	_	B-VAR
industries	_	_	I-VAR
.	_	_	O
The	_	_	O
annual	_	_	O
rate	_	_	O
of	_	_	O
return	_	_	B-OBJ_NAME
on	_	_	O
investment	_	_	O
in	_	_	O
each	_	_	O
of	_	_	O
the	_	_	O
industries	_	_	O
is	_	_	O
as	_	_	O
follows	_	_	O
:	_	_	O
fishing	_	_	B-VAR
,	_	_	O
5.5	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
education	_	_	B-VAR
,	_	_	O
3	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
clothing	_	_	B-VAR
,	_	_	O
7.6	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
pharmaceutical	_	_	B-VAR
,	_	_	O
11.3	_	_	B-PARAM
%	_	_	I-PARAM
.	_	_	O
A	_	_	O
financial	_	_	O
advisor	_	_	O
has	_	_	O
given	_	_	O
him	_	_	O
the	_	_	O
following	_	_	O
advice	_	_	O
.	_	_	O
The	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
pharmaceutical	_	_	B-VAR
industry	_	_	I-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
fishing	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
Also	_	_	O
,	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
education	_	_	B-VAR
industry	_	_	I-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
clothing	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
Finally	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
20	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
total	_	_	O
amount	_	_	O
of	_	_	O
money	_	_	O
can	_	_	O
be	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
pharmaceutical	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
return	_	_	B-OBJ_NAME
on	_	_	O
investment	_	_	O
.	_	_	O

Gabriel	_	_	O
is	_	_	O
growing	_	_	O
pumpkins	_	_	B-VAR
and	_	_	O
carrots	_	_	B-VAR
on	_	_	O
his	_	_	O
farm	_	_	O
.	_	_	O
He	_	_	O
has	_	_	O
100	_	_	B-LIMIT
acres	_	_	O
available	_	_	B-CONST_DIR
on	_	_	O
which	_	_	O
he	_	_	O
must	_	_	O
grow	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
7	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
pumpkins	_	_	B-VAR
and	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
12	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
carrots	_	_	B-VAR
to	_	_	O
meet	_	_	O
demands	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
pumpkin	_	_	B-VAR
is	_	_	O
$	_	_	O
2.5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
carrot	_	_	B-VAR
is	_	_	O
$	_	_	O
3.4	_	_	B-PARAM
.	_	_	O
He	_	_	O
prefers	_	_	O
to	_	_	O
grow	_	_	O
more	_	_	B-CONST_DIR
carrots	_	_	B-VAR
than	_	_	O
pumpkins	_	_	B-VAR
but	_	_	O
limitations	_	_	O
in	_	_	O
his	_	_	O
workforce	_	_	O
allow	_	_	O
him	_	_	O
to	_	_	O
grow	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	I-PARAM
the	_	_	O
amount	_	_	O
of	_	_	O
carrots	_	_	B-VAR
as	_	_	O
pumpkins	_	_	B-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
produce	_	_	O
should	_	_	O
Gabriel	_	_	O
grow	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
souvenir	_	_	O
shop	_	_	O
can	_	_	O
display	_	_	O
and	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
umbrellas	_	_	O
.	_	_	O
A	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
3	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
red	_	_	B-VAR
umbrella	_	_	I-VAR
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
5	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
blue	_	_	B-VAR
umbrella	_	_	I-VAR
.	_	_	O
The	_	_	O
souvenir	_	_	O
shop	_	_	O
makes	_	_	O
sure	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
10	_	_	B-LIMIT
umbrellas	_	_	O
displayed	_	_	O
are	_	_	O
red	_	_	B-VAR
.	_	_	O
However	_	_	O
,	_	_	O
due	_	_	O
to	_	_	O
their	_	_	O
popularity	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
4	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
many	_	_	O
customers	_	_	O
prefer	_	_	O
blue	_	_	B-VAR
umbrellas	_	_	I-VAR
to	_	_	O
red	_	_	B-VAR
umbrellas	_	_	I-VAR
.	_	_	O
Assuming	_	_	O
the	_	_	O
souvenir	_	_	O
shop	_	_	O
can	_	_	O
sell	_	_	O
all	_	_	O
their	_	_	O
umbrellas	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
umbrella	_	_	O
type	_	_	O
,	_	_	O
red	_	_	B-VAR
umbrella	_	_	I-VAR
and	_	_	O
blue	_	_	B-VAR
umbrella	_	_	I-VAR
,	_	_	O
should	_	_	O
be	_	_	O
displayed	_	_	O
and	_	_	O
sold	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Zeta	_	_	O
Monitor	_	_	O
makes	_	_	O
LCD	_	_	B-VAR
and	_	_	O
LED	_	_	B-VAR
monitors	_	_	I-VAR
.	_	_	O
Projections	_	_	O
indicate	_	_	O
a	_	_	O
demand	_	_	O
of	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
150	_	_	B-LIMIT
LCD	_	_	B-VAR
monitors	_	_	I-VAR
and	_	_	O
80	_	_	B-LIMIT
LED	_	_	B-VAR
monitors	_	_	I-VAR
each	_	_	O
day	_	_	O
.	_	_	O
Because	_	_	O
of	_	_	O
the	_	_	O
manual	_	_	O
labor	_	_	O
involved	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
300	_	_	B-LIMIT
LCD	_	_	B-VAR
monitors	_	_	I-VAR
and	_	_	O
280	_	_	B-LIMIT
LED	_	_	B-VAR
monitors	_	_	I-VAR
can	_	_	O
be	_	_	O
made	_	_	O
each	_	_	O
day	_	_	O
.	_	_	O
To	_	_	O
satisfy	_	_	O
a	_	_	O
contract	_	_	O
with	_	_	O
an	_	_	O
electronics	_	_	O
shop	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
250	_	_	B-LIMIT
total	_	_	O
monitors	_	_	O
must	_	_	O
be	_	_	O
made	_	_	O
each	_	_	O
day	_	_	O
.	_	_	O
The	_	_	O
factory	_	_	O
makes	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
25	_	_	B-PARAM
per	_	_	O
LCD	_	_	B-VAR
monitor	_	_	I-VAR
and	_	_	O
$	_	_	O
70	_	_	B-PARAM
per	_	_	O
LED	_	_	B-VAR
monitor	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
monitor	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Elias	_	_	O
Cookie	_	_	O
sells	_	_	O
chocolate	_	_	B-VAR
and	_	_	O
strawberry	_	_	B-VAR
cookies	_	_	I-VAR
.	_	_	O
The	_	_	O
store	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
200	_	_	B-LIMIT
cookies	_	_	O
total	_	_	O
.	_	_	O
To	_	_	O
stay	_	_	O
in	_	_	O
business	_	_	O
,	_	_	O
they	_	_	O
must	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
chocolate	_	_	B-VAR
cookies	_	_	I-VAR
and	_	_	O
70	_	_	B-LIMIT
strawberry	_	_	B-VAR
cookies	_	_	I-VAR
.	_	_	O
Due	_	_	O
to	_	_	O
raw	_	_	O
material	_	_	O
shortages	_	_	O
however	_	_	O
,	_	_	O
they	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
120	_	_	B-LIMIT
chocolate	_	_	B-VAR
cookies	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
150	_	_	B-LIMIT
strawberry	_	_	B-VAR
cookies	_	_	I-VAR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
chocolate	_	_	B-VAR
cookie	_	_	I-VAR
is	_	_	O
$	_	_	O
1.5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
strawberry	_	_	B-VAR
cookie	_	_	I-VAR
is	_	_	O
$	_	_	O
1.2	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
cookie	_	_	O
should	_	_	O
they	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Nolan	_	_	O
decides	_	_	O
to	_	_	O
take	_	_	O
part	_	_	O
in	_	_	O
a	_	_	O
physics	_	_	O
contest	_	_	O
with	_	_	O
multiple	_	_	B-VAR
choice	_	_	I-VAR
questions	_	_	I-VAR
worth	_	_	O
2	_	_	B-PARAM
points	_	_	B-OBJ_NAME
each	_	_	O
and	_	_	O
short	_	_	B-VAR
answer	_	_	I-VAR
questions	_	_	I-VAR
worth	_	_	O
5	_	_	B-PARAM
points	_	_	B-OBJ_NAME
each	_	_	O
.	_	_	O
In	_	_	O
this	_	_	O
contest	_	_	O
,	_	_	O
he	_	_	O
can	_	_	O
answer	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
questions	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
he	_	_	O
must	_	_	O
answer	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
15	_	_	B-LIMIT
multiple	_	_	B-VAR
choice	_	_	I-VAR
questions	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
short	_	_	B-VAR
answer	_	_	I-VAR
questions	_	_	I-VAR
.	_	_	O
Nolan	_	_	O
can	_	_	O
answer	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
20	_	_	B-LIMIT
multiple	_	_	B-VAR
choice	_	_	I-VAR
questions	_	_	I-VAR
and	_	_	O
20	_	_	B-LIMIT
short	_	_	B-VAR
answer	_	_	I-VAR
questions	_	_	I-VAR
.	_	_	O
Assuming	_	_	O
all	_	_	O
his	_	_	O
answers	_	_	O
are	_	_	O
correct	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
question	_	_	O
should	_	_	O
Nolan	_	_	O
answer	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
score	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
furniture	_	_	O
company	_	_	O
makes	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
tables	_	_	O
:	_	_	O
regular	_	_	B-VAR
tables	_	_	I-VAR
and	_	_	O
standing	_	_	B-VAR
tables	_	_	I-VAR
.	_	_	O
Different	_	_	O
sections	_	_	O
of	_	_	O
the	_	_	O
factory	_	_	O
with	_	_	O
different	_	_	O
teams	_	_	O
produce	_	_	O
each	_	_	O
table	_	_	O
.	_	_	O
Team	_	_	O
A	_	_	O
can	_	_	O
produce	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
25	_	_	B-LIMIT
regular	_	_	B-VAR
tables	_	_	I-VAR
per	_	_	O
day	_	_	O
while	_	_	O
team	_	_	O
B	_	_	O
can	_	_	O
produce	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
50	_	_	B-LIMIT
standing	_	_	B-VAR
tables	_	_	I-VAR
per	_	_	O
day	_	_	O
.	_	_	O
Both	_	_	O
teams	_	_	O
require	_	_	O
the	_	_	O
use	_	_	O
of	_	_	O
the	_	_	O
same	_	_	O
woodworking	_	_	O
machine	_	_	O
and	_	_	O
this	_	_	O
machine	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
60	_	_	B-LIMIT
total	_	_	O
tables	_	_	O
.	_	_	O
Each	_	_	O
regular	_	_	B-VAR
table	_	_	I-VAR
generates	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
150	_	_	B-PARAM
while	_	_	O
each	_	_	O
standing	_	_	B-VAR
table	_	_	I-VAR
generates	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
180	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
table	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
company	_	_	O
's	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
tea	_	_	O
shop	_	_	O
sells	_	_	O
two	_	_	O
products	_	_	O
:	_	_	O
oolong	_	_	B-VAR
tea	_	_	I-VAR
and	_	_	O
green	_	_	B-VAR
tea	_	_	I-VAR
.	_	_	O
The	_	_	O
shop	_	_	O
makes	_	_	O
x1	_	_	O
bottles	_	_	O
of	_	_	O
oolong	_	_	B-VAR
tea	_	_	I-VAR
per	_	_	O
day	_	_	O
and	_	_	O
x2	_	_	O
bottles	_	_	O
of	_	_	O
green	_	_	B-VAR
tea	_	_	I-VAR
per	_	_	O
day	_	_	O
(	_	_	O
x1	_	_	O
and	_	_	O
x2	_	_	O
are	_	_	O
unknown	_	_	O
values	_	_	O
greater	_	_	O
than	_	_	O
or	_	_	O
equal	_	_	O
to	_	_	O
0	_	_	O
)	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
bottle	_	_	O
of	_	_	O
oolong	_	_	B-VAR
tea	_	_	I-VAR
is	_	_	O
$	_	_	O
30	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
bottle	_	_	O
of	_	_	O
green	_	_	B-VAR
tea	_	_	I-VAR
is	_	_	O
$	_	_	O
20	_	_	B-PARAM
.	_	_	O
Current	_	_	O
demand	_	_	O
for	_	_	O
tea	_	_	O
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
bottles	_	_	O
of	_	_	O
oolong	_	_	B-VAR
tea	_	_	I-VAR
per	_	_	O
day	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
80	_	_	B-LIMIT
bottles	_	_	O
of	_	_	O
green	_	_	B-VAR
tea	_	_	I-VAR
per	_	_	O
day	_	_	O
.	_	_	O
The	_	_	O
shop	_	_	O
only	_	_	B-CONST_DIR
has	_	_	O
enough	_	_	O
supply	_	_	O
to	_	_	O
make	_	_	O
150	_	_	B-LIMIT
bottles	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
each	_	_	O
day	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
bottles	_	_	O
of	_	_	O
each	_	_	O
tea	_	_	O
,	_	_	O
oolong	_	_	B-VAR
tea	_	_	I-VAR
and	_	_	O
green	_	_	B-VAR
tea	_	_	I-VAR
,	_	_	O
should	_	_	O
the	_	_	O
shop	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Zeta	_	_	O
Investments	_	_	O
is	_	_	O
looking	_	_	O
to	_	_	O
diversify	_	_	O
its	_	_	O
investments	_	_	O
and	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
500,000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
a	_	_	O
24	_	_	O
-	_	_	O
month	_	_	O
commitment	_	_	O
.	_	_	O
They	_	_	O
can	_	_	O
invest	_	_	O
in	_	_	O
the	_	_	O
education	_	_	B-VAR
industry	_	_	I-VAR
yielding	_	_	O
a	_	_	O
2.5	_	_	B-PARAM
%	_	_	I-PARAM
return	_	_	B-OBJ_NAME
or	_	_	O
in	_	_	O
the	_	_	O
wood	_	_	B-VAR
industry	_	_	I-VAR
yielding	_	_	O
a	_	_	O
7	_	_	B-PARAM
%	_	_	I-PARAM
return	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
board	_	_	O
of	_	_	O
directors	_	_	O
requires	_	_	O
that	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
25	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
investment	_	_	O
be	_	_	O
placed	_	_	O
in	_	_	O
the	_	_	O
education	_	_	B-VAR
industry	_	_	I-VAR
and	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
70	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
investment	_	_	O
be	_	_	O
placed	_	_	O
in	_	_	O
the	_	_	O
wood	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
How	_	_	O
much	_	_	O
money	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
industry	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
its	_	_	O
return	_	_	B-OBJ_NAME
on	_	_	O
investments	_	_	O
?	_	_	O

Miles	_	_	O
has	_	_	O
up	_	_	B-CONST_DIR
to	_	_	I-CONST_DIR
$	_	_	O
10000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
the	_	_	O
floral	_	_	B-VAR
and	_	_	O
healthcare	_	_	B-VAR
industries	_	_	I-VAR
.	_	_	O
After	_	_	O
talking	_	_	O
to	_	_	O
his	_	_	O
friends	_	_	O
,	_	_	O
he	_	_	O
has	_	_	O
decided	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
25	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
all	_	_	O
the	_	_	O
money	_	_	O
invested	_	_	O
must	_	_	O
be	_	_	O
in	_	_	O
the	_	_	O
floral	_	_	B-VAR
industry	_	_	I-VAR
and	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
$	_	_	O
2000	_	_	B-LIMIT
must	_	_	O
be	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
healthcare	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
Each	_	_	O
dollar	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
floral	_	_	B-VAR
industry	_	_	I-VAR
yields	_	_	O
a	_	_	O
$	_	_	O
1.3	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
while	_	_	O
each	_	_	O
dollar	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
healthcare	_	_	B-VAR
industry	_	_	I-VAR
yields	_	_	O
a	_	_	O
$	_	_	O
1.5	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
Miles	_	_	O
's	_	_	O
investment	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
milk	_	_	O
tea	_	_	O
shop	_	_	O
has	_	_	B-CONST_DIR
50000	_	_	B-LIMIT
ml	_	_	O
of	_	_	O
milk	_	_	O
to	_	_	O
make	_	_	O
two	_	_	O
milk	_	_	O
teas	_	_	O
:	_	_	O
black	_	_	B-VAR
milk	_	_	I-VAR
tea	_	_	I-VAR
and	_	_	O
green	_	_	B-VAR
milk	_	_	I-VAR
tea	_	_	I-VAR
.	_	_	O
A	_	_	O
bottle	_	_	O
of	_	_	O
black	_	_	B-VAR
milk	_	_	I-VAR
tea	_	_	I-VAR
contains	_	_	O
300	_	_	B-PARAM
ml	_	_	O
of	_	_	O
milk	_	_	O
while	_	_	O
a	_	_	O
bottle	_	_	O
of	_	_	O
green	_	_	B-VAR
milk	_	_	I-VAR
tea	_	_	I-VAR
has	_	_	O
200	_	_	B-PARAM
ml	_	_	O
of	_	_	O
milk	_	_	O
.	_	_	O
The	_	_	O
shop	_	_	O
knows	_	_	O
that	_	_	O
they	_	_	O
need	_	_	O
to	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	I-PARAM
the	_	_	O
number	_	_	O
of	_	_	O
bottles	_	_	O
of	_	_	O
black	_	_	B-VAR
milk	_	_	I-VAR
tea	_	_	I-VAR
than	_	_	O
green	_	_	B-VAR
milk	_	_	I-VAR
tea	_	_	I-VAR
.	_	_	O
They	_	_	O
also	_	_	O
know	_	_	O
that	_	_	O
they	_	_	O
need	_	_	O
to	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
bottles	_	_	O
of	_	_	O
green	_	_	B-VAR
milk	_	_	I-VAR
tea	_	_	I-VAR
.	_	_	O
Each	_	_	O
bottle	_	_	O
of	_	_	O
black	_	_	B-VAR
milk	_	_	I-VAR
tea	_	_	I-VAR
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
2.5	_	_	B-PARAM
and	_	_	O
each	_	_	O
bottle	_	_	O
of	_	_	O
green	_	_	B-VAR
milk	_	_	I-VAR
tea	_	_	I-VAR
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
7	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
milk	_	_	O
tea	_	_	O
needs	_	_	O
to	_	_	O
be	_	_	O
made	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
furniture	_	_	O
store	_	_	O
sells	_	_	O
only	_	_	O
bookcases	_	_	B-VAR
and	_	_	O
dining	_	_	B-VAR
tables	_	_	I-VAR
.	_	_	O
They	_	_	O
have	_	_	O
1200	_	_	B-LIMIT
sq	_	_	O
ft	_	_	O
of	_	_	O
floor	_	_	O
space	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
A	_	_	O
bookcase	_	_	B-VAR
requires	_	_	O
15	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
of	_	_	O
floor	_	_	O
space	_	_	O
while	_	_	O
a	_	_	O
dining	_	_	B-VAR
table	_	_	I-VAR
requires	_	_	O
8	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
of	_	_	O
floor	_	_	O
space	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
bookcase	_	_	B-VAR
is	_	_	O
$	_	_	O
150	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
dining	_	_	B-VAR
table	_	_	I-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
.	_	_	O
Management	_	_	O
requires	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
all	_	_	O
items	_	_	O
in	_	_	O
stock	_	_	O
to	_	_	O
be	_	_	O
bookcases	_	_	B-VAR
.	_	_	O
While	_	_	O
a	_	_	O
bookcase	_	_	B-VAR
ties	_	_	O
up	_	_	O
$	_	_	O
1200	_	_	B-PARAM
in	_	_	O
capital	_	_	O
,	_	_	O
a	_	_	O
dining	_	_	B-VAR
table	_	_	I-VAR
ties	_	_	O
up	_	_	O
$	_	_	O
1500	_	_	B-PARAM
in	_	_	O
capital	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
wants	_	_	O
to	_	_	O
have	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
50000	_	_	B-LIMIT
worth	_	_	O
of	_	_	O
capital	_	_	O
tied	_	_	O
up	_	_	O
at	_	_	O
any	_	_	O
time	_	_	O
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
store	_	_	O
's	_	_	O
profit	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
clothing	_	_	O
store	_	_	O
can	_	_	O
spend	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
50000	_	_	B-LIMIT
on	_	_	O
coats	_	_	B-VAR
and	_	_	O
shirts	_	_	B-VAR
.	_	_	O
A	_	_	O
coat	_	_	B-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
55	_	_	B-PARAM
and	_	_	O
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
12	_	_	B-PARAM
.	_	_	O
A	_	_	O
shirt	_	_	B-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
25	_	_	B-PARAM
and	_	_	O
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
8	_	_	B-PARAM
.	_	_	O
The	_	_	O
store	_	_	O
owner	_	_	O
estimates	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
60	_	_	B-LIMIT
but	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
coats	_	_	B-VAR
are	_	_	O
sold	_	_	O
each	_	_	O
month	_	_	O
.	_	_	O
The	_	_	O
owner	_	_	O
also	_	_	O
estimates	_	_	O
that	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
shirts	_	_	B-VAR
sold	_	_	O
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
four	_	_	B-PARAM
times	_	_	I-PARAM
the	_	_	O
number	_	_	O
of	_	_	O
coats	_	_	B-VAR
sold	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
item	_	_	O
,	_	_	O
coats	_	_	B-VAR
and	_	_	O
shirts	_	_	B-VAR
,	_	_	O
should	_	_	O
be	_	_	O
sold	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Theta	_	_	O
Sandwich	_	_	O
wants	_	_	O
to	_	_	O
advertise	_	_	O
its	_	_	O
new	_	_	O
product	_	_	O
.	_	_	O
They	_	_	O
want	_	_	O
to	_	_	O
use	_	_	O
three	_	_	O
types	_	_	O
of	_	_	O
ads	_	_	O
:	_	_	O
newspaper	_	_	B-VAR
ads	_	_	I-VAR
,	_	_	O
radio	_	_	B-VAR
ads	_	_	I-VAR
,	_	_	O
and	_	_	O
television	_	_	B-VAR
ads	_	_	I-VAR
.	_	_	O
The	_	_	O
cost	_	_	O
for	_	_	O
each	_	_	O
option	_	_	O
along	_	_	O
with	_	_	O
the	_	_	O
expected	_	_	O
viewership	_	_	O
is	_	_	O
given	_	_	O
.	_	_	O
A	_	_	O
newspaper	_	_	B-VAR
ad	_	_	I-VAR
costs	_	_	O
$	_	_	O
1200	_	_	B-PARAM
and	_	_	O
attracts	_	_	O
5000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
A	_	_	O
radio	_	_	B-VAR
ad	_	_	I-VAR
costs	_	_	O
$	_	_	O
500	_	_	B-PARAM
and	_	_	O
attracts	_	_	O
1000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
A	_	_	O
television	_	_	B-VAR
ad	_	_	I-VAR
costs	_	_	O
$	_	_	O
2000	_	_	B-PARAM
and	_	_	O
attracts	_	_	O
8000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
To	_	_	O
avoid	_	_	O
annoying	_	_	O
customers	_	_	O
,	_	_	O
the	_	_	O
city	_	_	O
has	_	_	O
limited	_	_	B-CONST_DIR
the	_	_	I-CONST_DIR
number	_	_	I-CONST_DIR
of	_	_	O
radio	_	_	B-VAR
ads	_	_	I-VAR
from	_	_	O
a	_	_	O
single	_	_	O
company	_	_	O
to	_	_	O
10	_	_	B-LIMIT
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
a	_	_	O
third	_	_	B-LIMIT
of	_	_	O
the	_	_	O
total	_	_	O
number	_	_	O
of	_	_	O
ads	_	_	O
should	_	_	O
be	_	_	O
television	_	_	B-VAR
ads	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
ads	_	_	O
should	_	_	O
be	_	_	O
newspaper	_	_	B-VAR
ads	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
weekly	_	_	O
budget	_	_	B-CONST_DIR
is	_	_	O
$	_	_	O
100000	_	_	B-LIMIT
,	_	_	O
how	_	_	O
many	_	_	O
ads	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
be	_	_	O
run	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
viewers	_	_	I-OBJ_NAME
?	_	_	O

David	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
10000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
.	_	_	O
He	_	_	O
has	_	_	O
decided	_	_	O
to	_	_	O
invest	_	_	O
in	_	_	O
the	_	_	O
healthcare	_	_	B-VAR
industry	_	_	I-VAR
and	_	_	O
the	_	_	O
fishing	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
He	_	_	O
has	_	_	O
decided	_	_	O
that	_	_	O
the	_	_	O
money	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
healthcare	_	_	B-VAR
industry	_	_	I-VAR
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
much	_	_	O
as	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
fishing	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
He	_	_	O
has	_	_	O
also	_	_	O
limited	_	_	O
himself	_	_	O
to	_	_	O
invest	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
1000	_	_	B-LIMIT
in	_	_	O
the	_	_	O
fishing	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
money	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
healthcare	_	_	B-VAR
industry	_	_	I-VAR
earns	_	_	B-OBJ_NAME
7.5	_	_	B-PARAM
%	_	_	I-PARAM
and	_	_	O
the	_	_	O
money	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
fishing	_	_	B-VAR
industry	_	_	I-VAR
earns	_	_	B-OBJ_NAME
12	_	_	B-PARAM
%	_	_	I-PARAM
,	_	_	O
how	_	_	O
much	_	_	O
should	_	_	O
he	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

Nolan	_	_	O
Center	_	_	O
is	_	_	O
going	_	_	O
to	_	_	O
hold	_	_	O
a	_	_	O
concert	_	_	O
and	_	_	O
can	_	_	O
seat	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
200	_	_	B-LIMIT
people	_	_	O
.	_	_	O
A	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
30	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
VIP	_	_	B-VAR
seat	_	_	I-VAR
ticket	_	_	O
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
14	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
general	_	_	B-VAR
seat	_	_	I-VAR
ticket	_	_	O
.	_	_	O
Nolan	_	_	O
Center	_	_	O
reserves	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
seats	_	_	O
to	_	_	O
be	_	_	O
VIP	_	_	B-VAR
seats	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
because	_	_	O
many	_	_	O
people	_	_	O
find	_	_	O
them	_	_	O
expensive	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
4	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
many	_	_	O
people	_	_	O
prefer	_	_	O
sitting	_	_	O
in	_	_	O
general	_	_	B-VAR
seats	_	_	I-VAR
than	_	_	O
in	_	_	O
VIP	_	_	B-VAR
seats	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
tickets	_	_	O
for	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
seat	_	_	O
must	_	_	O
be	_	_	O
sold	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Bob	_	_	O
is	_	_	O
a	_	_	O
potato	_	_	O
farmer	_	_	O
and	_	_	O
he	_	_	O
has	_	_	O
to	_	_	O
transport	_	_	O
his	_	_	O
potatoes	_	_	O
using	_	_	O
trucks	_	_	B-VAR
and	_	_	O
vans	_	_	B-VAR
.	_	_	O
Each	_	_	O
truck	_	_	B-VAR
can	_	_	O
take	_	_	O
150	_	_	B-PARAM
potatoes	_	_	B-OBJ_NAME
and	_	_	O
each	_	_	O
van	_	_	B-VAR
can	_	_	O
take	_	_	O
80	_	_	B-PARAM
potatoes	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
cost	_	_	O
of	_	_	O
running	_	_	O
each	_	_	O
truck	_	_	B-VAR
is	_	_	O
$	_	_	O
20	_	_	B-PARAM
per	_	_	O
trip	_	_	O
and	_	_	O
the	_	_	O
cost	_	_	O
of	_	_	O
running	_	_	O
each	_	_	O
van	_	_	B-VAR
is	_	_	O
$	_	_	O
12	_	_	B-PARAM
per	_	_	O
trip	_	_	O
.	_	_	O
Bob	_	_	O
wants	_	_	O
to	_	_	O
spend	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
250	_	_	B-LIMIT
on	_	_	O
transporting	_	_	O
his	_	_	O
potatoes	_	_	O
.	_	_	O
Due	_	_	O
to	_	_	O
traffic	_	_	O
laws	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
trucks	_	_	B-VAR
must	_	_	O
be	_	_	O
less	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
vans	_	_	B-VAR
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
potatoes	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
transported	_	_	O
.	_	_	O

A	_	_	O
large	_	_	O
fast	_	_	O
-	_	_	O
food	_	_	O
restaurant	_	_	O
employs	_	_	O
waiters	_	_	B-VAR
and	_	_	O
managers	_	_	B-VAR
.	_	_	O
Waiters	_	_	B-VAR
earn	_	_	B-OBJ_NAME
$	_	_	O
1200	_	_	B-PARAM
per	_	_	O
week	_	_	O
and	_	_	O
managers	_	_	B-VAR
earn	_	_	B-OBJ_NAME
$	_	_	O
2000	_	_	B-PARAM
per	_	_	O
week	_	_	O
.	_	_	O
The	_	_	O
restaurant	_	_	O
requires	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
50	_	_	B-LIMIT
workers	_	_	O
of	_	_	O
whom	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
15	_	_	B-LIMIT
must	_	_	O
be	_	_	O
managers	_	_	B-VAR
.	_	_	O
To	_	_	O
keep	_	_	O
the	_	_	O
restaurant	_	_	O
clean	_	_	O
and	_	_	O
running	_	_	O
smoothly	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
managers	_	_	B-VAR
should	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
a	_	_	O
third	_	_	B-PARAM
of	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
waiters	_	_	B-VAR
.	_	_	O
The	_	_	O
restaurant	_	_	O
wants	_	_	O
to	_	_	O
keep	_	_	O
the	_	_	O
weekly	_	_	B-OBJ_NAME
wage	_	_	I-OBJ_NAME
bill	_	_	I-OBJ_NAME
below	_	_	B-CONST_DIR
$	_	_	O
500000	_	_	B-LIMIT
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	B-OBJ_NAME
wage	_	_	I-OBJ_NAME
bill	_	_	I-OBJ_NAME
.	_	_	O

Luke	_	_	O
has	_	_	O
200	_	_	B-LIMIT
hectares	_	_	O
available	_	_	B-CONST_DIR
to	_	_	O
grow	_	_	O
carrots	_	_	B-VAR
and	_	_	O
pumpkins	_	_	B-VAR
.	_	_	O
He	_	_	O
prefers	_	_	O
to	_	_	O
plant	_	_	O
more	_	_	B-CONST_DIR
carrots	_	_	B-VAR
than	_	_	O
pumpkins	_	_	B-VAR
,	_	_	O
but	_	_	O
the	_	_	O
soil	_	_	O
and	_	_	O
weather	_	_	O
conditions	_	_	O
allow	_	_	O
him	_	_	O
to	_	_	O
grow	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
twice	_	_	B-PARAM
the	_	_	O
amount	_	_	O
of	_	_	O
carrots	_	_	B-VAR
to	_	_	O
that	_	_	O
of	_	_	O
pumpkins	_	_	B-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
he	_	_	O
must	_	_	O
grow	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
25	_	_	B-LIMIT
hectares	_	_	O
of	_	_	O
carrots	_	_	B-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
hectares	_	_	O
of	_	_	O
pumpkins	_	_	B-VAR
to	_	_	O
meet	_	_	O
community	_	_	O
demands	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
hectare	_	_	O
of	_	_	O
carrots	_	_	B-VAR
is	_	_	O
$	_	_	O
300	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
hectare	_	_	O
of	_	_	O
pumpkins	_	_	B-VAR
is	_	_	O
$	_	_	O
500	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
hectares	_	_	O
of	_	_	O
each	_	_	O
item	_	_	O
should	_	_	O
he	_	_	O
plant	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O
What	_	_	O
is	_	_	O
this	_	_	O
profit	_	_	O
?	_	_	O

Matthew	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
2000000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
in	_	_	O
the	_	_	O
iron	_	_	B-VAR
and	_	_	I-VAR
steel	_	_	I-VAR
,	_	_	O
tobacco	_	_	B-VAR
,	_	_	O
healthcare	_	_	B-VAR
,	_	_	O
and	_	_	O
food	_	_	B-VAR
industries	_	_	I-VAR
.	_	_	O
Matthew	_	_	O
is	_	_	O
a	_	_	O
smart	_	_	O
investor	_	_	O
and	_	_	O
he	_	_	O
knows	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
food	_	_	B-VAR
industry	_	_	I-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
iron	_	_	B-VAR
and	_	_	I-VAR
steel	_	_	I-VAR
industry	_	_	I-VAR
.	_	_	O
Also	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
tobacco	_	_	B-VAR
industry	_	_	I-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
healthcare	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
Finally	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
20	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
total	_	_	O
amount	_	_	O
invested	_	_	O
can	_	_	O
be	_	_	O
in	_	_	O
the	_	_	O
food	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
The	_	_	O
return	_	_	B-OBJ_NAME
on	_	_	O
investment	_	_	O
in	_	_	O
each	_	_	O
of	_	_	O
the	_	_	O
industries	_	_	O
is	_	_	O
as	_	_	O
follows	_	_	O
:	_	_	O
iron	_	_	B-VAR
and	_	_	I-VAR
steel	_	_	I-VAR
,	_	_	O
9.5	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
tobacco	_	_	B-VAR
,	_	_	O
12.4	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
healthcare	_	_	B-VAR
,	_	_	O
5.6	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
food	_	_	B-VAR
,	_	_	O
4.8	_	_	B-PARAM
%	_	_	I-PARAM
.	_	_	O
Matthew	_	_	O
wants	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
return	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
movie	_	_	O
theatre	_	_	O
can	_	_	O
hold	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
250	_	_	B-LIMIT
people	_	_	O
and	_	_	O
has	_	_	O
both	_	_	O
zero	_	_	B-VAR
gravity	_	_	I-VAR
and	_	_	O
standard	_	_	B-VAR
seats	_	_	I-VAR
.	_	_	O
A	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
55	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
zero	_	_	B-VAR
gravity	_	_	I-VAR
seat	_	_	I-VAR
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
25	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
standard	_	_	B-VAR
seat	_	_	I-VAR
.	_	_	O
The	_	_	O
arena	_	_	O
reserves	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
40	_	_	B-LIMIT
seats	_	_	O
to	_	_	O
be	_	_	O
zero	_	_	B-VAR
gravity	_	_	I-VAR
seats	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
since	_	_	O
zero	_	_	B-VAR
gravity	_	_	I-VAR
seats	_	_	I-VAR
are	_	_	O
expensive	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
4	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
many	_	_	O
people	_	_	O
prefer	_	_	O
to	_	_	O
sit	_	_	O
in	_	_	O
standard	_	_	B-VAR
seats	_	_	I-VAR
than	_	_	O
zero	_	_	B-VAR
gravity	_	_	I-VAR
seats	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
seat	_	_	O
must	_	_	O
be	_	_	O
sold	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
food	_	_	O
truck	_	_	O
makes	_	_	O
beef	_	_	B-VAR
burritos	_	_	I-VAR
and	_	_	O
pork	_	_	B-VAR
burritos	_	_	I-VAR
.	_	_	O
They	_	_	O
only	_	_	O
has	_	_	O
enough	_	_	O
materials	_	_	O
to	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
burritos	_	_	O
.	_	_	O
To	_	_	O
stay	_	_	O
in	_	_	O
business	_	_	O
,	_	_	O
they	_	_	O
must	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
beef	_	_	B-VAR
burritos	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
pork	_	_	B-VAR
burritos	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
they	_	_	O
only	_	_	O
have	_	_	O
enough	_	_	O
materials	_	_	O
,	_	_	O
to	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
70	_	_	B-LIMIT
beef	_	_	B-VAR
burritos	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
80	_	_	B-LIMIT
pork	_	_	B-VAR
burritos	_	_	I-VAR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
beef	_	_	B-VAR
burritos	_	_	I-VAR
is	_	_	O
$	_	_	O
3.5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
pork	_	_	B-VAR
burritos	_	_	I-VAR
is	_	_	O
$	_	_	O
2.1	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
burrito	_	_	O
should	_	_	O
the	_	_	O
they	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
clothing	_	_	O
company	_	_	O
makes	_	_	O
flight	_	_	B-VAR
jackets	_	_	I-VAR
and	_	_	O
denim	_	_	B-VAR
jackets	_	_	I-VAR
in	_	_	O
their	_	_	O
factory	_	_	O
.	_	_	O
A	_	_	O
different	_	_	O
team	_	_	O
produces	_	_	O
each	_	_	O
kind	_	_	O
of	_	_	O
jacket	_	_	O
and	_	_	O
each	_	_	O
team	_	_	O
has	_	_	O
a	_	_	O
different	_	_	O
maximum	_	_	B-CONST_DIR
production	_	_	O
rate	_	_	O
:	_	_	O
10	_	_	B-LIMIT
flight	_	_	B-VAR
jackets	_	_	I-VAR
per	_	_	O
day	_	_	O
and	_	_	O
25	_	_	B-LIMIT
denim	_	_	B-VAR
jackets	_	_	I-VAR
per	_	_	O
day	_	_	O
respectively	_	_	O
.	_	_	O
Both	_	_	O
teams	_	_	O
require	_	_	O
the	_	_	O
use	_	_	O
of	_	_	O
a	_	_	O
sewing	_	_	O
machine	_	_	O
and	_	_	O
this	_	_	O
machine	_	_	O
can	_	_	O
process	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
jackets	_	_	O
per	_	_	O
day	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
.	_	_	O
While	_	_	O
the	_	_	O
flight	_	_	B-VAR
jackets	_	_	I-VAR
generate	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
70	_	_	B-PARAM
per	_	_	O
jacket	_	_	O
,	_	_	O
the	_	_	O
denim	_	_	B-VAR
jackets	_	_	I-VAR
generate	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
100	_	_	B-PARAM
per	_	_	O
jacket	_	_	O
.	_	_	O
Assuming	_	_	O
the	_	_	O
company	_	_	O
can	_	_	O
sell	_	_	O
all	_	_	O
the	_	_	O
jackets	_	_	O
they	_	_	O
make	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
jacket	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

The	_	_	O
Jockspring	_	_	O
company	_	_	O
wants	_	_	O
to	_	_	O
use	_	_	O
a	_	_	O
total	_	_	O
market	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
50,000	_	_	B-LIMIT
to	_	_	O
promote	_	_	O
a	_	_	O
new	_	_	O
brand	_	_	O
of	_	_	O
candy	_	_	O
.	_	_	O
To	_	_	O
do	_	_	O
the	_	_	O
promotion	_	_	O
,	_	_	O
the	_	_	O
company	_	_	O
needs	_	_	O
to	_	_	O
decide	_	_	O
how	_	_	O
much	_	_	O
to	_	_	O
allocate	_	_	O
to	_	_	O
each	_	_	O
of	_	_	O
its	_	_	O
two	_	_	O
advertising	_	_	O
channels	_	_	O
:	_	_	O
(	_	_	O
1	_	_	O
)	_	_	O
newspapers	_	_	B-VAR
and	_	_	O
(	_	_	O
2	_	_	O
)	_	_	O
radio	_	_	B-VAR
stations	_	_	I-VAR
.	_	_	O
Each	_	_	O
day	_	_	O
,	_	_	O
it	_	_	O
costs	_	_	O
the	_	_	O
company	_	_	O
$	_	_	O
2,500	_	_	B-PARAM
and	_	_	O
$	_	_	O
1,500	_	_	B-PARAM
to	_	_	O
run	_	_	O
advertisement	_	_	O
spots	_	_	O
on	_	_	O
newspapers	_	_	B-VAR
and	_	_	O
radio	_	_	B-VAR
stations	_	_	I-VAR
,	_	_	O
respectively	_	_	O
.	_	_	O
Based	_	_	O
on	_	_	O
past	_	_	O
ratings	_	_	O
,	_	_	O
the	_	_	O
expected	_	_	O
daily	_	_	O
reach	_	_	B-OBJ_NAME
is	_	_	O
10,000	_	_	B-PARAM
readers	_	_	O
for	_	_	O
each	_	_	O
newspaper	_	_	B-VAR
spot	_	_	I-VAR
and	_	_	O
20,000	_	_	B-PARAM
users	_	_	O
for	_	_	O
a	_	_	O
radio	_	_	B-VAR
station	_	_	I-VAR
spot	_	_	O
.	_	_	O
The	_	_	O
business	_	_	O
director	_	_	O
believes	_	_	O
that	_	_	O
both	_	_	O
channels	_	_	O
should	_	_	O
be	_	_	O
effectively	_	_	O
used	_	_	O
to	_	_	O
ensure	_	_	O
the	_	_	O
success	_	_	O
of	_	_	O
the	_	_	O
product	_	_	O
launch	_	_	O
.	_	_	O
She	_	_	O
wants	_	_	O
to	_	_	O
plan	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
but	_	_	O
no	_	_	B-CONST_DIR
more	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
10	_	_	B-LIMIT
newspaper	_	_	B-VAR
spots	_	_	I-VAR
.	_	_	O
Conversely	_	_	O
,	_	_	O
the	_	_	O
radio	_	_	B-VAR
station	_	_	I-VAR
spots	_	_	O
need	_	_	O
to	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
due	_	_	O
to	_	_	O
the	_	_	O
pricing	_	_	O
tier	_	_	O
policy	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
times	_	_	O
should	_	_	O
each	_	_	O
of	_	_	O
the	_	_	O
media	_	_	O
channels	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
reach	_	_	B-OBJ_NAME
of	_	_	O
the	_	_	O
campaign	_	_	O
?	_	_	O

Royal	_	_	O
Asset	_	_	O
Investment	_	_	O
plans	_	_	O
to	_	_	O
invest	_	_	O
a	_	_	O
total	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
200,000	_	_	B-LIMIT
in	_	_	O
mutual	_	_	B-VAR
funds	_	_	I-VAR
and	_	_	O
cryptocurrencies	_	_	B-VAR
,	_	_	O
which	_	_	O
yield	_	_	O
a	_	_	O
4.1	_	_	B-PARAM
%	_	_	I-PARAM
return	_	_	B-OBJ_NAME
and	_	_	O
a	_	_	O
7.5	_	_	B-PARAM
%	_	_	O
return	_	_	B-OBJ_NAME
,	_	_	O
respectively	_	_	O
.	_	_	O
Internal	_	_	O
policies	_	_	O
require	_	_	O
the	_	_	O
company	_	_	O
to	_	_	O
diversify	_	_	O
the	_	_	O
asset	_	_	O
allocation	_	_	O
so	_	_	O
that	_	_	O
the	_	_	O
minimum	_	_	B-CONST_DIR
investment	_	_	O
in	_	_	O
mutual	_	_	B-VAR
funds	_	_	I-VAR
is	_	_	O
45	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
total	_	_	O
investment	_	_	O
.	_	_	O
Due	_	_	O
to	_	_	O
the	_	_	O
risk	_	_	O
of	_	_	O
blockchain	_	_	O
technology	_	_	O
,	_	_	O
no	_	_	B-CONST_DIR
more	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
30	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
total	_	_	O
investment	_	_	O
should	_	_	O
be	_	_	O
allocated	_	_	O
to	_	_	O
cryptocurrencies	_	_	B-VAR
.	_	_	O
How	_	_	O
much	_	_	O
should	_	_	O
the	_	_	O
Royal	_	_	O
Asset	_	_	O
Investment	_	_	O
allocate	_	_	O
to	_	_	O
each	_	_	O
asset	_	_	O
so	_	_	O
as	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
its	_	_	O
average	_	_	O
return	_	_	B-OBJ_NAME
?	_	_	O

The	_	_	O
Curious	_	_	O
electronics	_	_	O
business	_	_	O
wants	_	_	O
to	_	_	O
determine	_	_	O
the	_	_	O
level	_	_	O
of	_	_	O
production	_	_	O
of	_	_	O
its	_	_	O
two	_	_	O
hottest	_	_	O
digital	_	_	O
keyboards	_	_	O
:	_	_	O
A400	_	_	B-VAR
and	_	_	O
P500	_	_	B-VAR
.	_	_	O
Making	_	_	O
one	_	_	O
A400	_	_	B-VAR
keyboard	_	_	I-VAR
requires	_	_	O
5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
labour	_	_	O
and	_	_	O
yields	_	_	O
a	_	_	O
$	_	_	O
35	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
.	_	_	O
On	_	_	O
the	_	_	O
other	_	_	O
hand	_	_	O
,	_	_	O
one	_	_	O
P500	_	_	B-VAR
keyboard	_	_	I-VAR
can	_	_	O
be	_	_	O
produced	_	_	O
in	_	_	O
9	_	_	B-PARAM
hours	_	_	O
and	_	_	O
offers	_	_	O
a	_	_	O
greater	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
80	_	_	B-PARAM
.	_	_	O
Given	_	_	O
the	_	_	O
demand	_	_	O
forecast	_	_	O
,	_	_	O
the	_	_	O
business	_	_	O
decides	_	_	O
to	_	_	O
produce	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
many	_	_	O
A400	_	_	B-VAR
keyboards	_	_	I-VAR
as	_	_	O
P500	_	_	B-VAR
ones	_	_	I-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
it	_	_	O
can	_	_	O
spend	_	_	O
up	_	_	B-CONST_DIR
to	_	_	I-CONST_DIR
45	_	_	B-LIMIT
hours	_	_	O
a	_	_	O
week	_	_	O
to	_	_	O
manufacture	_	_	O
these	_	_	O
keyboards	_	_	O
.	_	_	O
Can	_	_	O
you	_	_	O
help	_	_	O
the	_	_	O
business	_	_	O
determine	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
each	_	_	O
keyboard	_	_	O
to	_	_	O
be	_	_	O
produced	_	_	O
each	_	_	O
week	_	_	O
to	_	_	O
obtain	_	_	O
the	_	_	O
maximum	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Autumn	_	_	O
Auto	_	_	O
wants	_	_	O
to	_	_	O
promote	_	_	O
new	_	_	O
types	_	_	O
of	_	_	O
minivans	_	_	O
and	_	_	O
supercars	_	_	O
that	_	_	O
are	_	_	O
targeted	_	_	O
at	_	_	O
baby	_	_	O
boomers	_	_	O
and	_	_	O
millennials	_	_	O
.	_	_	O
To	_	_	O
market	_	_	O
these	_	_	O
products	_	_	O
,	_	_	O
Autumn	_	_	O
Auto	_	_	O
has	_	_	O
launched	_	_	O
a	_	_	O
boisterous	_	_	O
ads	_	_	O
campaign	_	_	O
and	_	_	O
has	_	_	O
decided	_	_	O
to	_	_	O
purchase	_	_	O
TV	_	_	O
commercial	_	_	O
spots	_	_	O
on	_	_	O
two	_	_	O
channels	_	_	O
:	_	_	O
(	_	_	O
1	_	_	O
)	_	_	O
global	_	_	B-VAR
news	_	_	I-VAR
and	_	_	O
(	_	_	O
2	_	_	O
)	_	_	O
talent	_	_	B-VAR
shows	_	_	I-VAR
.	_	_	O
Each	_	_	O
talent	_	_	B-VAR
show	_	_	I-VAR
ad	_	_	O
is	_	_	O
seen	_	_	O
by	_	_	O
5	_	_	B-PARAM
million	_	_	O
baby	_	_	O
boomers	_	_	O
and	_	_	O
20	_	_	B-PARAM
million	_	_	O
millennials	_	_	O
and	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
80,000	_	_	B-PARAM
.	_	_	O
Each	_	_	O
global	_	_	B-VAR
news	_	_	I-VAR
commercial	_	_	O
is	_	_	O
watched	_	_	O
by	_	_	O
13	_	_	B-PARAM
million	_	_	O
baby	_	_	O
boomers	_	_	O
and	_	_	O
7	_	_	B-PARAM
million	_	_	O
millennials	_	_	O
,	_	_	O
and	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
30,000	_	_	B-PARAM
.	_	_	O
Autumn	_	_	O
Auto	_	_	O
would	_	_	O
like	_	_	O
to	_	_	O
reach	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
million	_	_	O
baby	_	_	O
boomers	_	_	O
and	_	_	O
30	_	_	B-LIMIT
million	_	_	O
millennials	_	_	O
.	_	_	O
Determine	_	_	O
how	_	_	O
Autumn	_	_	O
Auto	_	_	O
can	_	_	O
meet	_	_	O
its	_	_	O
advertising	_	_	O
requirements	_	_	O
at	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
.	_	_	O

Adam	_	_	O
decides	_	_	O
to	_	_	O
invest	_	_	B-CONST_DIR
$	_	_	O
12,000	_	_	B-LIMIT
in	_	_	O
mutual	_	_	B-VAR
funds	_	_	I-VAR
and	_	_	O
the	_	_	O
stock	_	_	B-VAR
market	_	_	I-VAR
.	_	_	O
Mutual	_	_	B-VAR
funds	_	_	I-VAR
yield	_	_	O
a	_	_	O
2.5	_	_	B-PARAM
%	_	_	I-PARAM
return	_	_	B-OBJ_NAME
,	_	_	O
whereas	_	_	O
stock	_	_	B-VAR
yields	_	_	O
an	_	_	O
average	_	_	O
return	_	_	B-OBJ_NAME
of	_	_	O
5.5	_	_	B-PARAM
%	_	_	I-PARAM
.	_	_	O
To	_	_	O
meet	_	_	O
his	_	_	O
long	_	_	O
-	_	_	O
term	_	_	O
investment	_	_	O
goal	_	_	O
,	_	_	O
he	_	_	O
needs	_	_	O
to	_	_	O
place	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
$	_	_	O
5,000	_	_	B-LIMIT
in	_	_	O
the	_	_	O
stock	_	_	B-VAR
market	_	_	I-VAR
.	_	_	O
Nonetheless	_	_	O
,	_	_	O
he	_	_	O
is	_	_	O
risk	_	_	O
averse	_	_	O
and	_	_	O
wants	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
40	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
his	_	_	O
money	_	_	O
to	_	_	O
be	_	_	O
safely	_	_	O
invested	_	_	O
in	_	_	O
mutual	_	_	B-VAR
funds	_	_	I-VAR
.	_	_	O
Help	_	_	O
Adam	_	_	O
determine	_	_	O
an	_	_	O
asset	_	_	O
allocation	_	_	O
that	_	_	O
will	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
average	_	_	O
return	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
bubble	_	_	O
tea	_	_	O
truck	_	_	O
sells	_	_	O
and	_	_	O
delivers	_	_	O
regular	_	_	B-VAR
milk	_	_	I-VAR
tea	_	_	I-VAR
and	_	_	O
fresh	_	_	B-VAR
fruit	_	_	I-VAR
tea	_	_	I-VAR
during	_	_	O
the	_	_	O
pandemic	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
on	_	_	O
a	_	_	O
cup	_	_	O
of	_	_	O
regular	_	_	B-VAR
milk	_	_	I-VAR
tea	_	_	I-VAR
is	_	_	O
1.5	_	_	B-PARAM
$	_	_	O
,	_	_	O
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
on	_	_	O
a	_	_	O
cup	_	_	O
of	_	_	O
fresh	_	_	B-VAR
fruit	_	_	I-VAR
tea	_	_	I-VAR
is	_	_	O
1.8$.	_	_	B-PARAM
In	_	_	O
order	_	_	O
to	_	_	O
thrive	_	_	O
,	_	_	O
it	_	_	O
must	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
45	_	_	B-LIMIT
cups	_	_	O
of	_	_	O
regular	_	_	B-VAR
milk	_	_	I-VAR
tea	_	_	I-VAR
but	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
60	_	_	B-LIMIT
in	_	_	O
a	_	_	O
day	_	_	O
.	_	_	O
It	_	_	O
must	_	_	O
also	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
55	_	_	B-LIMIT
cups	_	_	O
of	_	_	O
fresh	_	_	B-VAR
fruit	_	_	I-VAR
tea	_	_	I-VAR
due	_	_	O
to	_	_	O
its	_	_	O
high	_	_	O
demand	_	_	O
,	_	_	O
but	_	_	O
can	_	_	O
not	_	_	B-CONST_DIR
prepare	_	_	I-CONST_DIR
more	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
75	_	_	B-LIMIT
a	_	_	O
day	_	_	O
.	_	_	O
Due	_	_	O
to	_	_	O
staff	_	_	O
shortage	_	_	O
,	_	_	O
the	_	_	O
bubble	_	_	O
tea	_	_	O
truck	_	_	O
can	_	_	O
only	_	_	O
prepare	_	_	O
up	_	_	O
to	_	_	O
120	_	_	B-LIMIT
items	_	_	O
in	_	_	B-CONST_DIR
total	_	_	I-CONST_DIR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
item	_	_	O
should	_	_	O
it	_	_	O
prepare	_	_	O
to	_	_	O
satisfy	_	_	O
its	_	_	O
customers	_	_	O
and	_	_	O
maximize	_	_	B-OBJ_DIR
its	_	_	O
daily	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

TomMusic	_	_	O
would	_	_	O
like	_	_	O
to	_	_	O
attract	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
250	_	_	B-LIMIT
customers	_	_	O
into	_	_	O
its	_	_	O
store	_	_	O
daily	_	_	O
.	_	_	O
Therefore	_	_	O
,	_	_	O
it	_	_	O
decides	_	_	O
to	_	_	O
sell	_	_	O
two	_	_	O
popular	_	_	O
digital	_	_	O
piano	_	_	O
models	_	_	O
,	_	_	O
Piano	_	_	B-VAR
A	_	_	I-VAR
and	_	_	O
Piano	_	_	B-VAR
B	_	_	I-VAR
,	_	_	O
at	_	_	O
a	_	_	O
steep	_	_	O
discount	_	_	O
to	_	_	O
attract	_	_	O
foot	_	_	O
traffic	_	_	O
.	_	_	O
TomMusic	_	_	O
owner	_	_	O
pays	_	_	O
$	_	_	O
20	_	_	B-PARAM
and	_	_	O
$	_	_	O
15	_	_	B-PARAM
for	_	_	O
each	_	_	O
unit	_	_	O
of	_	_	O
Piano	_	_	B-VAR
A	_	_	I-VAR
and	_	_	O
Piano	_	_	B-VAR
B	_	_	I-VAR
respectively	_	_	O
and	_	_	O
has	_	_	O
at	_	_	O
its	_	_	O
disposition	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
daily	_	_	O
budget	_	_	O
of	_	_	O
$	_	_	O
450	_	_	B-LIMIT
for	_	_	O
this	_	_	O
sales	_	_	O
campaign	_	_	O
.	_	_	O
For	_	_	O
each	_	_	O
unit	_	_	O
of	_	_	O
Piano	_	_	B-VAR
A	_	_	I-VAR
model	_	_	O
sold	_	_	O
,	_	_	O
TomMusic	_	_	O
incurs	_	_	O
a	_	_	O
cost	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
12	_	_	B-PARAM
and	_	_	O
attracts	_	_	O
25	_	_	B-PARAM
customers	_	_	O
into	_	_	O
its	_	_	O
store	_	_	O
on	_	_	O
average	_	_	O
.	_	_	O
In	_	_	O
comparison	_	_	O
,	_	_	O
each	_	_	O
unit	_	_	O
of	_	_	O
Piano	_	_	B-VAR
B	_	_	I-VAR
incurs	_	_	O
a	_	_	O
lower	_	_	O
cost	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
4	_	_	B-PARAM
but	_	_	O
only	_	_	B-CONST_DIR
attracts	_	_	O
10	_	_	B-PARAM
customers	_	_	O
on	_	_	O
average	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
units	_	_	O
of	_	_	O
each	_	_	O
model	_	_	O
should	_	_	O
be	_	_	O
stocked	_	_	O
daily	_	_	O
to	_	_	O
meet	_	_	O
his	_	_	O
campaign	_	_	O
while	_	_	O
minimizing	_	_	B-OBJ_DIR
its	_	_	O
cost	_	_	B-OBJ_NAME
?	_	_	O

CaMilk	_	_	O
has	_	_	O
25,000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
milk	_	_	O
available	_	_	B-CONST_DIR
to	_	_	O
make	_	_	O
muffins	_	_	B-VAR
and	_	_	O
milk	_	_	B-VAR
cakes	_	_	I-VAR
.	_	_	O
Consumer	_	_	O
research	_	_	O
determines	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-LIMIT
the	_	_	O
amount	_	_	O
of	_	_	O
the	_	_	O
milk	_	_	B-VAR
cakes	_	_	I-VAR
are	_	_	O
needed	_	_	O
than	_	_	O
the	_	_	O
muffins	_	_	B-VAR
and	_	_	O
there	_	_	O
need	_	_	O
to	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
muffins	_	_	B-VAR
made	_	_	O
.	_	_	O
Each	_	_	O
muffin	_	_	B-VAR
needs	_	_	O
15	_	_	B-PARAM
grams	_	_	O
of	_	_	O
milk	_	_	O
and	_	_	O
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
6.5	_	_	B-PARAM
.	_	_	O
In	_	_	O
contrast	_	_	O
,	_	_	O
a	_	_	O
milk	_	_	B-VAR
cake	_	_	I-VAR
needs	_	_	O
100	_	_	B-PARAM
grams	_	_	O
of	_	_	O
milk	_	_	O
each	_	_	O
and	_	_	O
sells	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
8.5	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
product	_	_	O
should	_	_	O
CaMilk	_	_	O
prepare	_	_	O
to	_	_	O
obtain	_	_	O
the	_	_	O
maximum	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Blue	_	_	O
Ocean	_	_	O
wants	_	_	O
to	_	_	O
allocate	_	_	O
resources	_	_	O
at	_	_	O
its	_	_	O
two	_	_	O
plants	_	_	O
Gamma	_	_	B-VAR
and	_	_	O
Delta	_	_	B-VAR
to	_	_	O
produce	_	_	O
two	_	_	O
products	_	_	O
:	_	_	O
asphalt	_	_	O
and	_	_	O
bricks	_	_	O
.	_	_	O
To	_	_	O
meet	_	_	O
customer	_	_	O
demands	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
90	_	_	B-LIMIT
units	_	_	O
of	_	_	O
asphalt	_	_	O
and	_	_	O
85	_	_	B-LIMIT
units	_	_	O
of	_	_	O
bricks	_	_	O
must	_	_	O
be	_	_	O
produced	_	_	O
daily	_	_	O
.	_	_	O
Running	_	_	O
the	_	_	O
plant	_	_	B-VAR
Gamma	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
35	_	_	B-PARAM
per	_	_	O
hour	_	_	O
and	_	_	O
yields	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
asphalt	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
bricks	_	_	O
.	_	_	O
Running	_	_	O
the	_	_	O
plant	_	_	B-VAR
Delta	_	_	I-VAR
for	_	_	O
an	_	_	O
hour	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
95	_	_	B-PARAM
and	_	_	O
produces	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
asphalt	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
bricks	_	_	O
.	_	_	O
Determine	_	_	O
the	_	_	O
daily	_	_	O
production	_	_	O
plan	_	_	O
at	_	_	O
its	_	_	O
plants	_	_	O
that	_	_	O
will	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
cost	_	_	B-OBJ_NAME
of	_	_	O
meeting	_	_	O
the	_	_	O
demands	_	_	O
.	_	_	O

CE	_	_	O
Chemicals	_	_	O
produces	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
products	_	_	O
,	_	_	O
adhesives	_	_	B-VAR
and	_	_	O
plasticizers	_	_	B-VAR
.	_	_	O
To	_	_	O
produce	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
product	_	_	O
,	_	_	O
we	_	_	O
need	_	_	O
to	_	_	O
use	_	_	O
both	_	_	O
an	_	_	O
automatic	_	_	O
device	_	_	O
and	_	_	O
a	_	_	O
human	_	_	O
-	_	_	O
operated	_	_	O
device	_	_	O
.	_	_	O
On	_	_	O
a	_	_	O
given	_	_	O
day	_	_	O
,	_	_	O
each	_	_	O
processing	_	_	O
device	_	_	O
is	_	_	O
available	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
450	_	_	B-LIMIT
minutes	_	_	O
.	_	_	O
To	_	_	O
extract	_	_	O
a	_	_	O
package	_	_	O
of	_	_	O
adhesives	_	_	B-VAR
,	_	_	O
it	_	_	O
takes	_	_	O
6	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
processing	_	_	O
on	_	_	O
the	_	_	O
automatic	_	_	O
device	_	_	O
and	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
human	_	_	O
-	_	_	O
operated	_	_	O
device	_	_	O
.	_	_	O
To	_	_	O
extract	_	_	O
a	_	_	O
package	_	_	O
of	_	_	O
plasticizers	_	_	B-VAR
,	_	_	O
the	_	_	O
automatic	_	_	O
device	_	_	O
needs	_	_	O
to	_	_	O
be	_	_	O
run	_	_	O
for	_	_	O
8	_	_	B-PARAM
minutes	_	_	O
and	_	_	O
the	_	_	O
human	_	_	O
-	_	_	O
operated	_	_	O
device	_	_	O
for	_	_	O
4	_	_	B-PARAM
minutes	_	_	O
.	_	_	O
The	_	_	O
manufacturer	_	_	O
can	_	_	O
sell	_	_	O
a	_	_	O
package	_	_	O
of	_	_	O
adhesives	_	_	B-VAR
for	_	_	O
a	_	_	O
revenue	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
8.5	_	_	B-PARAM
and	_	_	O
plasticizers	_	_	B-VAR
for	_	_	O
a	_	_	O
revenue	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
11.5	_	_	B-PARAM
.	_	_	O
Assuming	_	_	O
that	_	_	O
the	_	_	O
company	_	_	O
can	_	_	O
sell	_	_	O
all	_	_	O
the	_	_	O
products	_	_	O
it	_	_	O
produces	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
packages	_	_	O
of	_	_	O
each	_	_	O
product	_	_	O
should	_	_	O
be	_	_	O
produced	_	_	O
daily	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
revenue	_	_	B-OBJ_NAME
?	_	_	O

Blue	_	_	O
Novel	_	_	O
Furniture	_	_	O
produces	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
tables	_	_	O
,	_	_	O
coffee	_	_	B-VAR
table	_	_	I-VAR
and	_	_	O
bedside	_	_	B-VAR
table	_	_	I-VAR
.	_	_	O
It	_	_	O
takes	_	_	O
2.5	_	_	B-PARAM
hours	_	_	O
to	_	_	O
produce	_	_	O
the	_	_	O
parts	_	_	O
of	_	_	O
a	_	_	O
coffee	_	_	B-VAR
table	_	_	I-VAR
and	_	_	O
4.5	_	_	B-PARAM
hours	_	_	O
for	_	_	O
those	_	_	O
of	_	_	O
a	_	_	O
bedside	_	_	B-VAR
table	_	_	I-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
it	_	_	O
takes	_	_	O
2	_	_	B-PARAM
hours	_	_	O
and	_	_	O
3	_	_	B-PARAM
hours	_	_	O
to	_	_	O
assemble	_	_	O
a	_	_	O
bedside	_	_	B-VAR
table	_	_	I-VAR
and	_	_	O
coffee	_	_	B-VAR
table	_	_	I-VAR
,	_	_	O
respectively	_	_	O
.	_	_	O
Finally	_	_	O
,	_	_	O
polishing	_	_	O
a	_	_	O
bedside	_	_	B-VAR
table	_	_	I-VAR
takes	_	_	O
3.5	_	_	B-PARAM
hours	_	_	O
,	_	_	O
whereas	_	_	O
polishing	_	_	O
a	_	_	O
coffee	_	_	B-VAR
table	_	_	I-VAR
requires	_	_	O
1.5	_	_	B-PARAM
hours	_	_	O
.	_	_	O
Every	_	_	O
month	_	_	O
,	_	_	O
there	_	_	O
are	_	_	O
a	_	_	O
total	_	_	O
of	_	_	O
6500	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
producing	_	_	O
the	_	_	O
parts	_	_	O
,	_	_	O
3500	_	_	B-LIMIT
hours	_	_	O
for	_	_	O
assembling	_	_	O
the	_	_	O
parts	_	_	O
,	_	_	O
and	_	_	O
5000	_	_	B-LIMIT
hours	_	_	O
for	_	_	O
polishing	_	_	O
the	_	_	O
tables	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
made	_	_	O
on	_	_	O
a	_	_	O
coffee	_	_	B-VAR
table	_	_	I-VAR
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
on	_	_	O
a	_	_	O
bedside	_	_	B-VAR
table	_	_	I-VAR
is	_	_	O
$	_	_	O
90	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
table	_	_	O
should	_	_	O
be	_	_	O
manufactured	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
monthly	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

Bob	_	_	O
has	_	_	B-CONST_DIR
100	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
agricultural	_	_	O
land	_	_	O
in	_	_	O
which	_	_	O
he	_	_	O
wants	_	_	O
to	_	_	O
plant	_	_	O
daisies	_	_	B-VAR
and	_	_	O
peonies	_	_	B-VAR
.	_	_	O
The	_	_	O
seeds	_	_	O
for	_	_	O
daisies	_	_	B-VAR
costs	_	_	O
$	_	_	O
20	_	_	B-PARAM
per	_	_	O
acre	_	_	O
,	_	_	O
whereas	_	_	O
the	_	_	O
seeds	_	_	O
for	_	_	O
peonies	_	_	B-VAR
costs	_	_	O
$	_	_	O
35	_	_	B-PARAM
per	_	_	O
acre	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
daisies	_	_	B-VAR
is	_	_	O
$	_	_	O
55	_	_	B-PARAM
,	_	_	O
whereas	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
for	_	_	O
peonies	_	_	B-VAR
is	_	_	O
$	_	_	O
80	_	_	B-PARAM
an	_	_	O
acre	_	_	O
.	_	_	O
If	_	_	O
Bob	_	_	O
has	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
budget	_	_	O
of	_	_	O
$	_	_	O
3000	_	_	B-LIMIT
to	_	_	O
spend	_	_	O
on	_	_	O
seeds	_	_	O
,	_	_	O
determine	_	_	O
how	_	_	O
many	_	_	O
daisies	_	_	B-VAR
and	_	_	O
peonies	_	_	B-VAR
he	_	_	O
needs	_	_	O
to	_	_	O
plant	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
profit	_	_	B-OBJ_NAME
.	_	_	O

Bluelight	_	_	O
Kitchen	_	_	O
makes	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
dish	_	_	O
detergents	_	_	O
:	_	_	O
Clear	_	_	B-VAR
Liquid	_	_	I-VAR
and	_	_	O
Fresh	_	_	B-VAR
Mint	_	_	I-VAR
.	_	_	O
Clear	_	_	B-VAR
Liquid	_	_	I-VAR
consists	_	_	O
of	_	_	O
15	_	_	B-PARAM
%	_	_	I-PARAM
soap	_	_	O
and	_	_	O
6.5	_	_	B-PARAM
%	_	_	I-PARAM
citric	_	_	O
acid	_	_	O
and	_	_	O
Fresh	_	_	B-VAR
Mint	_	_	I-VAR
consists	_	_	O
of	_	_	O
7	_	_	B-PARAM
%	_	_	I-PARAM
soap	_	_	O
and	_	_	O
10.5	_	_	B-PARAM
%	_	_	I-PARAM
citric	_	_	O
acid	_	_	O
.	_	_	O
After	_	_	O
doing	_	_	O
some	_	_	O
research	_	_	O
,	_	_	O
the	_	_	O
company	_	_	O
realizes	_	_	O
that	_	_	O
it	_	_	O
needs	_	_	O
to	_	_	O
use	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
25	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
soap	_	_	O
and	_	_	O
20	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
citric	_	_	O
acid	_	_	O
.	_	_	O
If	_	_	O
Clear	_	_	B-VAR
Liquid	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
6.5	_	_	B-PARAM
per	_	_	O
kg	_	_	O
and	_	_	O
Fresh	_	_	B-VAR
Mint	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
5.5	_	_	B-PARAM
per	_	_	O
kg	_	_	O
,	_	_	O
determine	_	_	O
how	_	_	O
much	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
detergents	_	_	O
should	_	_	O
be	_	_	O
produced	_	_	O
so	_	_	O
that	_	_	O
chemical	_	_	O
requirements	_	_	O
are	_	_	O
met	_	_	O
at	_	_	O
a	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
.	_	_	O

West	_	_	O
Moon	_	_	O
Designs	_	_	O
are	_	_	O
famous	_	_	O
for	_	_	O
its	_	_	O
high	_	_	O
-	_	_	O
end	_	_	O
furniture	_	_	O
.	_	_	O
Each	_	_	O
coffee	_	_	B-VAR
table	_	_	I-VAR
produced	_	_	O
by	_	_	O
West	_	_	O
Moon	_	_	O
Designs	_	_	O
nets	_	_	O
the	_	_	O
company	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
200	_	_	B-PARAM
.	_	_	O
Each	_	_	O
bookcase	_	_	B-VAR
yields	_	_	O
a	_	_	O
$	_	_	O
300	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
.	_	_	O
Every	_	_	O
week	_	_	O
,	_	_	O
120	_	_	B-LIMIT
gallons	_	_	O
of	_	_	O
lacquer	_	_	O
and	_	_	O
250	_	_	B-LIMIT
lengths	_	_	O
of	_	_	O
high	_	_	O
-	_	_	O
quality	_	_	O
mahogany	_	_	O
are	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
Each	_	_	O
coffee	_	_	B-VAR
table	_	_	I-VAR
requires	_	_	O
approximately	_	_	O
5	_	_	B-PARAM
gallons	_	_	O
of	_	_	O
lacquer	_	_	O
and	_	_	O
15	_	_	B-PARAM
lengths	_	_	O
of	_	_	O
mahogany	_	_	O
.	_	_	O
Each	_	_	O
bookcase	_	_	B-VAR
takes	_	_	O
7	_	_	B-PARAM
gallons	_	_	O
of	_	_	O
lacquer	_	_	O
and	_	_	O
25	_	_	B-PARAM
lengths	_	_	O
of	_	_	O
mahogany	_	_	O
.	_	_	O
What	_	_	O
should	_	_	O
the	_	_	O
production	_	_	O
plan	_	_	O
be	_	_	O
for	_	_	O
West	_	_	O
Moon	_	_	O
Designs	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
maximum	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Eric	_	_	O
is	_	_	O
a	_	_	O
world	_	_	O
-	_	_	O
famous	_	_	O
wood	_	_	O
artist	_	_	O
.	_	_	O
He	_	_	O
manufactures	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
decors	_	_	O
made	_	_	O
of	_	_	O
oak	_	_	O
.	_	_	O
The	_	_	O
first	_	_	O
product	_	_	O
,	_	_	O
a	_	_	O
display	_	_	B-VAR
shelf	_	_	I-VAR
,	_	_	O
requires	_	_	O
25	_	_	B-PARAM
minutes	_	_	O
each	_	_	O
for	_	_	O
carving	_	_	O
and	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
each	_	_	O
for	_	_	O
polishing	_	_	O
.	_	_	O
The	_	_	O
second	_	_	O
decor	_	_	O
is	_	_	O
a	_	_	O
plant	_	_	B-VAR
stand	_	_	I-VAR
and	_	_	O
it	_	_	O
requires	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
each	_	_	O
for	_	_	O
carving	_	_	O
and	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
each	_	_	O
for	_	_	O
polishing	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
350	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
carving	_	_	O
and	_	_	O
600	_	_	B-LIMIT
for	_	_	O
polishing	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
is	_	_	O
$	_	_	O
55	_	_	B-PARAM
each	_	_	O
for	_	_	O
the	_	_	O
display	_	_	B-VAR
shelf	_	_	I-VAR
and	_	_	O
$	_	_	O
45	_	_	B-PARAM
for	_	_	O
each	_	_	O
plant	_	_	B-VAR
stand	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
decors	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
the	_	_	O
artist	_	_	O
create	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

Bob	_	_	O
has	_	_	B-CONST_DIR
a	_	_	O
250	_	_	B-LIMIT
acre	_	_	O
berry	_	_	O
farm	_	_	O
on	_	_	O
which	_	_	O
to	_	_	O
plant	_	_	O
cranberries	_	_	B-VAR
and	_	_	O
bilberries	_	_	B-VAR
.	_	_	O
Bob	_	_	O
has	_	_	O
$	_	_	O
9000	_	_	B-LIMIT
to	_	_	O
spend	_	_	O
on	_	_	O
watering	_	_	O
and	_	_	O
600	_	_	B-LIMIT
days	_	_	O
worth	_	_	O
of	_	_	O
labor	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
For	_	_	O
each	_	_	O
acre	_	_	O
of	_	_	O
cranberries	_	_	B-VAR
,	_	_	O
5	_	_	B-PARAM
days	_	_	O
worth	_	_	O
of	_	_	O
labor	_	_	O
and	_	_	O
$	_	_	O
25	_	_	B-PARAM
in	_	_	O
watering	_	_	O
costs	_	_	O
is	_	_	O
required	_	_	O
.	_	_	O
For	_	_	O
each	_	_	O
acre	_	_	O
of	_	_	O
bilberries	_	_	B-VAR
,	_	_	O
4	_	_	B-PARAM
days	_	_	O
worth	_	_	O
of	_	_	O
labor	_	_	O
and	_	_	O
$	_	_	O
30	_	_	B-PARAM
in	_	_	O
watering	_	_	O
costs	_	_	O
is	_	_	O
required	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
cranberries	_	_	B-VAR
is	_	_	O
$	_	_	O
66	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
bilberries	_	_	B-VAR
is	_	_	O
$	_	_	O
73	_	_	B-PARAM
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
problem	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
.	_	_	O

Amy	_	_	O
owns	_	_	O
a	_	_	O
bakery	_	_	O
and	_	_	O
sells	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
bread	_	_	O
:	_	_	O
croissant	_	_	B-VAR
and	_	_	O
ficelle	_	_	B-VAR
.	_	_	O
Each	_	_	O
croissant	_	_	B-VAR
requires	_	_	O
12	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
mixing	_	_	O
and	_	_	O
2	_	_	B-PARAM
tablespoons	_	_	O
of	_	_	O
vanilla	_	_	O
extract	_	_	O
.	_	_	O
Each	_	_	O
ficelle	_	_	B-VAR
requires	_	_	O
17	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
mixing	_	_	O
and	_	_	O
1	_	_	B-PARAM
tablespoon	_	_	O
of	_	_	O
vanilla	_	_	O
extract	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
350	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
mixing	_	_	O
time	_	_	O
available	_	_	B-CONST_DIR
and	_	_	O
45	_	_	B-LIMIT
tablespoons	_	_	O
of	_	_	O
vanilla	_	_	O
extract	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
Each	_	_	O
croissant	_	_	B-VAR
can	_	_	O
be	_	_	O
sold	_	_	B-OBJ_NAME
for	_	_	O
$	_	_	O
4.5	_	_	B-PARAM
and	_	_	O
each	_	_	O
ficelle	_	_	B-VAR
can	_	_	O
be	_	_	O
sold	_	_	B-OBJ_NAME
for	_	_	O
$	_	_	O
3.5	_	_	B-PARAM
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
Amy	_	_	O
's	_	_	O
revenue	_	_	B-OBJ_NAME
,	_	_	O
then	_	_	O
graphically	_	_	O
solve	_	_	O
the	_	_	O
LP	_	_	O
.	_	_	O
(	_	_	O
A	_	_	O
fractional	_	_	O
number	_	_	O
of	_	_	O
bread	_	_	O
is	_	_	O
okay	_	_	O
)	_	_	O

X	_	_	O
-	_	_	O
Luxury	_	_	O
Cloth	_	_	O
wants	_	_	O
to	_	_	O
add	_	_	O
coats	_	_	B-VAR
and	_	_	O
skirts	_	_	B-VAR
,	_	_	O
both	_	_	O
with	_	_	O
printed	_	_	O
designs	_	_	O
,	_	_	O
to	_	_	O
its	_	_	O
collection	_	_	O
.	_	_	O
Both	_	_	O
coats	_	_	B-VAR
and	_	_	O
skirts	_	_	B-VAR
require	_	_	O
designing	_	_	O
and	_	_	O
printing	_	_	O
.	_	_	O
Each	_	_	O
coat	_	_	B-VAR
requires	_	_	O
1.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
designing	_	_	O
time	_	_	O
and	_	_	O
2.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
printing	_	_	O
time	_	_	O
.	_	_	O
Each	_	_	O
skirt	_	_	B-VAR
requires	_	_	O
3	_	_	B-PARAM
hours	_	_	O
of	_	_	O
designing	_	_	O
time	_	_	O
and	_	_	O
3.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
printing	_	_	O
time	_	_	O
.	_	_	O
The	_	_	O
designers	_	_	O
are	_	_	O
available	_	_	B-CONST_DIR
45	_	_	B-LIMIT
hours	_	_	O
a	_	_	O
week	_	_	O
and	_	_	O
the	_	_	O
printing	_	_	O
machine	_	_	O
is	_	_	O
available	_	_	B-CONST_DIR
70	_	_	B-LIMIT
hours	_	_	O
per	_	_	O
week	_	_	O
.	_	_	O
Each	_	_	O
coat	_	_	B-VAR
nets	_	_	O
the	_	_	O
company	_	_	O
$	_	_	O
12	_	_	B-PARAM
in	_	_	O
profit	_	_	B-OBJ_NAME
,	_	_	O
and	_	_	O
each	_	_	O
skirt	_	_	B-VAR
nets	_	_	O
$	_	_	O
16	_	_	B-PARAM
in	_	_	O
profit	_	_	B-OBJ_NAME
.	_	_	O
What	_	_	O
ratio	_	_	O
of	_	_	O
coats	_	_	B-VAR
and	_	_	O
skirts	_	_	B-VAR
will	_	_	O
produce	_	_	O
the	_	_	O
most	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
within	_	_	O
the	_	_	O
constraints	_	_	O
?	_	_	O

John	_	_	O
wants	_	_	O
to	_	_	O
develop	_	_	O
a	_	_	O
weight	_	_	O
loss	_	_	O
program	_	_	O
that	_	_	O
includes	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
250	_	_	B-LIMIT
units	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
45	_	_	B-LIMIT
units	_	_	O
of	_	_	O
carbs	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
two	_	_	O
cuisine	_	_	O
options	_	_	O
available	_	_	O
:	_	_	O
Vietnamese	_	_	B-VAR
and	_	_	O
Korean	_	_	B-VAR
.	_	_	O
One	_	_	O
plate	_	_	O
of	_	_	O
Vietnamese	_	_	B-VAR
food	_	_	I-VAR
contains	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
carbs	_	_	O
.	_	_	O
One	_	_	O
plate	_	_	O
of	_	_	O
Korean	_	_	B-VAR
food	_	_	I-VAR
contains	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
14	_	_	B-PARAM
units	_	_	O
of	_	_	O
carbs	_	_	O
.	_	_	O
Vietnamese	_	_	B-VAR
food	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
12.5	_	_	B-PARAM
per	_	_	O
plate	_	_	O
food	_	_	O
and	_	_	O
Korean	_	_	B-VAR
food	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
16.5	_	_	B-PARAM
per	_	_	O
plate	_	_	O
.	_	_	O
Find	_	_	O
the	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
for	_	_	O
the	_	_	O
program	_	_	O
that	_	_	O
can	_	_	O
consist	_	_	O
of	_	_	O
a	_	_	O
mixture	_	_	O
of	_	_	O
the	_	_	O
cuisines	_	_	O
and	_	_	O
at	_	_	O
the	_	_	O
same	_	_	O
time	_	_	O
meet	_	_	O
the	_	_	O
minimal	_	_	O
protein	_	_	O
and	_	_	O
carb	_	_	O
requirements	_	_	O
.	_	_	O

A	_	_	O
small	_	_	O
tea	_	_	O
shop	_	_	O
wants	_	_	O
to	_	_	O
sell	_	_	O
cups	_	_	O
of	_	_	O
green	_	_	B-VAR
tea	_	_	I-VAR
and	_	_	O
black	_	_	B-VAR
tea	_	_	I-VAR
.	_	_	O
It	_	_	O
takes	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
cup	_	_	O
of	_	_	O
green	_	_	B-VAR
tea	_	_	I-VAR
and	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
cup	_	_	O
of	_	_	O
black	_	_	B-VAR
tea	_	_	I-VAR
.	_	_	O
The	_	_	O
shop	_	_	O
owner	_	_	O
only	_	_	B-CONST_DIR
has	_	_	O
560	_	_	B-LIMIT
minutes	_	_	O
a	_	_	O
week	_	_	O
to	_	_	O
make	_	_	O
drinks	_	_	O
(	_	_	O
green	_	_	B-VAR
tea	_	_	I-VAR
and	_	_	O
black	_	_	B-VAR
tea	_	_	I-VAR
)	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
the	_	_	O
owner	_	_	O
only	_	_	O
has	_	_	O
enough	_	_	O
product	_	_	O
to	_	_	O
make	_	_	O
150	_	_	B-LIMIT
total	_	_	B-CONST_DIR
cups	_	_	O
per	_	_	O
week	_	_	O
.	_	_	O
She	_	_	O
makes	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
2	_	_	B-PARAM
on	_	_	O
each	_	_	O
cup	_	_	O
of	_	_	O
green	_	_	B-VAR
tea	_	_	I-VAR
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
3	_	_	B-PARAM
on	_	_	O
each	_	_	O
cup	_	_	O
of	_	_	O
black	_	_	B-VAR
tea	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
cups	_	_	O
of	_	_	O
green	_	_	B-VAR
tea	_	_	I-VAR
and	_	_	O
black	_	_	B-VAR
tea	_	_	I-VAR
should	_	_	O
the	_	_	O
shop	_	_	O
owner	_	_	O
make	_	_	O
each	_	_	O
week	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
,	_	_	O
assuming	_	_	O
she	_	_	O
sells	_	_	O
all	_	_	O
her	_	_	O
cups	_	_	O
?	_	_	O

Jack	_	_	O
needs	_	_	O
to	_	_	O
find	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
80	_	_	B-LIMIT
shrimps	_	_	O
and	_	_	O
50	_	_	B-LIMIT
conches	_	_	O
to	_	_	O
pay	_	_	O
his	_	_	O
monthly	_	_	O
rent	_	_	O
for	_	_	O
his	_	_	O
beach	_	_	O
house	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
two	_	_	O
beaches	_	_	O
that	_	_	O
Jack	_	_	O
frequents	_	_	O
:	_	_	O
Silver	_	_	B-VAR
Beach	_	_	I-VAR
and	_	_	O
Lucent	_	_	B-VAR
Beach	_	_	I-VAR
.	_	_	O
Each	_	_	O
day	_	_	B-OBJ_NAME
at	_	_	O
Silver	_	_	B-VAR
beach	_	_	I-VAR
,	_	_	O
Jack	_	_	O
finds	_	_	O
7	_	_	B-PARAM
shrimps	_	_	O
and	_	_	O
3	_	_	B-PARAM
conches	_	_	O
.	_	_	O
Each	_	_	O
day	_	_	B-OBJ_NAME
at	_	_	O
Lucent	_	_	B-VAR
Beach	_	_	I-VAR
,	_	_	O
Jack	_	_	O
finds	_	_	O
4	_	_	B-PARAM
shrimps	_	_	O
and	_	_	O
6	_	_	B-PARAM
conches	_	_	O
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
to	_	_	O
help	_	_	O
Jack	_	_	O
meet	_	_	O
his	_	_	O
requirements	_	_	O
while	_	_	O
spending	_	_	O
a	_	_	O
minimal	_	_	B-OBJ_DIR
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
time	_	_	I-OBJ_NAME
.	_	_	O

An	_	_	O
electronics	_	_	O
store	_	_	O
owner	_	_	O
wants	_	_	O
to	_	_	O
know	_	_	O
how	_	_	O
many	_	_	O
headsets	_	_	B-VAR
and	_	_	O
keyboards	_	_	B-VAR
are	_	_	O
enough	_	_	O
to	_	_	O
keep	_	_	O
in	_	_	O
inventory	_	_	O
.	_	_	O
A	_	_	O
headset	_	_	B-VAR
will	_	_	O
earn	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
80	_	_	B-PARAM
in	_	_	O
profits	_	_	B-OBJ_NAME
,	_	_	O
and	_	_	O
a	_	_	O
keyboard	_	_	B-VAR
will	_	_	O
earn	_	_	O
$	_	_	O
50	_	_	B-PARAM
.	_	_	O
A	_	_	O
headset	_	_	B-VAR
requires	_	_	O
2.5	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
of	_	_	O
floor	_	_	O
space	_	_	O
,	_	_	O
whereas	_	_	O
a	_	_	O
keyboard	_	_	B-VAR
requires	_	_	O
1.5	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
.	_	_	O
In	_	_	O
total	_	_	O
,	_	_	O
200	_	_	B-LIMIT
sq	_	_	O
ft	_	_	O
of	_	_	O
floor	_	_	O
space	_	_	O
is	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
The	_	_	O
store	_	_	O
stocks	_	_	O
only	_	_	O
headsets	_	_	B-VAR
and	_	_	O
keyboards	_	_	B-VAR
.	_	_	O
Corporate	_	_	O
has	_	_	O
required	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
70	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
all	_	_	O
appliances	_	_	O
in	_	_	O
stock	_	_	O
be	_	_	O
keyboards	_	_	B-VAR
.	_	_	O
Finally	_	_	O
,	_	_	O
a	_	_	O
headset	_	_	B-VAR
costs	_	_	O
$	_	_	O
200	_	_	B-PARAM
for	_	_	O
the	_	_	O
store	_	_	O
,	_	_	O
and	_	_	O
a	_	_	O
keyboard	_	_	B-VAR
,	_	_	O
$	_	_	O
110	_	_	B-PARAM
.	_	_	O
The	_	_	O
store	_	_	O
wants	_	_	O
to	_	_	O
spend	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
10000	_	_	B-LIMIT
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
that	_	_	O
can	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
store	_	_	O
's	_	_	O
profit	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
small	_	_	O
wood	_	_	O
shop	_	_	O
specializing	_	_	O
in	_	_	O
furniture	_	_	O
can	_	_	O
make	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
40	_	_	B-LIMIT
bookcases	_	_	B-VAR
and	_	_	O
60	_	_	B-LIMIT
coffee	_	_	B-VAR
tables	_	_	I-VAR
in	_	_	O
a	_	_	O
week	_	_	O
.	_	_	O
It	_	_	O
takes	_	_	O
a	_	_	O
worker	_	_	O
7	_	_	B-PARAM
hours	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
bookcase	_	_	B-VAR
and	_	_	O
5	_	_	B-PARAM
hours	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
coffee	_	_	B-VAR
table	_	_	I-VAR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
on	_	_	O
a	_	_	O
bookcase	_	_	B-VAR
is	_	_	O
$	_	_	O
90	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
on	_	_	O
a	_	_	O
coffee	_	_	B-VAR
table	_	_	I-VAR
is	_	_	O
$	_	_	O
65	_	_	B-PARAM
.	_	_	O
The	_	_	O
total	_	_	O
number	_	_	O
of	_	_	O
hours	_	_	O
by	_	_	O
all	_	_	O
of	_	_	O
the	_	_	O
employees	_	_	O
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
150	_	_	B-LIMIT
hours	_	_	O
per	_	_	O
week	_	_	O
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
problem	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
gem	_	_	O
store	_	_	O
makes	_	_	O
earrings	_	_	B-VAR
and	_	_	O
watches	_	_	B-VAR
using	_	_	O
gems	_	_	O
,	_	_	O
each	_	_	O
requiring	_	_	O
the	_	_	O
use	_	_	O
of	_	_	O
a	_	_	O
heating	_	_	O
machine	_	_	O
and	_	_	O
a	_	_	O
polishing	_	_	O
machine	_	_	O
.	_	_	O
On	_	_	O
any	_	_	O
day	_	_	O
,	_	_	O
the	_	_	O
heating	_	_	O
machine	_	_	O
is	_	_	O
available	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
the	_	_	I-CONST_DIR
most	_	_	I-CONST_DIR
14	_	_	B-LIMIT
hours	_	_	O
and	_	_	O
the	_	_	O
polishing	_	_	O
machine	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
the	_	_	I-CONST_DIR
most	_	_	I-CONST_DIR
10	_	_	B-LIMIT
hours	_	_	O
.	_	_	O
It	_	_	O
takes	_	_	O
2	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
heating	_	_	O
machine	_	_	O
and	_	_	O
1.5	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
polishing	_	_	O
machine	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
pair	_	_	O
of	_	_	O
earrings	_	_	B-VAR
.	_	_	O
It	_	_	O
takes	_	_	O
3.5	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
heating	_	_	O
machine	_	_	O
and	_	_	O
2	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
polishing	_	_	O
machine	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
watch	_	_	B-VAR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
from	_	_	O
the	_	_	O
sale	_	_	O
of	_	_	O
a	_	_	O
pair	_	_	O
of	_	_	O
earrings	_	_	B-VAR
is	_	_	O
$	_	_	O
45	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
from	_	_	O
the	_	_	O
sale	_	_	O
of	_	_	O
a	_	_	O
watch	_	_	B-VAR
is	_	_	O
$	_	_	O
70	_	_	B-PARAM
.	_	_	O
Assuming	_	_	O
the	_	_	O
store	_	_	O
can	_	_	O
sell	_	_	O
all	_	_	O
the	_	_	O
earrings	_	_	B-VAR
and	_	_	O
watches	_	_	B-VAR
it	_	_	O
makes	_	_	O
,	_	_	O
how	_	_	O
should	_	_	O
the	_	_	O
store	_	_	O
owner	_	_	O
schedule	_	_	O
his	_	_	O
daily	_	_	O
production	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
food	_	_	O
store	_	_	O
owner	_	_	O
can	_	_	O
spend	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
1000	_	_	B-LIMIT
on	_	_	O
lemons	_	_	B-VAR
and	_	_	O
bananas	_	_	B-VAR
.	_	_	O
A	_	_	O
lemon	_	_	B-VAR
costs	_	_	O
the	_	_	O
food	_	_	O
store	_	_	O
owner	_	_	O
$	_	_	O
3	_	_	B-PARAM
and	_	_	O
a	_	_	O
banana	_	_	B-VAR
costs	_	_	O
him	_	_	O
$	_	_	O
1.5	_	_	B-PARAM
.	_	_	O
Spices	_	_	O
are	_	_	O
added	_	_	O
and	_	_	O
each	_	_	O
lemon	_	_	B-VAR
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
2	_	_	B-PARAM
while	_	_	O
each	_	_	O
banana	_	_	B-VAR
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
1	_	_	B-PARAM
.	_	_	O
The	_	_	O
owner	_	_	O
estimates	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
250	_	_	B-LIMIT
lemons	_	_	B-VAR
but	_	_	O
at	_	_	B-CONST_DIR
the	_	_	I-CONST_DIR
most	_	_	I-CONST_DIR
300	_	_	B-LIMIT
are	_	_	O
sold	_	_	O
each	_	_	O
month	_	_	O
.	_	_	O
He	_	_	O
also	_	_	O
estimates	_	_	O
that	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
bananas	_	_	B-VAR
sold	_	_	O
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
a	_	_	B-PARAM
third	_	_	I-PARAM
of	_	_	O
the	_	_	O
lemons	_	_	B-VAR
sold	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
lemons	_	_	B-VAR
and	_	_	O
bananas	_	_	B-VAR
should	_	_	O
be	_	_	O
sold	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
car	_	_	O
company	_	_	O
manufactures	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
vehicles	_	_	O
:	_	_	O
minivans	_	_	B-VAR
and	_	_	O
SUVs	_	_	B-VAR
.	_	_	O
A	_	_	O
minivan	_	_	B-VAR
requires	_	_	O
9	_	_	B-PARAM
hours	_	_	O
of	_	_	O
engineering	_	_	O
time	_	_	O
while	_	_	O
an	_	_	O
SUV	_	_	B-VAR
requires	_	_	O
7	_	_	B-PARAM
hours	_	_	O
of	_	_	O
engineering	_	_	O
time	_	_	O
.	_	_	O
Both	_	_	O
vehicles	_	_	O
require	_	_	O
25	_	_	B-PARAM
kg	_	_	O
of	_	_	O
steel	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
receives	_	_	B-CONST_DIR
1200	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
steel	_	_	O
each	_	_	O
week	_	_	O
and	_	_	O
a	_	_	O
total	_	_	O
of	_	_	O
450	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
engineering	_	_	O
time	_	_	O
is	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
Each	_	_	O
minivan	_	_	B-VAR
nets	_	_	O
$	_	_	O
5500	_	_	B-PARAM
in	_	_	O
profit	_	_	B-OBJ_NAME
,	_	_	O
while	_	_	O
each	_	_	O
SUV	_	_	B-VAR
nets	_	_	O
$	_	_	O
4000	_	_	B-PARAM
in	_	_	O
profit	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
company	_	_	O
wishes	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
.	_	_	O
Ignoring	_	_	O
the	_	_	O
divisibility	_	_	O
issues	_	_	O
,	_	_	O
construct	_	_	O
a	_	_	O
linear	_	_	O
programming	_	_	O
problem	_	_	O
whose	_	_	O
solution	_	_	O
will	_	_	O
determine	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
vehicle	_	_	O
the	_	_	O
company	_	_	O
should	_	_	O
produce	_	_	O
.	_	_	O

John	_	_	O
's	_	_	O
trainer	_	_	O
has	_	_	O
given	_	_	O
him	_	_	O
a	_	_	O
list	_	_	O
of	_	_	O
available	_	_	O
food	_	_	O
options	_	_	O
as	_	_	O
well	_	_	O
as	_	_	O
the	_	_	O
macronutrient	_	_	O
content	_	_	O
and	_	_	O
cost	_	_	O
per	_	_	O
serving	_	_	O
of	_	_	O
each	_	_	O
food	_	_	O
.	_	_	O
A	_	_	O
certain	_	_	O
amount	_	_	O
of	_	_	O
macronutrients	_	_	O
is	_	_	O
required	_	_	O
each	_	_	O
day	_	_	O
.	_	_	O
For	_	_	O
example	_	_	O
,	_	_	O
here	_	_	O
is	_	_	O
the	_	_	O
data	_	_	O
corresponding	_	_	O
to	_	_	O
rice	_	_	B-VAR
and	_	_	O
beef	_	_	B-VAR
and	_	_	O
the	_	_	O
three	_	_	O
macronutrients	_	_	O
(	_	_	O
proteins	_	_	O
,	_	_	O
carbs	_	_	O
,	_	_	O
and	_	_	O
fat	_	_	O
)	_	_	O
.	_	_	O
Each	_	_	O
serving	_	_	O
of	_	_	O
rice	_	_	B-VAR
contains	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
80	_	_	B-PARAM
units	_	_	O
of	_	_	O
carbs	_	_	O
,	_	_	O
and	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
Each	_	_	O
serving	_	_	O
of	_	_	O
beef	_	_	B-VAR
contains	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
200	_	_	B-PARAM
units	_	_	O
of	_	_	O
carbs	_	_	O
,	_	_	O
and	_	_	O
16	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
A	_	_	O
serving	_	_	O
of	_	_	O
rice	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
a	_	_	O
serving	_	_	O
of	_	_	O
beef	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
30	_	_	B-PARAM
.	_	_	O
John	_	_	O
's	_	_	O
trainer	_	_	O
requires	_	_	O
him	_	_	O
to	_	_	O
get	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
units	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
1000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
carbs	_	_	O
,	_	_	O
and	_	_	O
40	_	_	B-LIMIT
units	_	_	O
of	_	_	O
fat	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
Find	_	_	O
out	_	_	O
how	_	_	O
many	_	_	O
servings	_	_	O
of	_	_	O
each	_	_	O
food	_	_	O
to	_	_	O
consume	_	_	O
per	_	_	O
day	_	_	O
to	_	_	O
meet	_	_	O
the	_	_	O
requirements	_	_	O
at	_	_	O
minimal	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
fruit	_	_	O
store	_	_	O
wants	_	_	O
to	_	_	O
liquidate	_	_	O
its	_	_	O
stock	_	_	B-CONST_DIR
of	_	_	O
30	_	_	B-LIMIT
lemons	_	_	O
,	_	_	O
40	_	_	B-LIMIT
mangos	_	_	O
,	_	_	O
and	_	_	O
50	_	_	B-LIMIT
pears	_	_	O
.	_	_	O
Given	_	_	O
past	_	_	O
experience	_	_	O
,	_	_	O
the	_	_	O
store	_	_	O
knows	_	_	O
that	_	_	O
they	_	_	O
can	_	_	O
propose	_	_	O
a	_	_	O
mango	_	_	B-VAR
-	_	_	I-VAR
lovers	_	_	I-VAR
package	_	_	I-VAR
with	_	_	O
4	_	_	B-PARAM
lemons	_	_	O
and	_	_	O
8	_	_	B-PARAM
mangos	_	_	O
and	_	_	O
that	_	_	O
this	_	_	O
package	_	_	O
will	_	_	O
bring	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
5	_	_	B-PARAM
euros	_	_	O
.	_	_	O
Similarly	_	_	O
,	_	_	O
they	_	_	O
can	_	_	O
prepare	_	_	O
a	_	_	O
regular	_	_	B-VAR
package	_	_	I-VAR
with	_	_	O
3	_	_	B-PARAM
lemons	_	_	O
,	_	_	O
5	_	_	B-PARAM
mangos	_	_	O
,	_	_	O
and	_	_	O
10	_	_	B-PARAM
pears	_	_	O
,	_	_	O
yielding	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
6.5	_	_	B-PARAM
euros	_	_	O
.	_	_	O
They	_	_	O
know	_	_	O
they	_	_	O
can	_	_	O
sell	_	_	O
any	_	_	O
quantity	_	_	O
of	_	_	O
these	_	_	O
two	_	_	O
packages	_	_	O
within	_	_	O
the	_	_	O
availability	_	_	O
of	_	_	O
its	_	_	O
stock	_	_	O
.	_	_	O
What	_	_	O
quantity	_	_	O
of	_	_	O
each	_	_	O
package	_	_	O
,	_	_	O
mango	_	_	B-VAR
-	_	_	I-VAR
lovers	_	_	I-VAR
packages	_	_	I-VAR
and	_	_	O
regular	_	_	B-VAR
packages	_	_	I-VAR
,	_	_	O
should	_	_	O
the	_	_	O
store	_	_	O
prepare	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
net	_	_	B-OBJ_NAME
profit	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
paint	_	_	O
manufacturer	_	_	O
produces	_	_	B-CONST_DIR
350	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
dye	_	_	O
and	_	_	O
250	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
filler	_	_	O
each	_	_	O
week	_	_	O
.	_	_	O
By	_	_	O
using	_	_	O
different	_	_	O
techniques	_	_	O
,	_	_	O
they	_	_	O
can	_	_	O
produce	_	_	O
three	_	_	O
different	_	_	O
paint	_	_	O
products	_	_	O
for	_	_	O
sale	_	_	O
:	_	_	O
oil	_	_	B-VAR
paintings	_	_	I-VAR
,	_	_	O
acrylic	_	_	B-VAR
paintings	_	_	I-VAR
,	_	_	O
and	_	_	O
watercolor	_	_	B-VAR
paintings	_	_	I-VAR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
kg	_	_	O
for	_	_	O
selling	_	_	O
the	_	_	O
paint	_	_	O
is	_	_	O
$	_	_	O
150	_	_	B-PARAM
,	_	_	O
$	_	_	O
180	_	_	B-PARAM
,	_	_	O
$	_	_	O
220	_	_	B-PARAM
for	_	_	O
the	_	_	O
oil	_	_	B-VAR
painting	_	_	I-VAR
,	_	_	O
acrylic	_	_	B-VAR
painting	_	_	I-VAR
,	_	_	O
and	_	_	O
watercolor	_	_	B-VAR
painting	_	_	I-VAR
respectively	_	_	O
.	_	_	O
Producing	_	_	O
1	_	_	O
kg	_	_	O
of	_	_	O
oil	_	_	B-VAR
paintings	_	_	I-VAR
requires	_	_	O
6.5	_	_	B-PARAM
kg	_	_	O
of	_	_	O
dye	_	_	O
and	_	_	O
15	_	_	B-PARAM
kg	_	_	O
of	_	_	O
filler	_	_	O
.	_	_	O
Producing	_	_	O
1	_	_	O
kg	_	_	O
of	_	_	O
acrylic	_	_	B-VAR
paintings	_	_	I-VAR
requires	_	_	O
8	_	_	B-PARAM
kg	_	_	O
of	_	_	O
dye	_	_	O
and	_	_	O
12	_	_	B-PARAM
kg	_	_	O
of	_	_	O
filler	_	_	O
.	_	_	O
Producing	_	_	O
1	_	_	O
kg	_	_	O
of	_	_	O
watercolor	_	_	B-VAR
paintings	_	_	I-VAR
requires	_	_	O
16	_	_	B-PARAM
kg	_	_	O
of	_	_	O
dye	_	_	O
and	_	_	O
5	_	_	B-PARAM
kg	_	_	O
of	_	_	O
filler	_	_	O
.	_	_	O
Formulate	_	_	O
the	_	_	O
problem	_	_	O
of	_	_	O
deciding	_	_	O
how	_	_	O
much	_	_	O
of	_	_	O
each	_	_	O
paint	_	_	O
to	_	_	O
make	_	_	O
each	_	_	O
week	_	_	O
as	_	_	O
a	_	_	O
LP	_	_	O
problem	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
.	_	_	O

Julia	_	_	O
is	_	_	O
on	_	_	O
a	_	_	O
strict	_	_	O
diet	_	_	O
and	_	_	O
insists	_	_	O
on	_	_	O
only	_	_	O
taking	_	_	O
vanilla	_	_	B-VAR
protein	_	_	I-VAR
bars	_	_	I-VAR
and	_	_	O
organic	_	_	O
meal	_	_	B-VAR
replacement	_	_	I-VAR
shakes	_	_	I-VAR
.	_	_	O
She	_	_	O
wants	_	_	O
to	_	_	O
save	_	_	O
money	_	_	O
and	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
cost	_	_	B-OBJ_NAME
but	_	_	O
must	_	_	O
get	_	_	O
enough	_	_	O
protein	_	_	O
and	_	_	O
carbs	_	_	O
,	_	_	O
and	_	_	O
not	_	_	O
too	_	_	O
much	_	_	O
fat	_	_	O
.	_	_	O
Vanilla	_	_	B-VAR
protein	_	_	I-VAR
bars	_	_	I-VAR
cost	_	_	B-OBJ_NAME
$	_	_	O
10	_	_	B-PARAM
per	_	_	O
serving	_	_	O
and	_	_	O
contain	_	_	O
30	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
50	_	_	B-PARAM
units	_	_	O
of	_	_	O
carbs	_	_	O
,	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
Organic	_	_	O
meal	_	_	B-VAR
replacement	_	_	I-VAR
shakes	_	_	I-VAR
cost	_	_	B-OBJ_NAME
$	_	_	O
15	_	_	B-PARAM
per	_	_	O
serving	_	_	O
and	_	_	O
contain	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
carbs	_	_	O
,	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
Julia	_	_	O
requires	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
155	_	_	B-LIMIT
units	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
140	_	_	B-LIMIT
units	_	_	O
of	_	_	O
carbs	_	_	O
but	_	_	O
must	_	_	O
not	_	_	B-CONST_DIR
eat	_	_	I-CONST_DIR
more	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
55	_	_	B-LIMIT
units	_	_	O
of	_	_	O
fat	_	_	O
each	_	_	O
day	_	_	O
.	_	_	O
Formulate	_	_	O
the	_	_	O
problem	_	_	O
as	_	_	O
an	_	_	O
LP	_	_	O
problem	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
minimize	_	_	O
cost	_	_	O
.	_	_	O

One	_	_	O
batch	_	_	O
of	_	_	O
shortbread	_	_	B-VAR
cookies	_	_	I-VAR
is	_	_	O
made	_	_	O
of	_	_	O
256	_	_	B-PARAM
g	_	_	O
of	_	_	O
flour	_	_	O
and	_	_	O
200	_	_	B-PARAM
g	_	_	O
of	_	_	O
butter	_	_	O
while	_	_	O
a	_	_	O
batch	_	_	O
of	_	_	O
peanut	_	_	B-VAR
butter	_	_	I-VAR
cookies	_	_	I-VAR
requires	_	_	O
180	_	_	B-PARAM
g	_	_	O
of	_	_	O
flour	_	_	O
and	_	_	O
250	_	_	B-PARAM
g	_	_	O
of	_	_	O
butter	_	_	O
.	_	_	O
Please	_	_	O
find	_	_	O
the	_	_	O
maximum	_	_	B-OBJ_DIR
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
batches	_	_	I-OBJ_NAME
of	_	_	O
cookies	_	_	O
we	_	_	O
can	_	_	O
bake	_	_	O
using	_	_	B-OBJ_DIR
3500	_	_	B-PARAM
g	_	_	O
of	_	_	O
flour	_	_	O
and	_	_	O
2500	_	_	B-PARAM
g	_	_	O
of	_	_	O
butter	_	_	O
assuming	_	_	O
that	_	_	O
there	_	_	O
is	_	_	O
no	_	_	O
shortage	_	_	O
of	_	_	O
the	_	_	O
other	_	_	O
ingredients	_	_	O
used	_	_	O
in	_	_	O
making	_	_	O
the	_	_	O
cookies	_	_	O
.	_	_	O

Peter	_	_	O
produces	_	_	O
a	_	_	O
plant	_	_	O
growth	_	_	O
compound	_	_	O
by	_	_	O
mixing	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
fertilizer	_	_	O
:	_	_	O
GreenCycle	_	_	B-VAR
and	_	_	O
GrowSafe	_	_	B-VAR
.	_	_	O
This	_	_	O
growth	_	_	O
compound	_	_	O
must	_	_	O
contain	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
9	_	_	B-LIMIT
units	_	_	O
of	_	_	O
nitrous	_	_	O
oxide	_	_	O
and	_	_	O
5	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamin	_	_	O
mix	_	_	O
.	_	_	O
Fertilizer	_	_	O
GreenCycle	_	_	B-VAR
and	_	_	O
GrowSafe	_	_	B-VAR
cost	_	_	B-OBJ_NAME
$	_	_	O
1.5	_	_	B-PARAM
and	_	_	O
$	_	_	O
1.8	_	_	B-PARAM
per	_	_	O
kg	_	_	O
,	_	_	O
respectively	_	_	O
.	_	_	O
Fertilizer	_	_	O
GreenCycle	_	_	B-VAR
contains	_	_	O
2.1	_	_	B-PARAM
units	_	_	O
of	_	_	O
nitrous	_	_	O
oxide	_	_	O
per	_	_	O
kg	_	_	O
and	_	_	O
1.3	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
mix	_	_	O
per	_	_	O
kg	_	_	O
.	_	_	O
Fertilizer	_	_	O
GrowSafe	_	_	B-VAR
contains	_	_	O
3.5	_	_	B-PARAM
units	_	_	O
of	_	_	O
nitrous	_	_	O
oxide	_	_	O
per	_	_	O
kg	_	_	O
and	_	_	O
1.1	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
mix	_	_	O
per	_	_	O
kg	_	_	O
.	_	_	O
Determine	_	_	O
the	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
of	_	_	O
Peter	_	_	O
's	_	_	O
compound	_	_	O
.	_	_	O

Tom	_	_	O
Bakery	_	_	O
bakes	_	_	O
pancakes	_	_	B-VAR
and	_	_	O
pretzels	_	_	B-VAR
.	_	_	O
A	_	_	O
batch	_	_	O
of	_	_	O
pancakes	_	_	B-VAR
can	_	_	O
be	_	_	O
made	_	_	O
using	_	_	O
2.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
oven	_	_	O
time	_	_	O
and	_	_	O
0.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
pastry	_	_	O
chef	_	_	O
time	_	_	O
.	_	_	O
A	_	_	O
batch	_	_	O
of	_	_	O
pretzels	_	_	B-VAR
is	_	_	O
more	_	_	O
complicated	_	_	O
,	_	_	O
so	_	_	O
while	_	_	O
they	_	_	O
take	_	_	O
1.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
oven	_	_	O
time	_	_	O
,	_	_	O
they	_	_	O
take	_	_	O
3	_	_	B-PARAM
hours	_	_	O
of	_	_	O
pastry	_	_	O
chef	_	_	O
time	_	_	O
.	_	_	O
In	_	_	O
a	_	_	O
day	_	_	O
,	_	_	O
the	_	_	O
bakery	_	_	O
has	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
65	_	_	B-LIMIT
hours	_	_	O
available	_	_	O
for	_	_	O
the	_	_	O
oven	_	_	O
and	_	_	O
35	_	_	B-LIMIT
pastry	_	_	O
chef	_	_	O
hours	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
Using	_	_	O
all	_	_	O
the	_	_	O
available	_	_	O
capacity	_	_	O
,	_	_	O
what	_	_	O
is	_	_	O
the	_	_	O
maximum	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
the	_	_	O
bakery	_	_	O
can	_	_	O
generate	_	_	O
assuming	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
batch	_	_	O
is	_	_	O
$	_	_	O
25	_	_	B-PARAM
and	_	_	O
$	_	_	O
50	_	_	B-PARAM
respectively	_	_	O
for	_	_	O
a	_	_	O
batch	_	_	O
of	_	_	O
pancakes	_	_	B-VAR
and	_	_	O
a	_	_	O
batch	_	_	O
of	_	_	O
pretzels	_	_	B-VAR
.	_	_	O

A	_	_	O
bike	_	_	O
factory	_	_	O
builds	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
bikes	_	_	O
:	_	_	O
road	_	_	B-VAR
bikes	_	_	I-VAR
and	_	_	O
mountain	_	_	B-VAR
bikes	_	_	I-VAR
.	_	_	O
One	_	_	O
road	_	_	B-VAR
bike	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
hours	_	_	O
of	_	_	O
tooling	_	_	O
on	_	_	O
the	_	_	O
grinder	_	_	O
and	_	_	O
then	_	_	O
2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
tooling	_	_	O
on	_	_	O
the	_	_	O
polisher	_	_	O
.	_	_	O
One	_	_	O
mountain	_	_	B-VAR
bike	_	_	I-VAR
requires	_	_	O
5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
tooling	_	_	O
on	_	_	O
the	_	_	O
grinder	_	_	O
and	_	_	O
then	_	_	O
2.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
tooling	_	_	O
on	_	_	O
the	_	_	O
polisher	_	_	O
.	_	_	O
The	_	_	O
factory	_	_	O
makes	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
70	_	_	B-PARAM
per	_	_	O
road	_	_	B-VAR
bike	_	_	I-VAR
and	_	_	O
$	_	_	O
100	_	_	B-PARAM
per	_	_	O
mountain	_	_	B-VAR
bike	_	_	I-VAR
.	_	_	O
Each	_	_	O
machine	_	_	O
,	_	_	O
the	_	_	O
grinder	_	_	O
and	_	_	O
polisher	_	_	O
,	_	_	O
can	_	_	O
only	_	_	O
be	_	_	O
used	_	_	O
for	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
12	_	_	B-LIMIT
hours	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
units	_	_	O
of	_	_	O
each	_	_	O
,	_	_	O
road	_	_	B-VAR
bikes	_	_	I-VAR
and	_	_	O
mountain	_	_	B-VAR
bikes	_	_	I-VAR
,	_	_	O
should	_	_	O
the	_	_	O
factory	_	_	O
produce	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
furniture	_	_	O
factory	_	_	O
makes	_	_	O
two	_	_	O
products	_	_	O
:	_	_	O
bedside	_	_	B-VAR
tables	_	_	I-VAR
and	_	_	O
bookcases	_	_	B-VAR
.	_	_	O
Both	_	_	O
products	_	_	O
have	_	_	O
to	_	_	O
go	_	_	O
through	_	_	O
two	_	_	O
processes	_	_	O
:	_	_	O
crafting	_	_	O
and	_	_	O
polishing	_	_	O
.	_	_	O
For	_	_	O
each	_	_	O
bedside	_	_	B-VAR
table	_	_	I-VAR
,	_	_	O
the	_	_	O
workers	_	_	O
spend	_	_	O
2.5	_	_	B-PARAM
hours	_	_	O
crafting	_	_	O
and	_	_	O
1.5	_	_	B-PARAM
hours	_	_	O
polishing	_	_	O
.	_	_	O
For	_	_	O
each	_	_	O
bookcase	_	_	B-VAR
,	_	_	O
the	_	_	O
workers	_	_	O
spend	_	_	O
5	_	_	B-PARAM
hours	_	_	O
crafting	_	_	O
and	_	_	O
3	_	_	B-PARAM
hours	_	_	O
polishing	_	_	O
.	_	_	O
On	_	_	O
any	_	_	O
day	_	_	O
,	_	_	O
there	_	_	O
is	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
30	_	_	B-LIMIT
crafting	_	_	O
hours	_	_	O
available	_	_	O
and	_	_	O
20	_	_	B-LIMIT
polishing	_	_	O
hours	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
from	_	_	O
the	_	_	O
sale	_	_	O
of	_	_	O
each	_	_	O
bedside	_	_	B-VAR
table	_	_	I-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
from	_	_	O
the	_	_	O
sale	_	_	O
of	_	_	O
each	_	_	O
bookcase	_	_	B-VAR
is	_	_	O
$	_	_	O
500	_	_	B-PARAM
.	_	_	O
The	_	_	O
factory	_	_	O
can	_	_	O
sell	_	_	O
everything	_	_	O
they	_	_	O
make	_	_	O
.	_	_	O
How	_	_	O
should	_	_	O
they	_	_	O
schedule	_	_	O
daily	_	_	O
production	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

John	_	_	O
Designs	_	_	O
crafts	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
necklaces	_	_	O
:	_	_	O
platinum	_	_	B-VAR
and	_	_	O
silver	_	_	B-VAR
necklaces	_	_	I-VAR
.	_	_	O
Each	_	_	O
platinum	_	_	B-VAR
necklace	_	_	I-VAR
takes	_	_	O
4	_	_	B-PARAM
hours	_	_	O
to	_	_	O
design	_	_	O
and	_	_	O
15	_	_	B-PARAM
hours	_	_	O
to	_	_	O
craft	_	_	O
.	_	_	O
Each	_	_	O
silver	_	_	B-VAR
necklace	_	_	I-VAR
takes	_	_	O
7	_	_	B-PARAM
hours	_	_	O
to	_	_	O
design	_	_	O
and	_	_	O
5	_	_	B-PARAM
hours	_	_	O
to	_	_	O
craft	_	_	O
.	_	_	O
The	_	_	O
designing	_	_	O
team	_	_	O
is	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
35	_	_	B-LIMIT
hours	_	_	O
and	_	_	O
the	_	_	O
crafting	_	_	O
team	_	_	O
is	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
40	_	_	B-LIMIT
hours	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
is	_	_	O
$	_	_	O
2000	_	_	B-PARAM
per	_	_	O
platinum	_	_	B-VAR
necklace	_	_	I-VAR
and	_	_	O
$	_	_	O
700	_	_	B-PARAM
per	_	_	O
silver	_	_	B-VAR
necklace	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
necklaces	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
their	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

Emma	_	_	O
wants	_	_	O
to	_	_	O
eat	_	_	O
a	_	_	O
diet	_	_	O
that	_	_	O
includes	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
120	_	_	B-LIMIT
units	_	_	O
of	_	_	O
proteins	_	_	O
and	_	_	O
30	_	_	B-LIMIT
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
She	_	_	O
can	_	_	O
eat	_	_	O
pork	_	_	B-VAR
and	_	_	O
shrimp	_	_	B-VAR
to	_	_	O
supplement	_	_	O
her	_	_	O
current	_	_	O
vegetable	_	_	O
-	_	_	O
based	_	_	O
diet	_	_	O
.	_	_	O
Pork	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
3	_	_	B-PARAM
per	_	_	O
unit	_	_	O
and	_	_	O
shrimp	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
5.5	_	_	B-PARAM
per	_	_	O
unit	_	_	O
.	_	_	O
One	_	_	O
unit	_	_	O
of	_	_	O
Pork	_	_	B-VAR
has	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
proteins	_	_	O
and	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
One	_	_	O
unit	_	_	O
of	_	_	O
shrimp	_	_	B-VAR
has	_	_	O
22	_	_	B-PARAM
units	_	_	O
of	_	_	O
proteins	_	_	O
and	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
Formulate	_	_	O
this	_	_	O
as	_	_	O
a	_	_	O
linear	_	_	O
programming	_	_	O
problem	_	_	O
.	_	_	O
Find	_	_	O
the	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
for	_	_	O
a	_	_	O
diet	_	_	O
that	_	_	O
consists	_	_	O
of	_	_	O
a	_	_	O
mixture	_	_	O
of	_	_	O
these	_	_	O
foods	_	_	O
and	_	_	O
also	_	_	O
meets	_	_	O
the	_	_	O
minimal	_	_	O
nutritional	_	_	O
requirements	_	_	O
.	_	_	O

A	_	_	O
factory	_	_	O
makes	_	_	O
tomato	_	_	O
paste	_	_	O
using	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
tomatoes	_	_	O
.	_	_	O
Cherry	_	_	B-VAR
tomatoes	_	_	I-VAR
contain	_	_	O
5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
sugar	_	_	O
per	_	_	O
unit	_	_	O
and	_	_	O
1.5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
acid	_	_	O
per	_	_	O
unit	_	_	O
.	_	_	O
Cocktail	_	_	B-VAR
tomatoes	_	_	I-VAR
contain	_	_	O
2.5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
sugar	_	_	O
per	_	_	O
unit	_	_	O
and	_	_	O
3	_	_	B-PARAM
grams	_	_	O
of	_	_	O
acid	_	_	O
per	_	_	O
unit	_	_	O
.	_	_	O
Past	_	_	O
sales	_	_	O
has	_	_	O
shown	_	_	O
that	_	_	O
the	_	_	O
factory	_	_	O
needs	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
350	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
sugar	_	_	O
and	_	_	O
250	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
acid	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
tasty	_	_	O
tomato	_	_	O
paste	_	_	O
.	_	_	O
If	_	_	O
cherry	_	_	B-VAR
tomatoes	_	_	I-VAR
cost	_	_	B-OBJ_NAME
$	_	_	O
3	_	_	B-PARAM
per	_	_	O
unit	_	_	O
and	_	_	O
cocktail	_	_	B-VAR
tomatoes	_	_	I-VAR
cost	_	_	B-OBJ_NAME
$	_	_	O
4	_	_	B-PARAM
per	_	_	O
unit	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
units	_	_	O
of	_	_	O
each	_	_	O
tomato	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
make	_	_	O
the	_	_	O
tasty	_	_	O
tomato	_	_	O
paste	_	_	O
at	_	_	O
a	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
.	_	_	O
What	_	_	O
is	_	_	O
this	_	_	O
cost	_	_	O
?	_	_	O

A	_	_	O
farm	_	_	O
wants	_	_	O
to	_	_	O
manufacture	_	_	O
a	_	_	O
special	_	_	O
plant	_	_	O
growth	_	_	O
compound	_	_	O
using	_	_	O
two	_	_	O
fertilizers	_	_	O
:	_	_	O
P100	_	_	B-VAR
and	_	_	O
Y200	_	_	B-VAR
.	_	_	O
Each	_	_	O
kg	_	_	O
of	_	_	O
fertilizer	_	_	B-VAR
P100	_	_	I-VAR
contains	_	_	O
11	_	_	B-PARAM
units	_	_	O
of	_	_	O
nitrogen	_	_	O
,	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
phosphoric	_	_	O
acid	_	_	O
,	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
A	_	_	O
and	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	B-OBJ_NAME
B.	_	_	I-OBJ_NAME
Each	_	_	O
kg	_	_	O
of	_	_	O
fertilizer	_	_	B-VAR
Y200	_	_	I-VAR
contains	_	_	O
9	_	_	B-PARAM
units	_	_	O
of	_	_	O
nitrogen	_	_	O
,	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
phosphoric	_	_	O
acid	_	_	O
,	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
A	_	_	O
and	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	B-OBJ_NAME
B.	_	_	I-OBJ_NAME
To	_	_	O
be	_	_	O
effective	_	_	O
,	_	_	O
the	_	_	O
plant	_	_	O
growth	_	_	O
compound	_	_	O
requires	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
200	_	_	B-LIMIT
units	_	_	O
of	_	_	O
nitrogen	_	_	O
,	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
150	_	_	B-LIMIT
units	_	_	O
of	_	_	O
phosphoric	_	_	O
acid	_	_	O
,	_	_	O
and	_	_	O
no	_	_	B-CONST_DIR
more	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
300	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamin	_	_	O
A.	_	_	O
How	_	_	O
many	_	_	O
kg	_	_	O
of	_	_	O
each	_	_	O
fertilizer	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
vitamin	_	_	I-OBJ_NAME
B	_	_	I-OBJ_NAME
in	_	_	O
the	_	_	O
compound	_	_	O
?	_	_	O
What	_	_	O
is	_	_	O
the	_	_	O
minimum	_	_	O
amount	_	_	O
of	_	_	O
vitamin	_	_	O
B	_	_	O
?	_	_	O

Andy	_	_	O
likes	_	_	O
to	_	_	O
mix	_	_	O
his	_	_	O
two	_	_	O
post	_	_	O
-	_	_	O
workout	_	_	O
drinks	_	_	O
:	_	_	O
chocolate	_	_	B-VAR
milk	_	_	I-VAR
and	_	_	O
vegetable	_	_	B-VAR
juice	_	_	I-VAR
.	_	_	O
Chocolate	_	_	B-VAR
milk	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
3.5	_	_	B-PARAM
per	_	_	O
bottle	_	_	O
,	_	_	O
contains	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
potassium	_	_	O
,	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
magnesium	_	_	O
,	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
calcium	_	_	O
.	_	_	O
Vegetable	_	_	B-VAR
juice	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
6	_	_	B-PARAM
per	_	_	O
bottle	_	_	O
and	_	_	O
contains	_	_	O
9	_	_	B-PARAM
units	_	_	O
of	_	_	O
potassium	_	_	O
,	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
magnesium	_	_	O
,	_	_	O
and	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
calcium	_	_	O
.	_	_	O
David	_	_	O
likes	_	_	O
to	_	_	O
make	_	_	O
sure	_	_	O
he	_	_	O
gets	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
units	_	_	O
of	_	_	O
potassium	_	_	O
,	_	_	O
8	_	_	B-LIMIT
units	_	_	O
of	_	_	O
magnesium	_	_	O
,	_	_	O
and	_	_	O
12	_	_	B-LIMIT
units	_	_	O
of	_	_	O
calcium	_	_	O
after	_	_	O
each	_	_	O
workout	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
bottles	_	_	O
of	_	_	O
each	_	_	O
drink	_	_	O
should	_	_	O
he	_	_	O
buy	_	_	O
and	_	_	O
mix	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
ensure	_	_	O
a	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
?	_	_	O
What	_	_	O
is	_	_	O
the	_	_	O
minimum	_	_	O
cost	_	_	O
?	_	_	O

A	_	_	O
family	_	_	O
has	_	_	B-CONST_DIR
100	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
farmland	_	_	O
on	_	_	O
which	_	_	O
to	_	_	O
grow	_	_	O
carrots	_	_	B-VAR
and	_	_	O
green	_	_	B-VAR
peas	_	_	I-VAR
.	_	_	O
Both	_	_	O
vegetables	_	_	O
have	_	_	O
to	_	_	O
be	_	_	O
watered	_	_	O
and	_	_	O
sprayed	_	_	O
with	_	_	O
bug	_	_	O
repellant	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
135	_	_	B-LIMIT
days	_	_	O
per	_	_	O
year	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
watering	_	_	O
and	_	_	O
110	_	_	B-LIMIT
days	_	_	O
per	_	_	O
year	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
spraying	_	_	O
bug	_	_	O
spray	_	_	O
.	_	_	O
It	_	_	O
takes	_	_	O
0.7	_	_	B-PARAM
days	_	_	O
to	_	_	O
water	_	_	O
an	_	_	O
acre	_	_	O
of	_	_	O
carrots	_	_	B-VAR
and	_	_	O
1.2	_	_	B-PARAM
days	_	_	O
to	_	_	O
spray	_	_	O
an	_	_	O
acre	_	_	O
of	_	_	O
carrots	_	_	B-VAR
.	_	_	O
It	_	_	O
takes	_	_	O
0.4	_	_	B-PARAM
days	_	_	O
to	_	_	O
water	_	_	O
an	_	_	O
acre	_	_	O
of	_	_	O
green	_	_	B-VAR
peas	_	_	I-VAR
and	_	_	O
1.5	_	_	B-PARAM
days	_	_	O
to	_	_	O
spray	_	_	O
an	_	_	O
acre	_	_	O
of	_	_	O
green	_	_	B-VAR
peas	_	_	I-VAR
.	_	_	O
The	_	_	O
family	_	_	O
earns	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
250	_	_	B-PARAM
per	_	_	O
acre	_	_	O
of	_	_	O
carrots	_	_	B-VAR
and	_	_	O
$	_	_	O
340	_	_	B-PARAM
per	_	_	O
acre	_	_	O
of	_	_	O
green	_	_	B-VAR
peas	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
vegetable	_	_	O
should	_	_	O
be	_	_	O
planted	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Nova	_	_	O
Transport	_	_	O
can	_	_	O
host	_	_	O
up	_	_	B-CONST_DIR
to	_	_	I-CONST_DIR
600	_	_	B-LIMIT
passengers	_	_	O
on	_	_	O
a	_	_	O
scenic	_	_	O
train	_	_	O
ride	_	_	O
.	_	_	O
Business	_	_	B-VAR
class	_	_	I-VAR
seats	_	_	O
,	_	_	O
which	_	_	O
come	_	_	O
with	_	_	O
free	_	_	O
non	_	_	O
-	_	_	O
alcoholic	_	_	O
drinks	_	_	O
,	_	_	O
are	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
$	_	_	O
300	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
each	_	_	O
while	_	_	O
coach	_	_	B-VAR
class	_	_	I-VAR
tickets	_	_	O
are	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
$	_	_	O
150	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
each	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
due	_	_	O
to	_	_	O
the	_	_	O
high	_	_	O
costs	_	_	O
,	_	_	O
more	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
4	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
many	_	_	O
passengers	_	_	O
prefer	_	_	O
to	_	_	O
travel	_	_	O
by	_	_	O
coach	_	_	B-VAR
seating	_	_	I-VAR
than	_	_	O
by	_	_	O
business	_	_	B-VAR
class	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
there	_	_	O
are	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
45	_	_	B-LIMIT
seats	_	_	O
reserved	_	_	O
for	_	_	O
business	_	_	B-VAR
class	_	_	I-VAR
passengers	_	_	O
.	_	_	O
Determine	_	_	O
how	_	_	O
many	_	_	O
tickets	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
must	_	_	O
be	_	_	O
sold	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
profit	_	_	B-OBJ_NAME
for	_	_	O
the	_	_	O
company	_	_	O
.	_	_	O
What	_	_	O
is	_	_	O
the	_	_	O
maximum	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

Modern	_	_	O
Bicycle	_	_	O
sells	_	_	O
two	_	_	O
models	_	_	O
of	_	_	O
a	_	_	O
bike	_	_	O
:	_	_	O
a	_	_	O
folding	_	_	B-VAR
bike	_	_	I-VAR
and	_	_	O
a	_	_	O
touring	_	_	B-VAR
bike	_	_	I-VAR
.	_	_	O
The	_	_	O
folding	_	_	B-VAR
bike	_	_	I-VAR
costs	_	_	O
$	_	_	O
550	_	_	B-PARAM
and	_	_	O
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
200	_	_	B-PARAM
.	_	_	O
The	_	_	O
touring	_	_	B-VAR
bike	_	_	I-VAR
costs	_	_	O
$	_	_	O
700	_	_	B-PARAM
and	_	_	O
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
350	_	_	B-PARAM
.	_	_	O
The	_	_	O
bike	_	_	O
shop	_	_	O
owner	_	_	O
knows	_	_	O
that	_	_	O
the	_	_	O
monthly	_	_	O
demand	_	_	O
will	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
bikes	_	_	O
.	_	_	O
He	_	_	O
also	_	_	O
wants	_	_	O
to	_	_	O
make	_	_	O
sure	_	_	O
that	_	_	O
there	_	_	O
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
30000	_	_	B-LIMIT
worth	_	_	O
of	_	_	O
bikes	_	_	O
in	_	_	O
stock	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
bikes	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
be	_	_	O
stocked	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Two	_	_	O
colours	_	_	O
of	_	_	O
paints	_	_	O
:	_	_	O
Egret	_	_	B-VAR
and	_	_	O
Crane	_	_	B-VAR
,	_	_	O
have	_	_	O
quality	_	_	O
ratings	_	_	O
of	_	_	O
60	_	_	B-PARAM
and	_	_	O
85	_	_	B-PARAM
,	_	_	O
respectively	_	_	O
.	_	_	O
The	_	_	O
Egret	_	_	B-VAR
paint	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
0.40	_	_	B-PARAM
per	_	_	O
liter	_	_	O
while	_	_	O
the	_	_	O
Crane	_	_	B-VAR
paint	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
1.20	_	_	B-PARAM
per	_	_	O
liter	_	_	O
.	_	_	O
In	_	_	O
order	_	_	O
to	_	_	O
paint	_	_	O
his	_	_	O
fence	_	_	O
,	_	_	O
Bob	_	_	O
wants	_	_	O
to	_	_	O
use	_	_	O
a	_	_	O
mix	_	_	O
of	_	_	O
paint	_	_	O
with	_	_	O
a	_	_	O
quality	_	_	O
of	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
70	_	_	B-LIMIT
.	_	_	O
This	_	_	O
ensures	_	_	O
that	_	_	O
the	_	_	O
paint	_	_	O
on	_	_	O
the	_	_	O
fence	_	_	O
will	_	_	O
withstand	_	_	O
a	_	_	O
few	_	_	O
storms	_	_	O
.	_	_	O
What	_	_	O
blend	_	_	O
of	_	_	O
the	_	_	O
two	_	_	O
paints	_	_	O
should	_	_	O
he	_	_	O
mix	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
cost	_	_	B-OBJ_NAME
?	_	_	O
[	_	_	O
Hint	_	_	O
:	_	_	O
Let	_	_	O
x	_	_	O
be	_	_	O
the	_	_	O
fraction	_	_	O
of	_	_	O
each	_	_	O
liter	_	_	O
that	_	_	O
is	_	_	O
Egret	_	_	B-VAR
paint	_	_	I-VAR
and	_	_	O
y	_	_	O
be	_	_	O
the	_	_	O
fraction	_	_	O
that	_	_	O
is	_	_	O
Crane	_	_	B-VAR
paint	_	_	I-VAR
.	_	_	O
]	_	_	O

IND	_	_	O
Foods	_	_	O
factory	_	_	O
produces	_	_	O
basmati	_	_	B-VAR
rice	_	_	I-VAR
and	_	_	O
bananas	_	_	B-VAR
.	_	_	O
To	_	_	O
make	_	_	O
one	_	_	O
kilogram	_	_	O
of	_	_	O
basmati	_	_	B-VAR
rice	_	_	I-VAR
requires	_	_	O
1.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
human	_	_	O
labor	_	_	O
,	_	_	O
2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
machine	_	_	O
work	_	_	O
,	_	_	O
and	_	_	O
3	_	_	B-PARAM
hours	_	_	O
of	_	_	O
resting	_	_	O
under	_	_	O
the	_	_	O
sun	_	_	O
.	_	_	O
To	_	_	O
make	_	_	O
one	_	_	O
kilogram	_	_	O
of	_	_	O
bananas	_	_	B-VAR
requires	_	_	O
2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
human	_	_	O
labor	_	_	O
,	_	_	O
4	_	_	B-PARAM
hours	_	_	O
of	_	_	O
machine	_	_	O
work	_	_	O
,	_	_	O
and	_	_	O
1.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
resting	_	_	O
under	_	_	O
the	_	_	O
sun	_	_	O
.	_	_	O
The	_	_	O
factory	_	_	O
only	_	_	O
has	_	_	B-CONST_DIR
90	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
human	_	_	O
labor	_	_	O
,	_	_	O
150	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
machine	_	_	O
labor	_	_	O
,	_	_	O
and	_	_	O
70	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
time	_	_	O
under	_	_	O
the	_	_	O
sun	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
The	_	_	O
net	_	_	B-OBJ_NAME
profit	_	_	I-OBJ_NAME
per	_	_	O
kilogram	_	_	O
of	_	_	O
basmati	_	_	B-VAR
rice	_	_	I-VAR
is	_	_	O
$	_	_	O
15	_	_	B-PARAM
and	_	_	O
the	_	_	O
net	_	_	B-OBJ_NAME
profit	_	_	I-OBJ_NAME
per	_	_	O
kilogram	_	_	O
of	_	_	O
bananas	_	_	B-VAR
is	_	_	O
$	_	_	O
28	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
kilograms	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
factory	_	_	O
make	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
seafood	_	_	O
factory	_	_	O
packages	_	_	O
fish	_	_	B-VAR
meat	_	_	I-VAR
and	_	_	O
shrimp	_	_	B-VAR
meat	_	_	I-VAR
.	_	_	O
All	_	_	O
packages	_	_	O
must	_	_	O
pass	_	_	O
through	_	_	O
a	_	_	O
weight	_	_	O
checking	_	_	O
machine	_	_	O
and	_	_	O
a	_	_	O
packaging	_	_	O
inspection	_	_	O
machine	_	_	O
.	_	_	O
In	_	_	O
a	_	_	O
week	_	_	O
,	_	_	O
each	_	_	O
machine	_	_	O
is	_	_	O
available	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
1200	_	_	B-LIMIT
minutes	_	_	O
.	_	_	O
A	_	_	O
package	_	_	O
of	_	_	O
fish	_	_	B-VAR
meat	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
in	_	_	O
the	_	_	O
weight	_	_	O
checking	_	_	O
machine	_	_	O
and	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
in	_	_	O
the	_	_	O
packaging	_	_	O
inspection	_	_	O
machine	_	_	O
.	_	_	O
A	_	_	O
package	_	_	O
of	_	_	O
shrimp	_	_	B-VAR
meat	_	_	I-VAR
requires	_	_	O
1.5	_	_	B-PARAM
minutes	_	_	O
in	_	_	O
the	_	_	O
weight	_	_	O
checking	_	_	O
machine	_	_	O
and	_	_	O
7	_	_	B-PARAM
minutes	_	_	O
in	_	_	O
the	_	_	O
packaging	_	_	O
inspection	_	_	O
machine	_	_	O
.	_	_	O
A	_	_	O
package	_	_	O
of	_	_	O
fish	_	_	B-VAR
meat	_	_	I-VAR
generates	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
7	_	_	B-PARAM
while	_	_	O
a	_	_	O
package	_	_	O
of	_	_	O
shrimp	_	_	B-VAR
generates	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
3	_	_	B-PARAM
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
.	_	_	O

Two	_	_	O
sisters	_	_	O
,	_	_	O
Joy	_	_	O
and	_	_	O
Willa	_	_	O
,	_	_	O
run	_	_	O
a	_	_	O
stand	_	_	O
selling	_	_	O
green	_	_	B-VAR
tea	_	_	I-VAR
and	_	_	O
pancakes	_	_	B-VAR
.	_	_	O
A	_	_	O
pitcher	_	_	O
of	_	_	O
green	_	_	B-VAR
tea	_	_	I-VAR
takes	_	_	O
0.7	_	_	B-PARAM
hours	_	_	O
of	_	_	O
Joy	_	_	O
's	_	_	O
time	_	_	O
along	_	_	O
with	_	_	O
0.3	_	_	B-PARAM
hours	_	_	O
of	_	_	O
Willa	_	_	O
's	_	_	O
time	_	_	O
.	_	_	O
A	_	_	O
batch	_	_	O
of	_	_	O
pancakes	_	_	B-VAR
takes	_	_	O
1.2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
Joy	_	_	O
's	_	_	O
time	_	_	O
and	_	_	O
0.6	_	_	B-PARAM
hours	_	_	O
of	_	_	O
Willa	_	_	O
's	_	_	O
time	_	_	O
.	_	_	O
Joy	_	_	O
has	_	_	O
8	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
each	_	_	O
day	_	_	O
,	_	_	O
but	_	_	O
since	_	_	O
Willa	_	_	O
has	_	_	O
hockey	_	_	O
lessons	_	_	O
,	_	_	O
she	_	_	O
only	_	_	O
has	_	_	O
5	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
each	_	_	O
day	_	_	O
.	_	_	O
They	_	_	O
get	_	_	O
$	_	_	O
2.5	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
per	_	_	O
pitcher	_	_	O
of	_	_	O
green	_	_	B-VAR
tea	_	_	I-VAR
,	_	_	O
and	_	_	O
$	_	_	O
10	_	_	B-PARAM
per	_	_	O
batch	_	_	O
of	_	_	O
pancakes	_	_	B-VAR
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
.	_	_	O

GrusCreation	_	_	O
firm	_	_	O
employs	_	_	O
researchers	_	_	B-VAR
and	_	_	O
developers	_	_	B-VAR
.	_	_	O
Researchers	_	_	B-VAR
earn	_	_	B-OBJ_NAME
$	_	_	O
2500	_	_	B-PARAM
per	_	_	O
week	_	_	O
while	_	_	O
developers	_	_	B-VAR
earn	_	_	B-OBJ_NAME
$	_	_	O
1500	_	_	B-PARAM
per	_	_	O
week	_	_	O
.	_	_	O
The	_	_	O
project	_	_	O
requires	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
workers	_	_	O
,	_	_	O
of	_	_	O
whom	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
must	_	_	O
be	_	_	O
developers	_	_	B-VAR
.	_	_	O
To	_	_	O
achieve	_	_	O
novelty	_	_	O
in	_	_	O
the	_	_	O
project	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
researchers	_	_	B-VAR
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
a	_	_	O
third	_	_	B-PARAM
of	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
developers	_	_	B-VAR
.	_	_	O
The	_	_	O
company	_	_	O
wants	_	_	O
to	_	_	O
keep	_	_	O
the	_	_	O
weekly	_	_	O
payroll	_	_	O
to	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
250000	_	_	B-LIMIT
.	_	_	O
How	_	_	O
can	_	_	O
GrusCreation	_	_	O
firm	_	_	O
employ	_	_	O
the	_	_	O
different	_	_	O
type	_	_	O
of	_	_	O
staff	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
wages	_	_	B-OBJ_NAME
.	_	_	O

Steven	_	_	O
owns	_	_	O
two	_	_	O
rice	_	_	O
processing	_	_	O
machines	_	_	O
.	_	_	O
Machine	_	_	B-VAR
X	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
400	_	_	B-PARAM
to	_	_	O
operate	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
can	_	_	O
produce	_	_	O
and	_	_	O
deliver	_	_	O
3	_	_	B-PARAM
bags	_	_	O
of	_	_	O
basmati	_	_	O
rice	_	_	O
,	_	_	O
5	_	_	B-PARAM
bags	_	_	O
of	_	_	O
brown	_	_	O
rice	_	_	O
,	_	_	O
and	_	_	O
7	_	_	B-PARAM
bags	_	_	O
of	_	_	O
jasmine	_	_	O
rice	_	_	O
.	_	_	O
Machine	_	_	B-VAR
Y	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
500	_	_	B-PARAM
to	_	_	O
operate	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
can	_	_	O
produce	_	_	O
and	_	_	O
deliver	_	_	O
4	_	_	B-PARAM
bags	_	_	O
of	_	_	O
basmati	_	_	O
rice	_	_	O
,	_	_	O
8	_	_	B-PARAM
bags	_	_	O
of	_	_	O
brown	_	_	O
rice	_	_	O
,	_	_	O
and	_	_	O
3	_	_	B-PARAM
bag	_	_	O
of	_	_	O
jasmine	_	_	O
rice	_	_	O
.	_	_	O
Steven	_	_	O
recently	_	_	O
obtained	_	_	O
a	_	_	O
contract	_	_	O
to	_	_	O
provide	_	_	B-CONST_DIR
a	_	_	O
restaurant	_	_	O
with	_	_	O
20	_	_	B-LIMIT
bags	_	_	O
of	_	_	O
basmati	_	_	O
rice	_	_	O
,	_	_	O
30	_	_	B-LIMIT
bags	_	_	O
of	_	_	O
brown	_	_	O
rice	_	_	O
,	_	_	O
and	_	_	O
25	_	_	B-LIMIT
bags	_	_	O
of	_	_	O
jasmine	_	_	O
rice	_	_	O
.	_	_	O
How	_	_	O
can	_	_	O
we	_	_	O
minimize	_	_	B-OBJ_DIR
Steven	_	_	O
's	_	_	O
total	_	_	B-OBJ_NAME
costs	_	_	I-OBJ_NAME
?	_	_	O

Thunder	_	_	O
Wood	_	_	O
is	_	_	O
a	_	_	O
logging	_	_	O
company	_	_	O
and	_	_	O
it	_	_	O
cuts	_	_	O
three	_	_	O
specific	_	_	O
trees	_	_	O
:	_	_	O
Elm	_	_	O
,	_	_	O
Oak	_	_	O
,	_	_	O
and	_	_	O
Alder	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
two	_	_	O
operations	_	_	O
.	_	_	O
The	_	_	O
north	_	_	B-VAR
side	_	_	I-VAR
operation	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
450	_	_	B-PARAM
to	_	_	O
operate	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
produces	_	_	O
5	_	_	B-PARAM
elm	_	_	O
trees	_	_	O
,	_	_	O
5	_	_	B-PARAM
oak	_	_	O
trees	_	_	O
,	_	_	O
and	_	_	O
4	_	_	B-PARAM
alder	_	_	O
trees	_	_	O
daily	_	_	O
.	_	_	O
The	_	_	O
south	_	_	B-VAR
side	_	_	I-VAR
operation	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
550	_	_	B-PARAM
to	_	_	O
operate	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
produces	_	_	O
6	_	_	B-PARAM
elm	_	_	O
trees	_	_	O
,	_	_	O
4	_	_	B-PARAM
oak	_	_	O
trees	_	_	O
,	_	_	O
and	_	_	O
6	_	_	B-PARAM
alder	_	_	O
trees	_	_	O
daily	_	_	O
.	_	_	O
The	_	_	O
logging	_	_	O
company	_	_	O
must	_	_	O
provide	_	_	B-CONST_DIR
a	_	_	O
paper	_	_	O
pulp	_	_	O
with	_	_	O
25	_	_	B-LIMIT
elm	_	_	O
trees	_	_	O
,	_	_	O
15	_	_	B-LIMIT
oak	_	_	O
trees	_	_	O
,	_	_	O
and	_	_	O
30	_	_	B-LIMIT
alder	_	_	O
trees	_	_	O
per	_	_	O
week	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
days	_	_	O
a	_	_	O
week	_	_	O
should	_	_	O
each	_	_	O
operation	_	_	O
be	_	_	O
run	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
while	_	_	O
meeting	_	_	O
the	_	_	O
requirements	_	_	O
?	_	_	O

Joy	_	_	O
Bakery	_	_	O
uses	_	_	O
a	_	_	O
dough	_	_	O
mixer	_	_	O
and	_	_	O
a	_	_	O
commercial	_	_	O
bake	_	_	O
oven	_	_	O
to	_	_	O
make	_	_	O
bagels	_	_	B-VAR
and	_	_	O
croissants	_	_	B-VAR
.	_	_	O
Each	_	_	O
machine	_	_	O
can	_	_	O
run	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
2500	_	_	B-LIMIT
hours	_	_	O
per	_	_	O
year	_	_	O
.	_	_	O
To	_	_	O
bake	_	_	O
a	_	_	O
batch	_	_	O
of	_	_	O
bagels	_	_	B-VAR
takes	_	_	O
2	_	_	B-PARAM
hours	_	_	O
in	_	_	O
the	_	_	O
dough	_	_	O
mixer	_	_	O
and	_	_	O
3.5	_	_	B-PARAM
hours	_	_	O
in	_	_	O
the	_	_	O
oven	_	_	O
.	_	_	O
A	_	_	O
batch	_	_	O
of	_	_	O
croissants	_	_	B-VAR
requires	_	_	O
1.5	_	_	B-PARAM
hours	_	_	O
in	_	_	O
the	_	_	O
mixer	_	_	O
and	_	_	O
2	_	_	B-PARAM
hours	_	_	O
in	_	_	O
the	_	_	O
oven	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
batch	_	_	O
of	_	_	O
bagels	_	_	B-VAR
is	_	_	O
$	_	_	O
7.5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
batch	_	_	O
of	_	_	O
croissants	_	_	B-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
.	_	_	O
How	_	_	O
should	_	_	O
the	_	_	O
bakery	_	_	O
operate	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
total	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
underground	_	_	O
factory	_	_	O
has	_	_	B-CONST_DIR
120	_	_	B-LIMIT
sq	_	_	O
.	_	_	O
feet	_	_	O
of	_	_	O
space	_	_	O
.	_	_	O
It	_	_	O
makes	_	_	O
low	_	_	O
-	_	_	O
quality	_	_	O
headsets	_	_	B-VAR
and	_	_	O
keyboards	_	_	B-VAR
.	_	_	O
Headsets	_	_	B-VAR
require	_	_	O
2.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
labor	_	_	O
and	_	_	O
cost	_	_	O
$	_	_	O
10	_	_	B-PARAM
for	_	_	O
each	_	_	O
sq	_	_	O
.	_	_	O
foot	_	_	O
of	_	_	O
space	_	_	O
allocated	_	_	O
for	_	_	O
headset	_	_	B-VAR
production	_	_	O
(	_	_	O
cost	_	_	O
of	_	_	O
electricity	_	_	O
and	_	_	O
equipment	_	_	O
)	_	_	O
.	_	_	O
Keyboards	_	_	B-VAR
require	_	_	O
3.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
labor	_	_	O
and	_	_	O
cost	_	_	O
$	_	_	O
12	_	_	B-PARAM
for	_	_	O
each	_	_	O
sq	_	_	O
.	_	_	O
foot	_	_	O
of	_	_	O
space	_	_	O
allocated	_	_	O
for	_	_	O
keyboard	_	_	B-VAR
production	_	_	O
.	_	_	O
Headsets	_	_	B-VAR
produce	_	_	O
a	_	_	O
net	_	_	B-OBJ_NAME
revenue	_	_	I-OBJ_NAME
of	_	_	O
$	_	_	O
45	_	_	B-PARAM
per	_	_	O
sq	_	_	O
.	_	_	O
foot	_	_	O
while	_	_	O
keyboards	_	_	B-VAR
produce	_	_	O
a	_	_	O
net	_	_	B-OBJ_NAME
revenue	_	_	I-OBJ_NAME
of	_	_	O
$	_	_	O
80	_	_	B-PARAM
per	_	_	O
sq	_	_	O
.	_	_	O
foot	_	_	O
.	_	_	O
The	_	_	O
factory	_	_	O
wants	_	_	O
to	_	_	O
spend	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
5500	_	_	B-LIMIT
and	_	_	O
2500	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
labor	_	_	O
.	_	_	O
What	_	_	O
is	_	_	O
the	_	_	O
optimal	_	_	O
factory	_	_	O
layout	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
revenue	_	_	B-OBJ_NAME
?	_	_	O

Sweet	_	_	O
Popcorn	_	_	O
store	_	_	O
has	_	_	B-CONST_DIR
35	_	_	B-LIMIT
pounds	_	_	O
of	_	_	O
butter	_	_	O
popcorn	_	_	O
and	_	_	O
45	_	_	B-LIMIT
pounds	_	_	O
of	_	_	O
caramel	_	_	O
popcorn	_	_	O
.	_	_	O
They	_	_	O
sell	_	_	O
two	_	_	O
mixed	_	_	O
bags	_	_	O
:	_	_	O
a	_	_	O
family	_	_	B-VAR
mix	_	_	I-VAR
and	_	_	O
a	_	_	O
party	_	_	B-VAR
mix	_	_	I-VAR
.	_	_	O
The	_	_	O
family	_	_	B-VAR
mix	_	_	I-VAR
sells	_	_	B-OBJ_NAME
for	_	_	O
$	_	_	O
4.5	_	_	B-PARAM
a	_	_	O
pound	_	_	O
while	_	_	O
the	_	_	O
party	_	_	B-VAR
mix	_	_	I-VAR
sells	_	_	B-OBJ_NAME
for	_	_	O
$	_	_	O
6	_	_	B-PARAM
a	_	_	O
pound	_	_	O
.	_	_	O
The	_	_	O
family	_	_	B-VAR
mix	_	_	I-VAR
has	_	_	O
50	_	_	B-PARAM
%	_	_	I-PARAM
caramel	_	_	O
popcorn	_	_	O
and	_	_	O
50	_	_	B-PARAM
%	_	_	I-PARAM
butter	_	_	O
popcorn	_	_	O
.	_	_	O
The	_	_	O
party	_	_	B-VAR
mix	_	_	I-VAR
has	_	_	O
80	_	_	B-PARAM
%	_	_	I-PARAM
caramel	_	_	O
popcorn	_	_	O
and	_	_	O
20	_	_	B-PARAM
%	_	_	I-PARAM
butter	_	_	O
popcorn	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
bags	_	_	O
of	_	_	O
each	_	_	O
mix	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Julia	_	_	O
goes	_	_	O
to	_	_	O
a	_	_	O
supplement	_	_	O
store	_	_	O
that	_	_	O
sells	_	_	O
two	_	_	O
powders	_	_	O
,	_	_	O
Gamma	_	_	B-VAR
and	_	_	O
Delta	_	_	B-VAR
,	_	_	O
for	_	_	O
iron	_	_	O
and	_	_	O
biotin	_	_	O
.	_	_	O
The	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
scoop	_	_	O
of	_	_	O
Gamma	_	_	B-VAR
is	_	_	O
$	_	_	O
1.5	_	_	B-PARAM
while	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
scoop	_	_	O
of	_	_	O
Delta	_	_	B-VAR
is	_	_	O
$	_	_	O
2.5	_	_	B-PARAM
.	_	_	O
A	_	_	O
scoop	_	_	O
of	_	_	O
Gamma	_	_	B-VAR
contains	_	_	O
7	_	_	B-PARAM
grams	_	_	O
of	_	_	O
iron	_	_	O
and	_	_	O
10	_	_	B-PARAM
grams	_	_	O
of	_	_	O
biotin	_	_	O
.	_	_	O
A	_	_	O
scoop	_	_	O
of	_	_	O
Delta	_	_	B-VAR
contains	_	_	O
12	_	_	B-PARAM
grams	_	_	O
of	_	_	O
iron	_	_	O
and	_	_	O
9	_	_	B-PARAM
grams	_	_	O
of	_	_	O
biotin	_	_	O
.	_	_	O
A	_	_	O
doctor	_	_	O
has	_	_	O
recommended	_	_	O
that	_	_	O
Julia	_	_	O
takes	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
60	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
iron	_	_	O
and	_	_	O
45	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
biotin	_	_	O
daily	_	_	O
.	_	_	O
How	_	_	O
can	_	_	O
Julia	_	_	O
minimize	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
?	_	_	O

Nova	_	_	O
Furniture	_	_	O
sells	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
chairs	_	_	O
–	_	_	O
a	_	_	O
desk	_	_	B-VAR
chair	_	_	I-VAR
and	_	_	O
a	_	_	O
garden	_	_	B-VAR
chair	_	_	I-VAR
.	_	_	O
Each	_	_	O
desk	_	_	B-VAR
chair	_	_	I-VAR
costs	_	_	O
$	_	_	O
200	_	_	B-PARAM
to	_	_	O
make	_	_	O
and	_	_	O
each	_	_	O
garden	_	_	B-VAR
chair	_	_	I-VAR
costs	_	_	O
$	_	_	O
300	_	_	B-PARAM
to	_	_	O
make	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
estimates	_	_	O
that	_	_	O
the	_	_	O
total	_	_	O
monthly	_	_	O
demand	_	_	O
of	_	_	O
these	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
chairs	_	_	O
combined	_	_	O
will	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
250	_	_	B-LIMIT
units	_	_	O
.	_	_	O
The	_	_	O
monthly	_	_	O
manufacturing	_	_	O
budget	_	_	B-CONST_DIR
for	_	_	O
chairs	_	_	O
is	_	_	O
$	_	_	O
35000	_	_	B-LIMIT
.	_	_	O
Determine	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
units	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
chair	_	_	O
the	_	_	O
company	_	_	O
should	_	_	O
make	_	_	O
to	_	_	O
get	_	_	O
maximum	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
if	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
on	_	_	O
each	_	_	O
desk	_	_	B-VAR
chair	_	_	I-VAR
and	_	_	O
garden	_	_	B-VAR
chair	_	_	I-VAR
are	_	_	O
$	_	_	O
100	_	_	B-PARAM
and	_	_	O
$	_	_	O
150	_	_	B-PARAM
,	_	_	O
respectively	_	_	O
.	_	_	O

An	_	_	O
electronics	_	_	O
factory	_	_	O
makes	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
products	_	_	O
:	_	_	O
DVD	_	_	B-VAR
players	_	_	I-VAR
and	_	_	O
projectors	_	_	B-VAR
.	_	_	O
Demand	_	_	O
is	_	_	O
high	_	_	O
but	_	_	O
production	_	_	O
is	_	_	O
limited	_	_	O
since	_	_	O
the	_	_	O
global	_	_	O
chip	_	_	O
shortage	_	_	O
is	_	_	O
a	_	_	O
long	_	_	O
-	_	_	O
lasting	_	_	O
problem	_	_	O
.	_	_	O
Each	_	_	O
DVD	_	_	B-VAR
player	_	_	I-VAR
requires	_	_	O
5	_	_	B-PARAM
silicon	_	_	O
chips	_	_	O
,	_	_	O
6	_	_	B-PARAM
hours	_	_	O
of	_	_	O
engineering	_	_	O
time	_	_	O
,	_	_	O
and	_	_	O
2.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
assembly	_	_	O
time	_	_	O
.	_	_	O
Each	_	_	O
projector	_	_	B-VAR
requires	_	_	O
3	_	_	B-PARAM
silicon	_	_	O
chips	_	_	O
,	_	_	O
5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
engineering	_	_	O
time	_	_	O
,	_	_	O
and	_	_	O
2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
assembly	_	_	O
time	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
can	_	_	B-CONST_DIR
buy	_	_	I-CONST_DIR
250	_	_	B-LIMIT
silicon	_	_	O
chips	_	_	O
per	_	_	O
week	_	_	O
,	_	_	O
and	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
200	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
engineering	_	_	O
and	_	_	O
240	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
assembly	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
DVD	_	_	B-VAR
player	_	_	I-VAR
is	_	_	O
$	_	_	O
250	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
projector	_	_	B-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
problem	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
company	_	_	O
's	_	_	O
profit	_	_	B-OBJ_NAME
if	_	_	O
they	_	_	O
want	_	_	O
to	_	_	O
produce	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
units	_	_	O
of	_	_	O
DVD	_	_	B-VAR
players	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
units	_	_	O
of	_	_	O
projectors	_	_	B-VAR
each	_	_	O
week	_	_	O
.	_	_	O

There	_	_	O
will	_	_	O
be	_	_	O
a	_	_	O
concert	_	_	O
hosted	_	_	O
by	_	_	O
the	_	_	O
local	_	_	O
community	_	_	O
and	_	_	O
it	_	_	O
has	_	_	B-CONST_DIR
250	_	_	B-LIMIT
seats	_	_	O
.	_	_	O
The	_	_	O
first	_	_	B-VAR
-	_	_	I-VAR
floor	_	_	I-VAR
seats	_	_	I-VAR
make	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
100	_	_	B-PARAM
each	_	_	O
and	_	_	O
the	_	_	O
second	_	_	B-VAR
-	_	_	I-VAR
floor	_	_	I-VAR
seats	_	_	I-VAR
make	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
70	_	_	B-PARAM
each	_	_	O
.	_	_	O
At	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
70	_	_	B-LIMIT
seats	_	_	O
will	_	_	O
be	_	_	O
assigned	_	_	O
as	_	_	O
first	_	_	B-VAR
-	_	_	I-VAR
floor	_	_	I-VAR
seats	_	_	I-VAR
.	_	_	O
On	_	_	O
the	_	_	O
other	_	_	O
hand	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
2	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
many	_	_	O
people	_	_	O
prefer	_	_	O
the	_	_	O
second	_	_	B-VAR
-	_	_	I-VAR
floor	_	_	I-VAR
seats	_	_	I-VAR
to	_	_	O
the	_	_	O
first	_	_	B-VAR
-	_	_	I-VAR
floor	_	_	I-VAR
seats	_	_	I-VAR
.	_	_	O
Find	_	_	O
the	_	_	O
maximum	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
.	_	_	O
Also	_	_	O
,	_	_	O
determine	_	_	O
how	_	_	O
many	_	_	O
seats	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
must	_	_	O
be	_	_	O
sold	_	_	O
to	_	_	O
reach	_	_	O
this	_	_	O
amount	_	_	O
.	_	_	O

A	_	_	O
milk	_	_	O
tea	_	_	O
store	_	_	O
wants	_	_	O
to	_	_	O
make	_	_	O
milk	_	_	O
tea	_	_	O
that	_	_	O
has	_	_	O
some	_	_	O
red	_	_	B-VAR
bean	_	_	I-VAR
and	_	_	O
pudding	_	_	B-VAR
toppings	_	_	I-VAR
.	_	_	O
Each	_	_	O
red	_	_	B-VAR
bean	_	_	I-VAR
topping	_	_	I-VAR
contains	_	_	O
1.5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
sugar	_	_	O
and	_	_	O
2.5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
butter	_	_	O
;	_	_	O
each	_	_	O
pudding	_	_	B-VAR
topping	_	_	I-VAR
contains	_	_	O
3	_	_	B-PARAM
grams	_	_	O
of	_	_	O
sugar	_	_	O
and	_	_	O
1.2	_	_	B-PARAM
grams	_	_	O
of	_	_	O
butter	_	_	O
.	_	_	O
For	_	_	O
health	_	_	O
reasons	_	_	O
,	_	_	O
the	_	_	O
milk	_	_	O
tea	_	_	O
will	_	_	O
have	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
3	_	_	B-LIMIT
red	_	_	B-VAR
bean	_	_	I-VAR
toppings	_	_	I-VAR
.	_	_	O
To	_	_	O
make	_	_	O
the	_	_	O
milk	_	_	O
tea	_	_	O
tasty	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
7	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
sugar	_	_	O
and	_	_	O
10	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
butter	_	_	O
must	_	_	O
be	_	_	O
used	_	_	O
in	_	_	O
the	_	_	O
toppings	_	_	O
of	_	_	O
the	_	_	O
milk	_	_	O
tea	_	_	O
.	_	_	O
If	_	_	O
it	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
1.5	_	_	B-PARAM
to	_	_	O
make	_	_	O
one	_	_	O
red	_	_	B-VAR
bean	_	_	I-VAR
topping	_	_	I-VAR
and	_	_	O
$	_	_	O
2	_	_	B-PARAM
for	_	_	O
one	_	_	O
pudding	_	_	B-VAR
topping	_	_	I-VAR
,	_	_	O
what	_	_	O
is	_	_	O
the	_	_	O
optimal	_	_	O
combination	_	_	O
of	_	_	O
red	_	_	B-VAR
bean	_	_	I-VAR
and	_	_	O
pudding	_	_	B-VAR
toppings	_	_	I-VAR
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
cost	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
food	_	_	O
truck	_	_	O
wants	_	_	O
to	_	_	O
make	_	_	O
sausages	_	_	O
using	_	_	O
shrimp	_	_	B-VAR
and	_	_	O
beef	_	_	B-VAR
.	_	_	O
The	_	_	O
mixture	_	_	O
needs	_	_	O
to	_	_	O
contain	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
units	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
25	_	_	B-LIMIT
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
Shrimp	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
36	_	_	B-PARAM
per	_	_	O
kg	_	_	O
and	_	_	O
beef	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
40	_	_	B-PARAM
per	_	_	O
kg	_	_	O
.	_	_	O
Per	_	_	O
kilogram	_	_	O
,	_	_	O
shrimp	_	_	B-VAR
contains	_	_	O
2.5	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
Per	_	_	O
kilogram	_	_	O
,	_	_	O
beef	_	_	B-VAR
contains	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
2.5	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
Determine	_	_	O
the	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
of	_	_	O
the	_	_	O
mixture	_	_	O
.	_	_	O

An	_	_	O
electronics	_	_	O
factory	_	_	O
manufactures	_	_	O
two	_	_	O
calculators	_	_	O
:	_	_	O
solar	_	_	B-VAR
calculators	_	_	I-VAR
and	_	_	O
finance	_	_	B-VAR
calculators	_	_	I-VAR
,	_	_	O
using	_	_	O
silicon	_	_	O
,	_	_	O
plastic	_	_	O
,	_	_	O
and	_	_	O
steel	_	_	O
.	_	_	O
To	_	_	O
make	_	_	O
a	_	_	O
solar	_	_	B-VAR
calculator	_	_	I-VAR
,	_	_	O
5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
silicon	_	_	O
,	_	_	O
4	_	_	B-PARAM
grams	_	_	O
of	_	_	O
plastic	_	_	O
,	_	_	O
and	_	_	O
2	_	_	B-PARAM
grams	_	_	O
of	_	_	O
steel	_	_	O
are	_	_	O
needed	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
solar	_	_	B-VAR
calculator	_	_	I-VAR
is	_	_	O
$	_	_	O
12	_	_	B-PARAM
.	_	_	O
To	_	_	O
make	_	_	O
a	_	_	O
finance	_	_	B-VAR
calculator	_	_	I-VAR
,	_	_	O
3	_	_	B-PARAM
grams	_	_	O
of	_	_	O
silicon	_	_	O
,	_	_	O
5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
plastic	_	_	O
,	_	_	O
and	_	_	O
3	_	_	B-PARAM
grams	_	_	O
of	_	_	O
steel	_	_	O
are	_	_	O
needed	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
finance	_	_	B-VAR
calculator	_	_	I-VAR
is	_	_	O
$	_	_	O
9	_	_	B-PARAM
.	_	_	O
Even	_	_	O
though	_	_	O
the	_	_	O
company	_	_	O
can	_	_	O
sell	_	_	O
as	_	_	O
many	_	_	O
calculators	_	_	O
as	_	_	O
it	_	_	O
produces	_	_	O
,	_	_	O
there	_	_	O
is	_	_	O
only	_	_	O
150	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
silicon	_	_	O
,	_	_	O
150	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
plastic	_	_	O
,	_	_	O
and	_	_	O
70	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
steel	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
tea	_	_	O
shop	_	_	O
offers	_	_	O
two	_	_	O
promotion	_	_	O
packages	_	_	O
,	_	_	O
package	_	_	B-VAR
X	_	_	I-VAR
and	_	_	O
package	_	_	B-VAR
Y.	_	_	I-VAR
Each	_	_	O
promotion	_	_	O
package	_	_	O
consists	_	_	O
of	_	_	O
some	_	_	O
combination	_	_	O
of	_	_	O
green	_	_	O
and	_	_	O
black	_	_	O
tea	_	_	O
.	_	_	O
One	_	_	O
package	_	_	B-VAR
X	_	_	I-VAR
has	_	_	O
5	_	_	B-PARAM
bottles	_	_	O
of	_	_	O
green	_	_	O
tea	_	_	O
and	_	_	O
2	_	_	B-PARAM
bottles	_	_	O
of	_	_	O
black	_	_	O
tea	_	_	O
,	_	_	O
and	_	_	O
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
70	_	_	B-PARAM
.	_	_	O
In	_	_	O
comparison	_	_	O
,	_	_	O
a	_	_	O
package	_	_	B-VAR
Y	_	_	I-VAR
contains	_	_	O
3	_	_	B-PARAM
bottles	_	_	O
of	_	_	O
green	_	_	O
tea	_	_	O
and	_	_	O
4	_	_	B-PARAM
bottles	_	_	O
of	_	_	O
black	_	_	O
tea	_	_	O
,	_	_	O
and	_	_	O
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
120	_	_	B-PARAM
.	_	_	O
However	_	_	O
,	_	_	O
the	_	_	O
shop	_	_	O
only	_	_	B-CONST_DIR
has	_	_	O
1200	_	_	B-LIMIT
bottles	_	_	O
of	_	_	O
green	_	_	O
tea	_	_	O
and	_	_	O
900	_	_	B-LIMIT
bottles	_	_	O
of	_	_	O
black	_	_	O
tea	_	_	O
.	_	_	O
Find	_	_	O
the	_	_	O
best	_	_	O
mix	_	_	O
of	_	_	O
packages	_	_	O
to	_	_	O
achieve	_	_	O
maximum	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
.	_	_	O

The	_	_	O
company	_	_	O
would	_	_	O
like	_	_	O
to	_	_	O
design	_	_	O
an	_	_	O
office	_	_	O
space	_	_	O
with	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
desks	_	_	O
:	_	_	O
regular	_	_	B-VAR
desks	_	_	I-VAR
and	_	_	O
standing	_	_	B-VAR
desks	_	_	I-VAR
.	_	_	O
The	_	_	O
company	_	_	O
can	_	_	O
spend	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
2500	_	_	B-LIMIT
.	_	_	O
Regular	_	_	B-VAR
desks	_	_	I-VAR
cost	_	_	O
$	_	_	O
150	_	_	B-PARAM
,	_	_	O
take	_	_	O
up	_	_	O
6	_	_	B-PARAM
square	_	_	O
feet	_	_	O
of	_	_	O
space	_	_	O
,	_	_	O
and	_	_	O
seat	_	_	B-OBJ_NAME
4	_	_	B-PARAM
employees	_	_	O
.	_	_	O
Standing	_	_	B-VAR
desks	_	_	I-VAR
cost	_	_	O
$	_	_	O
200	_	_	B-PARAM
,	_	_	O
take	_	_	O
up	_	_	O
5	_	_	B-PARAM
square	_	_	O
feet	_	_	O
of	_	_	O
space	_	_	O
,	_	_	O
and	_	_	O
seat	_	_	B-OBJ_NAME
6	_	_	B-PARAM
employees	_	_	O
.	_	_	O
The	_	_	O
office	_	_	O
can	_	_	O
have	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
250	_	_	B-LIMIT
square	_	_	O
feet	_	_	O
of	_	_	O
desks	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
desk	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
buy	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
seating	_	_	B-OBJ_NAME
availability	_	_	I-OBJ_NAME
?	_	_	O

An	_	_	O
investment	_	_	O
bank	_	_	O
has	_	_	O
$	_	_	O
200000	_	_	B-LIMIT
available	_	_	B-CONST_DIR
to	_	_	O
invest	_	_	O
in	_	_	O
a	_	_	O
24	_	_	O
-	_	_	O
month	_	_	O
commitment	_	_	O
.	_	_	O
The	_	_	O
bank	_	_	O
can	_	_	O
either	_	_	O
invest	_	_	O
in	_	_	O
the	_	_	O
stock	_	_	B-VAR
market	_	_	I-VAR
or	_	_	O
cryptocurrency	_	_	B-VAR
.	_	_	O
The	_	_	O
money	_	_	O
placed	_	_	O
in	_	_	O
the	_	_	O
stock	_	_	B-VAR
market	_	_	I-VAR
yields	_	_	O
a	_	_	O
2.5	_	_	B-PARAM
%	_	_	I-PARAM
return	_	_	B-OBJ_NAME
,	_	_	O
while	_	_	O
the	_	_	O
money	_	_	O
placed	_	_	O
in	_	_	O
cryptocurrency	_	_	B-VAR
yields	_	_	O
a	_	_	O
7	_	_	B-PARAM
%	_	_	I-PARAM
return	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
bank	_	_	O
has	_	_	O
been	_	_	O
advised	_	_	O
to	_	_	O
place	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
45	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
investment	_	_	O
in	_	_	O
the	_	_	O
stock	_	_	B-VAR
market	_	_	I-VAR
.	_	_	O
Due	_	_	O
to	_	_	O
recent	_	_	O
issues	_	_	O
with	_	_	O
cryptocurrency	_	_	B-VAR
,	_	_	O
the	_	_	O
bank	_	_	O
has	_	_	O
decided	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
25	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
investment	_	_	O
be	_	_	O
placed	_	_	O
in	_	_	O
cryptocurrency	_	_	B-VAR
.	_	_	O
How	_	_	O
much	_	_	O
should	_	_	O
the	_	_	O
bank	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
area	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
its	_	_	O
return	_	_	B-OBJ_NAME
on	_	_	O
investment	_	_	O
?	_	_	O

A	_	_	O
beverage	_	_	O
company	_	_	O
wants	_	_	O
to	_	_	O
promote	_	_	O
their	_	_	O
new	_	_	O
product	_	_	O
.	_	_	O
They	_	_	O
want	_	_	O
to	_	_	O
maximize	_	_	O
the	_	_	O
exposure	_	_	B-OBJ_NAME
with	_	_	O
a	_	_	O
budget	_	_	O
of	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
200000	_	_	B-LIMIT
.	_	_	O
To	_	_	O
do	_	_	O
so	_	_	O
,	_	_	O
the	_	_	O
company	_	_	O
needs	_	_	O
to	_	_	O
decide	_	_	O
how	_	_	O
much	_	_	O
of	_	_	O
the	_	_	O
budget	_	_	O
to	_	_	O
spend	_	_	O
on	_	_	O
each	_	_	O
of	_	_	O
its	_	_	O
two	_	_	O
most	_	_	O
effective	_	_	O
media	_	_	O
:	_	_	O
(	_	_	O
1	_	_	O
)	_	_	O
newspaper	_	_	B-VAR
and	_	_	O
(	_	_	O
2	_	_	O
)	_	_	O
television	_	_	B-VAR
.	_	_	O
Each	_	_	O
newspaper	_	_	B-VAR
advertisement	_	_	I-VAR
costs	_	_	O
$	_	_	O
2500	_	_	B-PARAM
;	_	_	O
each	_	_	O
television	_	_	B-VAR
advertisement	_	_	I-VAR
cover	_	_	O
costs	_	_	O
$	_	_	O
5000	_	_	B-PARAM
.	_	_	O
The	_	_	O
company	_	_	O
knows	_	_	O
from	_	_	O
experience	_	_	O
that	_	_	O
it	_	_	O
is	_	_	O
important	_	_	O
to	_	_	O
use	_	_	O
both	_	_	O
media	_	_	O
.	_	_	O
The	_	_	O
product	_	_	O
exposure	_	_	B-OBJ_NAME
is	_	_	O
30000	_	_	B-PARAM
readers	_	_	O
for	_	_	O
each	_	_	O
newspaper	_	_	B-VAR
advertisement	_	_	I-VAR
and	_	_	O
50000	_	_	B-PARAM
viewers	_	_	O
for	_	_	O
each	_	_	O
television	_	_	B-VAR
advertisement	_	_	I-VAR
.	_	_	O
It	_	_	O
makes	_	_	O
a	_	_	O
decision	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
12	_	_	B-LIMIT
but	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
24	_	_	B-LIMIT
newspaper	_	_	B-VAR
advertisements	_	_	I-VAR
be	_	_	O
ordered	_	_	O
,	_	_	O
and	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
television	_	_	B-VAR
advertisements	_	_	I-VAR
should	_	_	O
be	_	_	O
contracted	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
times	_	_	O
should	_	_	O
each	_	_	O
of	_	_	O
the	_	_	O
two	_	_	O
media	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
obtain	_	_	O
maximum	_	_	B-OBJ_DIR
exposure	_	_	B-OBJ_NAME
while	_	_	O
staying	_	_	O
within	_	_	O
the	_	_	O
budget	_	_	O
?	_	_	O

Nova	_	_	O
Network	_	_	O
wants	_	_	O
to	_	_	O
design	_	_	O
a	_	_	O
plan	_	_	O
to	_	_	O
bid	_	_	O
for	_	_	O
the	_	_	O
job	_	_	O
of	_	_	O
providing	_	_	O
a	_	_	O
computer	_	_	O
network	_	_	O
for	_	_	O
city	_	_	O
offices	_	_	O
.	_	_	O
It	_	_	O
can	_	_	O
build	_	_	O
three	_	_	O
types	_	_	O
of	_	_	O
layouts	_	_	O
using	_	_	O
workstations	_	_	O
,	_	_	O
servers	_	_	O
,	_	_	O
and	_	_	O
switches	_	_	O
.	_	_	O
It	_	_	O
has	_	_	B-CONST_DIR
2000	_	_	B-LIMIT
workstations	_	_	O
,	_	_	O
500	_	_	B-LIMIT
servers	_	_	O
,	_	_	O
and	_	_	O
300	_	_	B-LIMIT
switches	_	_	O
.	_	_	O
A	_	_	O
ring	_	_	B-VAR
layout	_	_	I-VAR
uses	_	_	O
50	_	_	B-PARAM
workstations	_	_	O
,	_	_	O
20	_	_	B-PARAM
servers	_	_	O
,	_	_	O
and	_	_	O
10	_	_	B-PARAM
switches	_	_	O
;	_	_	O
a	_	_	O
tree	_	_	B-VAR
layout	_	_	I-VAR
uses	_	_	O
30	_	_	B-PARAM
workstations	_	_	O
,	_	_	O
15	_	_	B-PARAM
servers	_	_	O
,	_	_	O
and	_	_	O
7	_	_	B-PARAM
switches	_	_	O
;	_	_	O
and	_	_	O
a	_	_	O
mesh	_	_	B-VAR
layout	_	_	I-VAR
uses	_	_	O
100	_	_	B-PARAM
workstations	_	_	O
,	_	_	O
50	_	_	B-PARAM
servers	_	_	O
,	_	_	O
and	_	_	O
30	_	_	B-PARAM
switches	_	_	O
.	_	_	O
The	_	_	O
net	_	_	O
profit	_	_	B-OBJ_NAME
is	_	_	O
$	_	_	O
2000	_	_	B-PARAM
for	_	_	O
each	_	_	O
ring	_	_	B-VAR
layout	_	_	I-VAR
,	_	_	O
$	_	_	O
4000	_	_	B-PARAM
for	_	_	O
each	_	_	O
tree	_	_	B-VAR
layout	_	_	I-VAR
,	_	_	O
and	_	_	O
$	_	_	O
8000	_	_	B-PARAM
for	_	_	O
each	_	_	O
mesh	_	_	B-VAR
layout	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
layouts	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
yield	_	_	O
maximum	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
cosmetics	_	_	O
company	_	_	O
makes	_	_	O
high	_	_	O
-	_	_	O
end	_	_	O
skincare	_	_	O
products	_	_	O
whose	_	_	O
main	_	_	O
customers	_	_	O
are	_	_	O
wealthy	_	_	O
women	_	_	O
,	_	_	O
both	_	_	O
young	_	_	O
girls	_	_	O
and	_	_	O
middle	_	_	O
-	_	_	O
aged	_	_	O
women	_	_	O
.	_	_	O
In	_	_	O
order	_	_	O
to	_	_	O
promote	_	_	O
their	_	_	O
product	_	_	O
line	_	_	O
,	_	_	O
they	_	_	O
decided	_	_	O
to	_	_	O
invest	_	_	O
in	_	_	O
short	_	_	O
commercial	_	_	O
spots	_	_	O
on	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
programs	_	_	O
:	_	_	O
social	_	_	B-VAR
media	_	_	I-VAR
and	_	_	O
television	_	_	B-VAR
.	_	_	O
While	_	_	O
each	_	_	O
social	_	_	B-VAR
media	_	_	I-VAR
commercial	_	_	I-VAR
is	_	_	O
seen	_	_	O
by	_	_	O
5	_	_	B-PARAM
million	_	_	O
young	_	_	O
girls	_	_	O
and	_	_	O
1	_	_	B-PARAM
million	_	_	O
middle	_	_	O
-	_	_	O
aged	_	_	O
women	_	_	O
,	_	_	O
each	_	_	O
television	_	_	B-VAR
commercial	_	_	I-VAR
is	_	_	O
seen	_	_	O
by	_	_	O
3	_	_	B-PARAM
million	_	_	O
young	_	_	O
girls	_	_	O
and	_	_	O
7	_	_	B-PARAM
million	_	_	O
middle	_	_	O
-	_	_	O
aged	_	_	O
women	_	_	O
.	_	_	O
A	_	_	O
1	_	_	O
-	_	_	O
minute	_	_	O
social	_	_	B-VAR
media	_	_	I-VAR
ad	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
30,000	_	_	B-PARAM
,	_	_	O
and	_	_	O
a	_	_	O
1	_	_	O
-	_	_	O
minute	_	_	O
television	_	_	B-VAR
ad	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
50,000	_	_	B-PARAM
.	_	_	O
The	_	_	O
company	_	_	O
would	_	_	O
like	_	_	O
the	_	_	O
commercials	_	_	O
to	_	_	O
be	_	_	O
seen	_	_	O
by	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
million	_	_	O
young	_	_	O
girls	_	_	O
and	_	_	O
30	_	_	B-LIMIT
million	_	_	O
middle	_	_	O
-	_	_	O
aged	_	_	O
women	_	_	O
.	_	_	O
Use	_	_	O
linear	_	_	O
programming	_	_	O
to	_	_	O
determine	_	_	O
how	_	_	O
the	_	_	O
cosmetics	_	_	O
company	_	_	O
can	_	_	O
meet	_	_	O
its	_	_	O
advertising	_	_	O
requirements	_	_	O
at	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
.	_	_	O

Steven	_	_	O
wants	_	_	O
to	_	_	O
invest	_	_	O
in	_	_	O
pharmaceutical	_	_	O
companies	_	_	O
and	_	_	O
has	_	_	O
a	_	_	O
total	_	_	O
budget	_	_	O
of	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
100000	_	_	B-LIMIT
.	_	_	O
He	_	_	O
has	_	_	O
two	_	_	O
choices	_	_	O
which	_	_	O
include	_	_	O
Delta	_	_	B-VAR
and	_	_	O
Omega	_	_	B-VAR
.	_	_	O
Each	_	_	O
dollar	_	_	O
invested	_	_	O
in	_	_	O
Delta	_	_	B-VAR
yields	_	_	O
a	_	_	O
$	_	_	O
0.80	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
and	_	_	O
each	_	_	O
dollar	_	_	O
invested	_	_	O
in	_	_	O
Omega	_	_	B-VAR
yields	_	_	O
a	_	_	O
$	_	_	O
1.2	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
.	_	_	O
A	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
25	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
all	_	_	O
money	_	_	O
invested	_	_	O
must	_	_	O
be	_	_	O
in	_	_	O
Delta	_	_	B-VAR
,	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
$	_	_	O
10000	_	_	B-LIMIT
must	_	_	O
be	_	_	O
in	_	_	O
Omega	_	_	B-VAR
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
that	_	_	O
can	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
total	_	_	O
profit	_	_	B-OBJ_NAME
earned	_	_	O
from	_	_	O
Steven	_	_	O
's	_	_	O
investment	_	_	O
.	_	_	O

An	_	_	O
ice	_	_	O
cream	_	_	O
truck	_	_	O
sells	_	_	O
strawberry	_	_	B-VAR
and	_	_	O
mint	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
cakes	_	_	I-VAR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
strawberry	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
cake	_	_	I-VAR
is	_	_	O
$	_	_	O
2.5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
mint	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
cake	_	_	I-VAR
is	_	_	O
$	_	_	O
4	_	_	B-PARAM
.	_	_	O
The	_	_	O
ice	_	_	O
cream	_	_	O
truck	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
cakes	_	_	O
of	_	_	O
strawberry	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
but	_	_	O
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
make	_	_	I-CONST_DIR
more	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
20	_	_	B-LIMIT
cakes	_	_	O
.	_	_	O
It	_	_	O
must	_	_	O
also	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
mint	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
cakes	_	_	I-VAR
but	_	_	O
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
make	_	_	I-CONST_DIR
more	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
40	_	_	B-LIMIT
cakes	_	_	O
.	_	_	O
In	_	_	O
total	_	_	O
,	_	_	O
the	_	_	O
ice	_	_	O
cream	_	_	O
truck	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
50	_	_	B-LIMIT
total	_	_	O
cakes	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
cakes	_	_	O
of	_	_	O
each	_	_	O
flavor	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Tim	_	_	O
Bakery	_	_	O
sells	_	_	O
chocolate	_	_	B-VAR
croissants	_	_	I-VAR
and	_	_	O
strawberry	_	_	B-VAR
croissants	_	_	I-VAR
.	_	_	O
The	_	_	O
store	_	_	O
pays	_	_	O
a	_	_	O
baker	_	_	O
$	_	_	O
3	_	_	B-PARAM
and	_	_	O
$	_	_	O
5	_	_	B-PARAM
for	_	_	O
each	_	_	O
unit	_	_	O
of	_	_	O
a	_	_	O
chocolate	_	_	B-VAR
and	_	_	O
strawberry	_	_	B-VAR
croissant	_	_	I-VAR
respectively	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
makes	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
4	_	_	B-PARAM
per	_	_	O
chocolate	_	_	B-VAR
croissant	_	_	I-VAR
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
6	_	_	B-PARAM
per	_	_	O
strawberry	_	_	B-VAR
croissant	_	_	I-VAR
.	_	_	O
In	_	_	O
a	_	_	O
month	_	_	O
,	_	_	O
the	_	_	O
store	_	_	O
owner	_	_	O
expects	_	_	O
to	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
1200	_	_	B-LIMIT
croissants	_	_	O
and	_	_	O
wants	_	_	O
to	_	_	O
spend	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
6000	_	_	B-LIMIT
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
croissant	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
monthly	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

Natural	_	_	O
Pharmacy	_	_	O
is	_	_	O
using	_	_	B-CONST_DIR
2000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
a	_	_	O
rare	_	_	O
plant	_	_	O
extract	_	_	O
to	_	_	O
make	_	_	O
two	_	_	O
drugs	_	_	O
:	_	_	O
Alpha	_	_	B-VAR
and	_	_	O
Beta	_	_	B-VAR
.	_	_	O
One	_	_	O
bottle	_	_	O
of	_	_	O
Alpha	_	_	B-VAR
contains	_	_	O
15	_	_	B-PARAM
grams	_	_	O
of	_	_	O
extract	_	_	O
and	_	_	O
one	_	_	O
bottle	_	_	O
of	_	_	O
Beta	_	_	B-VAR
contains	_	_	O
25	_	_	B-PARAM
grams	_	_	O
.	_	_	O
Demand	_	_	O
is	_	_	O
such	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
many	_	_	O
Alpha	_	_	B-VAR
are	_	_	O
needed	_	_	O
than	_	_	O
Beta	_	_	B-VAR
.	_	_	O
A	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
10	_	_	B-LIMIT
bottles	_	_	O
of	_	_	O
Beta	_	_	B-VAR
need	_	_	O
to	_	_	O
be	_	_	O
made	_	_	O
.	_	_	O
One	_	_	O
bottle	_	_	O
of	_	_	O
Alpha	_	_	B-VAR
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
4	_	_	B-PARAM
while	_	_	O
one	_	_	O
bottle	_	_	O
of	_	_	O
Beta	_	_	B-VAR
is	_	_	O
sold	_	_	O
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
6	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
drug	_	_	O
should	_	_	O
be	_	_	O
prepared	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Tom	_	_	O
Designs	_	_	O
manufactures	_	_	O
three	_	_	O
coats	_	_	O
:	_	_	O
long	_	_	O
,	_	_	O
short	_	_	O
,	_	_	O
and	_	_	O
mini	_	_	O
.	_	_	O
These	_	_	O
coats	_	_	O
are	_	_	O
produced	_	_	O
in	_	_	O
two	_	_	O
different	_	_	O
factories	_	_	O
:	_	_	O
a	_	_	O
north	_	_	B-VAR
one	_	_	I-VAR
and	_	_	O
a	_	_	O
south	_	_	B-VAR
one	_	_	I-VAR
.	_	_	O
Running	_	_	O
the	_	_	O
north	_	_	B-VAR
factory	_	_	I-VAR
for	_	_	O
an	_	_	O
hour	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
produces	_	_	O
20	_	_	B-PARAM
long	_	_	O
coats	_	_	O
,	_	_	O
15	_	_	B-PARAM
short	_	_	O
coats	_	_	O
,	_	_	O
and	_	_	O
10	_	_	B-PARAM
mini	_	_	O
coats	_	_	O
.	_	_	O
Running	_	_	O
the	_	_	O
south	_	_	B-VAR
factory	_	_	I-VAR
for	_	_	O
an	_	_	O
hour	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
400	_	_	B-PARAM
and	_	_	O
yields	_	_	O
30	_	_	B-PARAM
long	_	_	O
coats	_	_	O
,	_	_	O
25	_	_	B-PARAM
short	_	_	O
coats	_	_	O
,	_	_	O
and	_	_	O
30	_	_	B-PARAM
mini	_	_	O
coats	_	_	O
.	_	_	O
To	_	_	O
meet	_	_	O
customer	_	_	O
demands	_	_	O
,	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
75	_	_	B-LIMIT
long	_	_	O
coats	_	_	O
,	_	_	O
30	_	_	B-LIMIT
short	_	_	O
coats	_	_	O
,	_	_	O
and	_	_	O
40	_	_	B-LIMIT
mini	_	_	O
coats	_	_	O
must	_	_	O
be	_	_	O
produced	_	_	O
daily	_	_	O
.	_	_	O
Determine	_	_	O
a	_	_	O
daily	_	_	O
production	_	_	O
plan	_	_	O
that	_	_	O
minimizes	_	_	B-OBJ_DIR
the	_	_	O
cost	_	_	B-OBJ_NAME
of	_	_	O
meeting	_	_	O
the	_	_	O
company	_	_	O
’s	_	_	O
daily	_	_	O
demands	_	_	O
.	_	_	O

A	_	_	O
factory	_	_	O
manufactures	_	_	O
2	_	_	O
types	_	_	O
of	_	_	O
tools	_	_	O
,	_	_	O
drills	_	_	B-VAR
and	_	_	O
saws	_	_	B-VAR
,	_	_	O
which	_	_	O
require	_	_	O
the	_	_	O
use	_	_	O
of	_	_	O
two	_	_	O
machines	_	_	O
,	_	_	O
a	_	_	O
milling	_	_	O
machine	_	_	O
and	_	_	O
a	_	_	O
CNG	_	_	O
.	_	_	O
It	_	_	O
takes	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
milling	_	_	O
machine	_	_	O
and	_	_	O
70	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
CNG	_	_	O
machine	_	_	O
to	_	_	O
manufacture	_	_	O
a	_	_	O
package	_	_	O
of	_	_	O
drills	_	_	B-VAR
,	_	_	O
while	_	_	O
it	_	_	O
takes	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
milling	_	_	O
machine	_	_	O
and	_	_	O
90	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
CNG	_	_	O
machine	_	_	O
to	_	_	O
manufacture	_	_	O
a	_	_	O
package	_	_	O
of	_	_	O
saws	_	_	B-VAR
.	_	_	O
Each	_	_	O
machine	_	_	O
is	_	_	O
available	_	_	O
for	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
800	_	_	B-LIMIT
minutes	_	_	O
on	_	_	O
any	_	_	O
day	_	_	O
.	_	_	O
The	_	_	O
manufacturer	_	_	O
can	_	_	O
sell	_	_	O
a	_	_	O
package	_	_	O
of	_	_	O
drills	_	_	B-VAR
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
35	_	_	B-PARAM
and	_	_	O
a	_	_	O
package	_	_	O
of	_	_	O
saws	_	_	B-VAR
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
100	_	_	B-PARAM
.	_	_	O
Assuming	_	_	O
that	_	_	O
he	_	_	O
can	_	_	O
sell	_	_	O
all	_	_	O
the	_	_	O
tools	_	_	O
he	_	_	O
manufactures	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
packages	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
the	_	_	O
factory	_	_	O
owner	_	_	O
produce	_	_	O
in	_	_	O
a	_	_	O
day	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O
Determine	_	_	O
the	_	_	O
maximum	_	_	O
profit	_	_	O
.	_	_	O

Bob	_	_	O
Fashion	_	_	O
produces	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
lipsticks	_	_	O
:	_	_	O
cream	_	_	B-VAR
lipsticks	_	_	I-VAR
and	_	_	O
matte	_	_	B-VAR
lipsticks	_	_	I-VAR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
cream	_	_	B-VAR
lipstick	_	_	I-VAR
is	_	_	O
$	_	_	O
70	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
matte	_	_	B-VAR
lipstick	_	_	I-VAR
is	_	_	O
$	_	_	O
100	_	_	B-PARAM
.	_	_	O
It	_	_	O
takes	_	_	O
3.5	_	_	B-PARAM
hours	_	_	O
to	_	_	O
produce	_	_	O
the	_	_	O
raw	_	_	O
materials	_	_	O
for	_	_	O
one	_	_	O
cream	_	_	B-VAR
lipstick	_	_	I-VAR
,	_	_	O
5	_	_	B-PARAM
hours	_	_	O
to	_	_	O
mix	_	_	O
and	_	_	O
2	_	_	B-PARAM
hours	_	_	O
in	_	_	O
packing	_	_	O
.	_	_	O
It	_	_	O
takes	_	_	O
5	_	_	B-PARAM
hours	_	_	O
to	_	_	O
produce	_	_	O
the	_	_	O
raw	_	_	O
materials	_	_	O
for	_	_	O
one	_	_	O
matte	_	_	B-VAR
lipstick	_	_	I-VAR
,	_	_	O
3	_	_	B-PARAM
hours	_	_	O
to	_	_	O
mix	_	_	O
and	_	_	O
1.5	_	_	B-PARAM
hours	_	_	O
in	_	_	O
packing	_	_	O
.	_	_	O
Per	_	_	O
month	_	_	O
,	_	_	O
300	_	_	B-LIMIT
hours	_	_	O
are	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
preparing	_	_	O
the	_	_	O
raw	_	_	O
materials	_	_	O
,	_	_	O
400	_	_	B-LIMIT
hours	_	_	O
for	_	_	O
mixing	_	_	O
and	_	_	O
200	_	_	B-LIMIT
hours	_	_	O
for	_	_	O
packing	_	_	O
the	_	_	O
lipsticks	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
lipstick	_	_	O
should	_	_	O
be	_	_	O
produced	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
monthly	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

James	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
a	_	_	O
field	_	_	O
of	_	_	O
120	_	_	B-LIMIT
square	_	_	O
feet	_	_	O
in	_	_	O
which	_	_	O
he	_	_	O
plants	_	_	O
aster	_	_	B-VAR
flowers	_	_	I-VAR
and	_	_	O
stonecrops	_	_	B-VAR
.	_	_	I-VAR
The	_	_	O
seed	_	_	O
for	_	_	O
aster	_	_	B-VAR
costs	_	_	O
$	_	_	O
20	_	_	B-PARAM
per	_	_	O
square	_	_	O
foot	_	_	O
.	_	_	O
The	_	_	O
seed	_	_	O
for	_	_	O
stonecrops	_	_	B-VAR
costs	_	_	O
$	_	_	O
45	_	_	B-PARAM
per	_	_	O
square	_	_	O
foot	_	_	O
.	_	_	O
James	_	_	O
has	_	_	O
available	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
5000	_	_	B-LIMIT
to	_	_	O
spend	_	_	O
on	_	_	O
seeds	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
square	_	_	O
foot	_	_	O
of	_	_	O
aster	_	_	B-VAR
flowers	_	_	I-VAR
is	_	_	O
$	_	_	O
60	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
square	_	_	O
foot	_	_	O
of	_	_	O
stonecrops	_	_	B-VAR
is	_	_	O
$	_	_	O
80	_	_	B-PARAM
.	_	_	O
Find	_	_	O
the	_	_	O
optimal	_	_	O
solution	_	_	O
for	_	_	O
James	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
.	_	_	O

Robert	_	_	O
would	_	_	O
like	_	_	O
to	_	_	O
mix	_	_	O
his	_	_	O
colored	_	_	O
cocktails	_	_	O
.	_	_	O
He	_	_	O
has	_	_	O
a	_	_	O
white	_	_	B-VAR
cocktail	_	_	I-VAR
that	_	_	O
has	_	_	O
7	_	_	B-PARAM
%	_	_	I-PARAM
alcohol	_	_	O
and	_	_	O
10	_	_	B-PARAM
%	_	_	I-PARAM
sugar	_	_	O
and	_	_	O
a	_	_	O
green	_	_	B-VAR
cocktail	_	_	I-VAR
that	_	_	O
has	_	_	O
2	_	_	B-PARAM
%	_	_	I-PARAM
alcohol	_	_	O
and	_	_	O
25	_	_	B-PARAM
%	_	_	I-PARAM
sugar	_	_	O
.	_	_	O
The	_	_	O
white	_	_	B-VAR
cocktail	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
5.5	_	_	B-PARAM
per	_	_	O
kilogram	_	_	O
and	_	_	O
the	_	_	O
green	_	_	B-VAR
cocktail	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
12	_	_	B-PARAM
per	_	_	O
kilogram	_	_	O
.	_	_	O
He	_	_	O
wants	_	_	O
to	_	_	O
create	_	_	O
a	_	_	O
super	_	_	O
cocktail	_	_	O
that	_	_	O
has	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
5	_	_	B-LIMIT
kilograms	_	_	O
of	_	_	O
alcohol	_	_	O
and	_	_	O
25	_	_	B-LIMIT
kilograms	_	_	O
of	_	_	O
sugar	_	_	O
.	_	_	O
How	_	_	O
much	_	_	O
of	_	_	O
each	_	_	O
cocktail	_	_	O
should	_	_	O
he	_	_	O
mix	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
create	_	_	O
the	_	_	O
super	_	_	O
cocktail	_	_	O
at	_	_	O
the	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
factory	_	_	O
makes	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
bags	_	_	O
:	_	_	O
laptop	_	_	B-VAR
bags	_	_	I-VAR
and	_	_	O
briefcases	_	_	B-VAR
.	_	_	O
Each	_	_	O
laptop	_	_	B-VAR
bag	_	_	I-VAR
requires	_	_	O
12	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
sewing	_	_	O
while	_	_	O
each	_	_	O
briefcase	_	_	B-VAR
requires	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
sewing	_	_	O
.	_	_	O
Each	_	_	O
laptop	_	_	B-VAR
bag	_	_	I-VAR
requires	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
painting	_	_	O
while	_	_	O
each	_	_	O
briefcase	_	_	B-VAR
requires	_	_	O
9	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
painting	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
300	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
sewing	_	_	O
and	_	_	O
500	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
painting	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
laptop	_	_	B-VAR
bag	_	_	I-VAR
is	_	_	O
$	_	_	O
80	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
briefcase	_	_	B-VAR
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
bag	_	_	O
should	_	_	O
the	_	_	O
factory	_	_	O
make	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
food	_	_	O
truck	_	_	O
makes	_	_	O
two	_	_	O
different	_	_	O
sandwiches	_	_	O
:	_	_	O
an	_	_	O
egg	_	_	B-VAR
sandwich	_	_	I-VAR
and	_	_	O
a	_	_	O
ham	_	_	B-VAR
sandwich	_	_	I-VAR
.	_	_	O
Both	_	_	O
need	_	_	O
eggs	_	_	O
and	_	_	O
ham	_	_	O
.	_	_	O
Each	_	_	O
egg	_	_	B-VAR
sandwich	_	_	I-VAR
requires	_	_	O
5	_	_	B-PARAM
eggs	_	_	O
and	_	_	O
2	_	_	B-PARAM
slices	_	_	O
of	_	_	O
ham	_	_	O
.	_	_	O
Each	_	_	O
ham	_	_	B-VAR
sandwich	_	_	I-VAR
requires	_	_	O
1	_	_	B-PARAM
egg	_	_	O
and	_	_	O
4	_	_	B-PARAM
slices	_	_	O
of	_	_	O
ham	_	_	O
.	_	_	O
The	_	_	O
truck	_	_	O
has	_	_	O
a	_	_	B-CONST_DIR
total	_	_	I-CONST_DIR
of	_	_	I-CONST_DIR
50	_	_	B-LIMIT
eggs	_	_	O
and	_	_	O
60	_	_	B-LIMIT
slices	_	_	O
of	_	_	O
ham	_	_	O
.	_	_	O
It	_	_	O
makes	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
3.5	_	_	B-PARAM
per	_	_	O
egg	_	_	B-VAR
sandwich	_	_	I-VAR
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
5	_	_	B-PARAM
per	_	_	O
ham	_	_	B-VAR
sandwich	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
sandwich	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Lucas	_	_	O
has	_	_	O
acquired	_	_	B-CONST_DIR
150	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
tropical	_	_	O
land	_	_	O
.	_	_	O
He	_	_	O
wants	_	_	O
to	_	_	O
plant	_	_	O
mango	_	_	B-VAR
trees	_	_	I-VAR
and	_	_	O
durian	_	_	B-VAR
trees	_	_	I-VAR
,	_	_	O
as	_	_	O
he	_	_	O
knows	_	_	O
he	_	_	O
can	_	_	O
sell	_	_	O
all	_	_	O
the	_	_	O
durians	_	_	B-VAR
and	_	_	O
mangos	_	_	B-VAR
harvested	_	_	O
.	_	_	O
Mango	_	_	B-VAR
trees	_	_	I-VAR
cost	_	_	O
$	_	_	O
150	_	_	B-PARAM
per	_	_	O
acre	_	_	O
to	_	_	O
maintain	_	_	O
,	_	_	O
yield	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
200	_	_	B-PARAM
per	_	_	O
acre	_	_	O
,	_	_	O
and	_	_	O
require	_	_	O
6	_	_	B-PARAM
days	_	_	O
worth	_	_	O
of	_	_	O
labor	_	_	O
per	_	_	O
acre	_	_	O
.	_	_	O
Durian	_	_	B-VAR
trees	_	_	I-VAR
cost	_	_	O
$	_	_	O
180	_	_	B-PARAM
per	_	_	O
acre	_	_	O
to	_	_	O
maintain	_	_	O
,	_	_	O
yield	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
300	_	_	B-PARAM
per	_	_	O
acre	_	_	O
,	_	_	O
and	_	_	O
require	_	_	O
3	_	_	B-PARAM
days	_	_	O
worth	_	_	O
of	_	_	O
labor	_	_	O
per	_	_	O
acre	_	_	O
.	_	_	O
Lucas	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
20000	_	_	B-LIMIT
and	_	_	O
700	_	_	B-LIMIT
days	_	_	O
worth	_	_	O
of	_	_	O
labor	_	_	O
available	_	_	B-CONST_DIR
(	_	_	O
among	_	_	O
all	_	_	O
his	_	_	O
workers	_	_	O
)	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
tree	_	_	O
should	_	_	O
Lucas	_	_	O
plant	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
film	_	_	O
company	_	_	O
is	_	_	O
deciding	_	_	O
where	_	_	O
to	_	_	O
promote	_	_	O
their	_	_	O
new	_	_	O
movie	_	_	O
.	_	_	O
Some	_	_	O
options	_	_	O
include	_	_	O
Banana	_	_	B-VAR
Livestream	_	_	I-VAR
,	_	_	O
Durian	_	_	B-VAR
TV	_	_	I-VAR
,	_	_	O
and	_	_	O
Orange	_	_	B-VAR
Premium	_	_	I-VAR
Video	_	_	I-VAR
advertisements	_	_	O
.	_	_	O
The	_	_	O
cost	_	_	O
for	_	_	O
each	_	_	O
option	_	_	O
and	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
viewers	_	_	B-OBJ_NAME
they	_	_	O
each	_	_	O
attract	_	_	O
are	_	_	O
given	_	_	O
.	_	_	O
On	_	_	O
Banana	_	_	B-VAR
Livestream	_	_	I-VAR
,	_	_	O
each	_	_	O
ad	_	_	O
costs	_	_	O
$	_	_	O
1500	_	_	B-PARAM
and	_	_	O
attracts	_	_	O
300,000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
On	_	_	O
Durian	_	_	B-VAR
TV	_	_	I-VAR
,	_	_	O
each	_	_	O
ad	_	_	O
costs	_	_	O
$	_	_	O
300	_	_	B-PARAM
and	_	_	O
attracts	_	_	O
10,000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
On	_	_	O
Orange	_	_	B-VAR
Premium	_	_	I-VAR
Video	_	_	I-VAR
,	_	_	O
each	_	_	O
ad	_	_	O
costs	_	_	O
$	_	_	O
500	_	_	B-PARAM
and	_	_	O
attracts	_	_	O
12,000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
Durian	_	_	B-VAR
TV	_	_	I-VAR
limits	_	_	B-CONST_DIR
the	_	_	I-CONST_DIR
number	_	_	I-CONST_DIR
of	_	_	O
advertisements	_	_	O
from	_	_	O
a	_	_	O
single	_	_	O
company	_	_	O
to	_	_	O
fifteen	_	_	B-LIMIT
.	_	_	O
Moreover	_	_	O
,	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
balance	_	_	O
the	_	_	O
advertising	_	_	O
among	_	_	O
the	_	_	O
three	_	_	O
types	_	_	O
of	_	_	O
media	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
a	_	_	O
third	_	_	B-LIMIT
of	_	_	O
the	_	_	O
total	_	_	O
number	_	_	O
of	_	_	O
advertisements	_	_	O
should	_	_	O
occur	_	_	O
on	_	_	O
Orange	_	_	B-VAR
Premium	_	_	I-VAR
Video	_	_	O
.	_	_	O
And	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
%	_	_	I-LIMIT
should	_	_	O
occur	_	_	O
on	_	_	O
Banana	_	_	B-VAR
Livestream	_	_	I-VAR
.	_	_	O
The	_	_	O
weekly	_	_	O
advertising	_	_	O
budget	_	_	B-CONST_DIR
is	_	_	O
$	_	_	O
20000	_	_	B-LIMIT
.	_	_	O
How	_	_	O
many	_	_	O
advertisements	_	_	O
should	_	_	O
be	_	_	O
run	_	_	O
in	_	_	O
each	_	_	O
of	_	_	O
the	_	_	O
three	_	_	O
types	_	_	O
of	_	_	O
media	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
audience	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
sports	_	_	O
company	_	_	O
makes	_	_	O
shuttlecocks	_	_	B-VAR
and	_	_	O
volleyballs	_	_	B-VAR
by	_	_	O
hand	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
shuttlecock	_	_	B-VAR
is	_	_	O
$	_	_	O
3.5	_	_	B-PARAM
,	_	_	O
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
volleyball	_	_	B-VAR
is	_	_	O
$	_	_	O
10	_	_	B-PARAM
.	_	_	O
To	_	_	O
make	_	_	O
one	_	_	O
shuttlecock	_	_	B-VAR
,	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
sewing	_	_	O
and	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
quality	_	_	O
checking	_	_	O
are	_	_	O
required	_	_	O
.	_	_	O
To	_	_	O
make	_	_	O
a	_	_	O
volleyball	_	_	B-VAR
,	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
sewing	_	_	O
and	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
quality	_	_	O
checking	_	_	O
are	_	_	O
required	_	_	O
.	_	_	O
In	_	_	O
a	_	_	O
month	_	_	O
,	_	_	O
4000	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
sewing	_	_	O
time	_	_	O
and	_	_	O
3000	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
quality	_	_	O
checking	_	_	O
time	_	_	O
are	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
product	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Tom	_	_	O
's	_	_	O
Florist	_	_	O
sells	_	_	O
sunflowers	_	_	B-VAR
and	_	_	O
roses	_	_	B-VAR
every	_	_	O
day	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
bouquet	_	_	O
of	_	_	O
sunflowers	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
7	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
bouquet	_	_	O
of	_	_	O
roses	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
12	_	_	B-PARAM
.	_	_	O
Each	_	_	O
bouquet	_	_	O
of	_	_	O
sunflowers	_	_	B-VAR
needs	_	_	O
4	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
clipping	_	_	O
and	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
packaging	_	_	O
.	_	_	O
Each	_	_	O
bouquet	_	_	O
of	_	_	O
roses	_	_	B-VAR
requires	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
clipping	_	_	O
and	_	_	O
7	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
packaging	_	_	O
.	_	_	O
In	_	_	O
total	_	_	O
,	_	_	O
there	_	_	O
are	_	_	O
1200	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
clipping	_	_	O
and	_	_	O
800	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
packaging	_	_	O
.	_	_	O
Having	_	_	O
signed	_	_	O
a	_	_	O
contract	_	_	O
with	_	_	O
a	_	_	O
local	_	_	O
restaurant	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
bouquets	_	_	O
of	_	_	O
sunflowers	_	_	B-VAR
must	_	_	O
be	_	_	O
picked	_	_	O
.	_	_	O
There	_	_	O
is	_	_	O
no	_	_	O
such	_	_	O
limit	_	_	O
on	_	_	O
bouquets	_	_	O
of	_	_	O
roses	_	_	B-VAR
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
.	_	_	O

Emma	_	_	O
is	_	_	O
required	_	_	O
to	_	_	O
take	_	_	O
two	_	_	O
medicines	_	_	O
AX7	_	_	O
and	_	_	O
BY5	_	_	O
every	_	_	O
day	_	_	O
.	_	_	O
She	_	_	O
needs	_	_	O
to	_	_	O
take	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
6	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
AX7	_	_	O
and	_	_	O
8	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
BY5	_	_	O
every	_	_	O
day	_	_	O
.	_	_	O
These	_	_	O
medicines	_	_	O
are	_	_	O
available	_	_	O
in	_	_	O
two	_	_	O
pills	_	_	O
named	_	_	O
Klun	_	_	B-VAR
and	_	_	O
Tao	_	_	B-VAR
.	_	_	O
One	_	_	O
pill	_	_	O
of	_	_	O
Klun	_	_	B-VAR
contains	_	_	O
1.5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
AX7	_	_	O
while	_	_	O
one	_	_	O
pill	_	_	O
of	_	_	O
Tao	_	_	B-VAR
contains	_	_	O
1.3	_	_	B-PARAM
grams	_	_	O
of	_	_	O
AX7	_	_	O
.	_	_	O
On	_	_	O
the	_	_	O
other	_	_	O
hand	_	_	O
,	_	_	O
one	_	_	O
pill	_	_	O
of	_	_	O
Klun	_	_	B-VAR
contains	_	_	O
1.8	_	_	B-PARAM
grams	_	_	O
of	_	_	O
BY5	_	_	O
and	_	_	O
one	_	_	O
pill	_	_	O
of	_	_	O
Tao	_	_	B-VAR
contains	_	_	O
2	_	_	B-PARAM
grams	_	_	O
of	_	_	O
BY5	_	_	O
.	_	_	O
The	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
pill	_	_	O
of	_	_	O
Klun	_	_	B-VAR
is	_	_	O
$	_	_	O
2.6	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
pill	_	_	O
of	_	_	O
Tao	_	_	B-VAR
is	_	_	O
$	_	_	O
3.2	_	_	B-PARAM
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
such	_	_	O
that	_	_	O
the	_	_	O
medicine	_	_	O
requirement	_	_	O
can	_	_	O
be	_	_	O
fulfilled	_	_	O
at	_	_	O
the	_	_	O
lowest	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
.	_	_	O

Vitamin	_	_	O
A	_	_	O
and	_	_	O
vitamin	_	_	O
B	_	_	O
can	_	_	O
be	_	_	O
obtained	_	_	O
in	_	_	O
two	_	_	O
supplement	_	_	O
drinks	_	_	O
.	_	_	O
One	_	_	O
is	_	_	O
carrot	_	_	B-VAR
juice	_	_	I-VAR
and	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
3.5	_	_	B-PARAM
per	_	_	O
serving	_	_	O
.	_	_	O
The	_	_	O
other	_	_	O
is	_	_	O
lemon	_	_	B-VAR
juice	_	_	I-VAR
and	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
6	_	_	B-PARAM
per	_	_	O
serving	_	_	O
.	_	_	O
One	_	_	O
serving	_	_	O
of	_	_	O
carrot	_	_	B-VAR
juice	_	_	I-VAR
contains	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
A	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
B.	_	_	O
One	_	_	O
serving	_	_	O
of	_	_	O
lemon	_	_	B-VAR
juice	_	_	I-VAR
contains	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
A	_	_	O
and	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
B.	_	_	O
In	_	_	O
a	_	_	O
day	_	_	O
,	_	_	O
it	_	_	O
is	_	_	O
recommended	_	_	O
to	_	_	O
get	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
25	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamin	_	_	O
A	_	_	O
and	_	_	O
vitamin	_	_	O
B	_	_	O
each	_	_	O
.	_	_	O
Find	_	_	O
the	_	_	O
optimal	_	_	O
mix	_	_	O
of	_	_	O
these	_	_	O
supplement	_	_	O
drinks	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
scooter	_	_	O
company	_	_	O
sells	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
scooters	_	_	O
:	_	_	O
foldable	_	_	B-VAR
scooters	_	_	I-VAR
and	_	_	O
electric	_	_	B-VAR
scooters	_	_	I-VAR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
foldable	_	_	B-VAR
scooter	_	_	I-VAR
is	_	_	O
$	_	_	O
150	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
electric	_	_	B-VAR
scooter	_	_	I-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
.	_	_	O
Each	_	_	O
product	_	_	O
requires	_	_	O
time	_	_	O
with	_	_	O
the	_	_	O
design	_	_	O
team	_	_	O
and	_	_	O
engineering	_	_	O
team	_	_	O
.	_	_	O
Each	_	_	O
foldable	_	_	B-VAR
scooter	_	_	I-VAR
needs	_	_	O
1.5	_	_	B-PARAM
hours	_	_	O
with	_	_	O
the	_	_	O
design	_	_	O
team	_	_	O
and	_	_	O
4	_	_	B-PARAM
hours	_	_	O
with	_	_	O
the	_	_	O
engineering	_	_	O
team	_	_	O
.	_	_	O
Each	_	_	O
electric	_	_	B-VAR
scooter	_	_	I-VAR
needs	_	_	O
3	_	_	B-PARAM
hours	_	_	O
with	_	_	O
the	_	_	O
design	_	_	O
team	_	_	O
and	_	_	O
6	_	_	B-PARAM
hours	_	_	O
with	_	_	O
the	_	_	O
engineering	_	_	O
team	_	_	O
.	_	_	O
Per	_	_	O
month	_	_	O
,	_	_	O
there	_	_	O
are	_	_	O
4000	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
on	_	_	O
the	_	_	O
design	_	_	O
team	_	_	O
and	_	_	O
5000	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
on	_	_	O
the	_	_	O
engineering	_	_	O
team	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
make	_	_	O
per	_	_	O
month	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Frank	_	_	O
has	_	_	B-CONST_DIR
1500	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
on	_	_	O
which	_	_	O
he	_	_	O
plans	_	_	O
to	_	_	O
grow	_	_	O
carrots	_	_	B-VAR
and	_	_	O
pumpkins	_	_	B-VAR
.	_	_	O
He	_	_	O
has	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
1000	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
tractor	_	_	O
time	_	_	O
available	_	_	O
and	_	_	O
$	_	_	O
25000	_	_	B-LIMIT
of	_	_	O
capital	_	_	O
available	_	_	O
.	_	_	O
Each	_	_	O
acre	_	_	O
of	_	_	O
carrots	_	_	B-VAR
requires	_	_	O
15	_	_	B-PARAM
hours	_	_	O
of	_	_	O
tractor	_	_	O
work	_	_	O
and	_	_	O
$	_	_	O
12	_	_	B-PARAM
of	_	_	O
capital	_	_	O
,	_	_	O
and	_	_	O
each	_	_	O
acre	_	_	O
of	_	_	O
pumpkins	_	_	B-VAR
requires	_	_	O
20	_	_	B-PARAM
hours	_	_	O
of	_	_	O
tractor	_	_	O
work	_	_	O
and	_	_	O
$	_	_	O
55	_	_	B-PARAM
of	_	_	O
capital	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
from	_	_	O
an	_	_	O
acre	_	_	O
of	_	_	O
carrots	_	_	B-VAR
is	_	_	O
$	_	_	O
80	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
from	_	_	O
an	_	_	O
acre	_	_	O
of	_	_	O
pumpkins	_	_	B-VAR
is	_	_	O
$	_	_	O
124	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
crop	_	_	O
should	_	_	O
he	_	_	O
plant	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
investment	_	_	O
institution	_	_	O
has	_	_	O
decided	_	_	O
to	_	_	O
invest	_	_	O
in	_	_	O
the	_	_	O
stock	_	_	O
market	_	_	O
for	_	_	O
the	_	_	O
first	_	_	O
time	_	_	O
.	_	_	O
Currently	_	_	O
,	_	_	O
it	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
800,000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
,	_	_	O
some	_	_	O
in	_	_	O
ABC	_	_	B-VAR
Software	_	_	I-VAR
and	_	_	O
the	_	_	O
rest	_	_	O
in	_	_	O
XYZ	_	_	B-VAR
Designs	_	_	I-VAR
.	_	_	O
The	_	_	O
money	_	_	O
invested	_	_	O
in	_	_	O
ABC	_	_	B-VAR
Software	_	_	I-VAR
must	_	_	O
not	_	_	B-CONST_DIR
be	_	_	I-CONST_DIR
greater	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
$	_	_	O
300,000	_	_	B-LIMIT
.	_	_	O
The	_	_	O
institution	_	_	O
has	_	_	O
decided	_	_	O
that	_	_	O
the	_	_	O
money	_	_	O
invested	_	_	O
in	_	_	O
ABC	_	_	B-VAR
Software	_	_	I-VAR
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
a	_	_	O
half	_	_	B-PARAM
as	_	_	O
much	_	_	O
as	_	_	O
that	_	_	O
in	_	_	O
XYZ	_	_	B-VAR
Designs	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
ABC	_	_	B-VAR
Software	_	_	I-VAR
earns	_	_	B-OBJ_NAME
12	_	_	B-PARAM
%	_	_	I-PARAM
,	_	_	O
and	_	_	O
the	_	_	O
XYZ	_	_	B-VAR
Designs	_	_	I-VAR
earns	_	_	B-OBJ_NAME
7.5	_	_	B-PARAM
%	_	_	I-PARAM
,	_	_	O
how	_	_	O
much	_	_	O
money	_	_	O
should	_	_	O
it	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
clothing	_	_	O
company	_	_	O
makes	_	_	O
coats	_	_	B-VAR
and	_	_	O
shirts	_	_	B-VAR
.	_	_	O
Each	_	_	O
coat	_	_	B-VAR
and	_	_	O
shirt	_	_	B-VAR
requires	_	_	O
operations	_	_	O
done	_	_	O
by	_	_	O
three	_	_	O
teams	_	_	O
:	_	_	O
measuring	_	_	O
,	_	_	O
cutting	_	_	O
,	_	_	O
and	_	_	O
sewing	_	_	O
.	_	_	O
The	_	_	O
measuring	_	_	O
team	_	_	O
is	_	_	O
available	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
50	_	_	B-LIMIT
hours	_	_	O
,	_	_	O
the	_	_	O
cutting	_	_	O
team	_	_	O
is	_	_	O
available	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
35	_	_	B-LIMIT
hours	_	_	O
,	_	_	O
and	_	_	O
the	_	_	O
sewing	_	_	O
team	_	_	O
is	_	_	O
available	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
40	_	_	B-LIMIT
hours	_	_	O
.	_	_	O
A	_	_	O
coat	_	_	B-VAR
requires	_	_	O
0.7	_	_	B-PARAM
hours	_	_	O
of	_	_	O
measuring	_	_	O
,	_	_	O
0.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
cutting	_	_	O
,	_	_	O
and	_	_	O
0.9	_	_	B-PARAM
hours	_	_	O
of	_	_	O
sewing	_	_	O
.	_	_	O
A	_	_	O
shirt	_	_	B-VAR
requires	_	_	O
0.2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
measuring	_	_	O
,	_	_	O
0.3	_	_	B-PARAM
hours	_	_	O
of	_	_	O
cutting	_	_	O
,	_	_	O
and	_	_	O
0.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
sewing	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
coat	_	_	B-VAR
is	_	_	O
$	_	_	O
6	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
shirt	_	_	B-VAR
is	_	_	O
$	_	_	O
11	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
factory	_	_	O
makes	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
car	_	_	O
oils	_	_	O
:	_	_	O
Regular	_	_	B-VAR
Synthetic	_	_	I-VAR
and	_	_	O
Premium	_	_	B-VAR
Synthetic	_	_	I-VAR
.	_	_	O
A	_	_	O
container	_	_	O
of	_	_	O
Regular	_	_	B-VAR
Synthetic	_	_	I-VAR
contains	_	_	O
25	_	_	B-PARAM
grams	_	_	O
of	_	_	O
substance	_	_	O
A	_	_	O
,	_	_	O
40	_	_	B-PARAM
grams	_	_	O
of	_	_	O
substance	_	_	O
B	_	_	O
and	_	_	O
36	_	_	B-PARAM
grams	_	_	O
of	_	_	O
substance	_	_	O
C.	_	_	O
A	_	_	O
container	_	_	O
of	_	_	O
Premium	_	_	B-VAR
Synthetic	_	_	I-VAR
contains	_	_	O
10	_	_	B-PARAM
grams	_	_	O
of	_	_	O
substance	_	_	O
A	_	_	O
,	_	_	O
25	_	_	B-PARAM
grams	_	_	O
of	_	_	O
substance	_	_	O
B	_	_	O
and	_	_	O
40	_	_	B-PARAM
grams	_	_	O
of	_	_	O
substance	_	_	O
C.	_	_	O
The	_	_	O
factory	_	_	O
has	_	_	B-CONST_DIR
1000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
substance	_	_	O
A	_	_	O
,	_	_	O
500	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
substance	_	_	O
B	_	_	O
,	_	_	O
900	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
substance	_	_	O
C.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
container	_	_	O
of	_	_	O
Regular	_	_	B-VAR
Synthetic	_	_	I-VAR
is	_	_	O
$	_	_	O
17.4	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
container	_	_	O
of	_	_	O
Premium	_	_	B-VAR
Synthetic	_	_	I-VAR
is	_	_	O
$	_	_	O
11.1	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
containers	_	_	O
of	_	_	O
each	_	_	O
oil	_	_	O
should	_	_	O
the	_	_	O
factory	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
steel	_	_	O
company	_	_	O
produces	_	_	B-CONST_DIR
120	_	_	B-LIMIT
tons	_	_	O
of	_	_	O
iron	_	_	O
ore	_	_	O
and	_	_	O
70	_	_	B-LIMIT
tons	_	_	O
of	_	_	O
zinc	_	_	O
ore	_	_	O
each	_	_	O
month	_	_	O
.	_	_	O
These	_	_	O
can	_	_	O
be	_	_	O
treated	_	_	O
in	_	_	O
different	_	_	O
ways	_	_	O
to	_	_	O
produce	_	_	O
three	_	_	O
types	_	_	O
of	_	_	O
vessels	_	_	O
:	_	_	O
general	_	_	B-VAR
purpose	_	_	I-VAR
vessels	_	_	I-VAR
,	_	_	O
pharmaceutical	_	_	B-VAR
vessels	_	_	I-VAR
or	_	_	O
pressure	_	_	B-VAR
vessels	_	_	I-VAR
.	_	_	O
To	_	_	O
produce	_	_	O
1	_	_	O
set	_	_	O
of	_	_	O
general	_	_	B-VAR
purpose	_	_	I-VAR
vessels	_	_	I-VAR
requires	_	_	O
3.5	_	_	B-PARAM
tons	_	_	O
of	_	_	O
iron	_	_	O
ore	_	_	O
and	_	_	O
2	_	_	B-PARAM
tons	_	_	O
of	_	_	O
zinc	_	_	O
ore	_	_	O
.	_	_	O
To	_	_	O
produce	_	_	O
1	_	_	O
set	_	_	O
of	_	_	O
pharmaceutical	_	_	B-VAR
vessels	_	_	I-VAR
requires	_	_	O
4	_	_	B-PARAM
tons	_	_	O
of	_	_	O
iron	_	_	O
ore	_	_	O
and	_	_	O
5	_	_	B-PARAM
tons	_	_	O
of	_	_	O
zinc	_	_	O
ore	_	_	O
.	_	_	O
Finally	_	_	O
,	_	_	O
to	_	_	O
produce	_	_	O
1	_	_	O
set	_	_	O
of	_	_	O
pressure	_	_	B-VAR
vessels	_	_	I-VAR
requires	_	_	O
2	_	_	B-PARAM
tons	_	_	O
of	_	_	O
iron	_	_	O
ore	_	_	O
and	_	_	O
3.5	_	_	B-PARAM
tons	_	_	O
of	_	_	O
zinc	_	_	O
ore	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
set	_	_	O
from	_	_	O
selling	_	_	O
the	_	_	O
vessels	_	_	O
are	_	_	O
$	_	_	O
2000	_	_	B-PARAM
,	_	_	O
$	_	_	O
3000	_	_	B-PARAM
and	_	_	O
$	_	_	O
4500	_	_	B-PARAM
for	_	_	O
the	_	_	O
general	_	_	B-VAR
purpose	_	_	I-VAR
,	_	_	O
pharmaceutical	_	_	B-VAR
,	_	_	O
and	_	_	O
pressure	_	_	B-VAR
vessels	_	_	I-VAR
respectively	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
sets	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
vessel	_	_	O
should	_	_	O
be	_	_	O
produced	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Boarstone	_	_	O
factory	_	_	O
has	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
machines	_	_	O
:	_	_	O
a	_	_	O
regular	_	_	B-VAR
one	_	_	O
and	_	_	O
an	_	_	O
advanced	_	_	B-VAR
one	_	_	O
.	_	_	O
A	_	_	O
regular	_	_	B-VAR
machine	_	_	I-VAR
can	_	_	O
perform	_	_	O
5	_	_	B-PARAM
tasks	_	_	O
per	_	_	O
hour	_	_	O
,	_	_	O
requires	_	_	O
2	_	_	B-PARAM
workers	_	_	O
,	_	_	O
and	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
1000	_	_	B-PARAM
.	_	_	O
An	_	_	O
advanced	_	_	B-VAR
machine	_	_	I-VAR
can	_	_	O
perform	_	_	O
25	_	_	B-PARAM
tasks	_	_	O
per	_	_	O
hour	_	_	O
,	_	_	O
requires	_	_	O
5	_	_	B-PARAM
workers	_	_	O
,	_	_	O
and	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
10000	_	_	B-PARAM
.	_	_	O
The	_	_	O
factory	_	_	O
wants	_	_	O
to	_	_	O
complete	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
120	_	_	B-LIMIT
tasks	_	_	O
per	_	_	O
hour	_	_	O
with	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
20	_	_	B-LIMIT
workers	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
machine	_	_	O
,	_	_	O
regular	_	_	B-VAR
and	_	_	O
advanced	_	_	B-VAR
,	_	_	O
need	_	_	O
to	_	_	O
be	_	_	O
used	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
and	_	_	O
meet	_	_	O
the	_	_	O
requirements	_	_	O
?	_	_	O

Eric	_	_	O
wants	_	_	O
to	_	_	O
sell	_	_	O
his	_	_	O
inventory	_	_	B-CONST_DIR
of	_	_	O
25	_	_	B-LIMIT
wireless	_	_	O
keyboards	_	_	O
,	_	_	O
13	_	_	B-LIMIT
wired	_	_	O
earbuds	_	_	O
,	_	_	O
and	_	_	O
19	_	_	B-LIMIT
USB	_	_	O
hubs	_	_	O
.	_	_	O
He	_	_	O
decides	_	_	O
to	_	_	O
offer	_	_	O
two	_	_	O
combos	_	_	O
:	_	_	O
Combo	_	_	B-VAR
X	_	_	I-VAR
and	_	_	O
Combo	_	_	B-VAR
Y.	_	_	I-VAR
Combo	_	_	B-VAR
X	_	_	I-VAR
brings	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
12	_	_	B-PARAM
and	_	_	O
contains	_	_	O
2	_	_	B-PARAM
wireless	_	_	O
keyboards	_	_	O
and	_	_	O
2	_	_	B-PARAM
USB	_	_	O
hubs	_	_	O
.	_	_	O
Combo	_	_	B-VAR
Y	_	_	I-VAR
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
15	_	_	B-PARAM
and	_	_	O
contains	_	_	O
1	_	_	B-PARAM
wireless	_	_	O
keyboard	_	_	O
,	_	_	O
3	_	_	B-PARAM
wired	_	_	O
earbuds	_	_	O
,	_	_	O
and	_	_	O
1	_	_	B-PARAM
USB	_	_	O
hub	_	_	O
.	_	_	O
Assuming	_	_	O
he	_	_	O
can	_	_	O
sell	_	_	O
all	_	_	O
combos	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
prepare	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

Thomas	_	_	O
has	_	_	O
50	_	_	O
cows	_	_	O
and	_	_	O
feeds	_	_	O
them	_	_	O
on	_	_	O
silage	_	_	B-VAR
and	_	_	O
mixed	_	_	B-VAR
grains	_	_	I-VAR
.	_	_	O
Silage	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
215	_	_	B-PARAM
per	_	_	O
kilogram	_	_	O
while	_	_	O
mixed	_	_	B-VAR
grains	_	_	I-VAR
cost	_	_	B-OBJ_NAME
$	_	_	O
320	_	_	B-PARAM
per	_	_	O
kilogram	_	_	O
.	_	_	O
Each	_	_	O
kilogram	_	_	O
of	_	_	O
silage	_	_	B-VAR
contains	_	_	O
0.5	_	_	B-PARAM
kilograms	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
0.2	_	_	B-PARAM
kilograms	_	_	O
of	_	_	O
vitamins	_	_	O
,	_	_	O
and	_	_	O
0.1	_	_	B-PARAM
kilograms	_	_	O
of	_	_	O
minerals	_	_	O
.	_	_	O
Each	_	_	O
kilogram	_	_	O
of	_	_	O
mixed	_	_	B-VAR
grains	_	_	I-VAR
contains	_	_	O
0.2	_	_	B-PARAM
kilograms	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
0.1	_	_	B-PARAM
kilograms	_	_	O
of	_	_	O
vitamins	_	_	O
,	_	_	O
and	_	_	O
0.2	_	_	B-PARAM
kilograms	_	_	O
of	_	_	O
minerals	_	_	O
.	_	_	O
Each	_	_	O
cow	_	_	O
requires	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
2	_	_	B-LIMIT
kilograms	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
1.5	_	_	B-LIMIT
kilograms	_	_	O
of	_	_	O
minerals	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
each	_	_	O
cow	_	_	O
can	_	_	O
have	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
1.0	_	_	B-LIMIT
kilograms	_	_	O
of	_	_	O
vitamins	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
How	_	_	O
should	_	_	O
Thomas	_	_	O
feed	_	_	O
his	_	_	O
cows	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
while	_	_	O
ensuring	_	_	O
the	_	_	O
cows	_	_	O
get	_	_	O
the	_	_	O
required	_	_	O
nutrition	_	_	O
?	_	_	O

Bob	_	_	O
wants	_	_	O
to	_	_	O
mix	_	_	O
his	_	_	O
animal	_	_	O
feeds	_	_	O
,	_	_	O
oats	_	_	B-VAR
and	_	_	O
sunflower	_	_	B-VAR
seeds	_	_	I-VAR
,	_	_	O
in	_	_	O
such	_	_	O
a	_	_	O
way	_	_	O
that	_	_	O
the	_	_	O
mixture	_	_	O
will	_	_	O
contain	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
250	_	_	B-LIMIT
units	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
400	_	_	B-LIMIT
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
Oats	_	_	B-VAR
cost	_	_	B-OBJ_NAME
$	_	_	O
50	_	_	B-PARAM
per	_	_	O
kilogram	_	_	O
and	_	_	O
contain	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
16	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
Sunflower	_	_	B-VAR
seeds	_	_	I-VAR
cost	_	_	B-OBJ_NAME
$	_	_	O
70	_	_	B-PARAM
per	_	_	O
kilogram	_	_	O
and	_	_	O
contain	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
22	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
Minimize	_	_	B-OBJ_DIR
the	_	_	O
cost	_	_	B-OBJ_NAME
of	_	_	O
the	_	_	O
mixture	_	_	O
.	_	_	O

A	_	_	O
violin	_	_	O
factory	_	_	O
makes	_	_	O
modern	_	_	B-VAR
violins	_	_	I-VAR
and	_	_	O
baroque	_	_	B-VAR
violin	_	_	I-VAR
.	_	_	O
A	_	_	O
modern	_	_	B-VAR
violin	_	_	I-VAR
takes	_	_	O
5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
woodworking	_	_	O
time	_	_	O
and	_	_	O
3.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
assembling	_	_	O
time	_	_	O
.	_	_	O
A	_	_	O
baroque	_	_	B-VAR
violin	_	_	I-VAR
takes	_	_	O
4	_	_	B-PARAM
hours	_	_	O
of	_	_	O
woodworking	_	_	O
time	_	_	O
and	_	_	O
5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
assembling	_	_	O
time	_	_	O
.	_	_	O
The	_	_	O
factory	_	_	O
has	_	_	O
150	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
woodworking	_	_	O
time	_	_	O
and	_	_	O
200	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
assembling	_	_	O
time	_	_	O
available	_	_	B-CONST_DIR
per	_	_	O
day	_	_	O
among	_	_	O
all	_	_	O
the	_	_	O
workers	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
modern	_	_	B-VAR
violin	_	_	I-VAR
is	_	_	O
$	_	_	O
150	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
baroque	_	_	B-VAR
violin	_	_	I-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
instrument	_	_	O
should	_	_	O
the	_	_	O
factory	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profits	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
food	_	_	O
truck	_	_	O
makes	_	_	O
apple	_	_	B-VAR
and	_	_	O
orange	_	_	B-VAR
smoothies	_	_	I-VAR
.	_	_	O
It	_	_	O
takes	_	_	O
6	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
cutting	_	_	O
machine	_	_	O
and	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
blending	_	_	O
machine	_	_	O
to	_	_	O
make	_	_	O
an	_	_	O
apple	_	_	B-VAR
smoothie	_	_	I-VAR
.	_	_	O
It	_	_	O
takes	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
cutting	_	_	O
machine	_	_	O
and	_	_	O
2	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
blending	_	_	O
machine	_	_	O
to	_	_	O
make	_	_	O
an	_	_	O
orange	_	_	B-VAR
smoothie	_	_	I-VAR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
apple	_	_	B-VAR
smoothie	_	_	I-VAR
is	_	_	O
$	_	_	O
3.5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
orange	_	_	B-VAR
smoothie	_	_	I-VAR
is	_	_	O
$	_	_	O
4.5	_	_	B-PARAM
.	_	_	O
If	_	_	O
both	_	_	O
the	_	_	O
cutting	_	_	O
machine	_	_	O
and	_	_	O
blending	_	_	O
machine	_	_	O
are	_	_	O
available	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
500	_	_	B-LIMIT
minutes	_	_	O
per	_	_	O
day	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
smoothie	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Alpha	_	_	O
Glass	_	_	O
makes	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
glass	_	_	O
panes	_	_	O
:	_	_	O
a	_	_	O
bulletproof	_	_	B-VAR
glass	_	_	I-VAR
pane	_	_	I-VAR
and	_	_	O
a	_	_	O
fire	_	_	B-VAR
-	_	_	I-VAR
rated	_	_	I-VAR
glass	_	_	I-VAR
pane	_	_	I-VAR
.	_	_	O
Both	_	_	O
require	_	_	O
time	_	_	O
on	_	_	O
a	_	_	O
heating	_	_	O
and	_	_	O
cooling	_	_	O
machine	_	_	O
.	_	_	O
Both	_	_	O
machines	_	_	O
are	_	_	O
available	_	_	O
for	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
350	_	_	B-LIMIT
minutes	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
It	_	_	O
takes	_	_	O
4	_	_	B-PARAM
minutes	_	_	O
in	_	_	O
the	_	_	O
heating	_	_	O
machine	_	_	O
and	_	_	O
6	_	_	B-PARAM
minutes	_	_	O
in	_	_	O
the	_	_	O
cooling	_	_	O
machine	_	_	O
to	_	_	O
make	_	_	O
one	_	_	O
bulletproof	_	_	B-VAR
glass	_	_	I-VAR
pane	_	_	I-VAR
.	_	_	O
It	_	_	O
takes	_	_	O
7	_	_	B-PARAM
minutes	_	_	O
in	_	_	O
the	_	_	O
heating	_	_	O
machine	_	_	O
and	_	_	O
9	_	_	B-PARAM
minutes	_	_	O
in	_	_	O
the	_	_	O
cooling	_	_	O
machine	_	_	O
to	_	_	O
make	_	_	O
one	_	_	O
fire	_	_	B-VAR
-	_	_	I-VAR
rated	_	_	I-VAR
glass	_	_	I-VAR
pane	_	_	I-VAR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
pane	_	_	O
of	_	_	O
bulletproof	_	_	B-VAR
glass	_	_	I-VAR
is	_	_	O
$	_	_	O
12	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
pane	_	_	O
of	_	_	O
fire	_	_	B-VAR
-	_	_	I-VAR
rated	_	_	I-VAR
glass	_	_	I-VAR
is	_	_	O
$	_	_	O
9.5	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
panes	_	_	O
of	_	_	O
each	_	_	O
glass	_	_	O
type	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O
What	_	_	O
is	_	_	O
the	_	_	O
maximum	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

Kald	_	_	O
Vehicle	_	_	O
makes	_	_	O
minivans	_	_	B-VAR
and	_	_	O
trucks	_	_	B-VAR
,	_	_	O
each	_	_	O
requiring	_	_	O
the	_	_	O
use	_	_	O
of	_	_	O
an	_	_	O
assembly	_	_	O
machine	_	_	O
and	_	_	O
a	_	_	O
painting	_	_	O
machine	_	_	O
.	_	_	O
It	_	_	O
takes	_	_	O
2	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
assembly	_	_	O
machine	_	_	O
and	_	_	O
1.5	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
painting	_	_	O
machine	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
minivan	_	_	B-VAR
.	_	_	O
On	_	_	O
the	_	_	O
other	_	_	O
hand	_	_	O
,	_	_	O
it	_	_	O
takes	_	_	O
4	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
assembly	_	_	O
machine	_	_	O
and	_	_	O
2	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
painting	_	_	O
machine	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
truck	_	_	B-VAR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
minivan	_	_	B-VAR
is	_	_	O
$	_	_	O
1200	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
truck	_	_	B-VAR
is	_	_	O
$	_	_	O
1700	_	_	B-PARAM
.	_	_	O
The	_	_	O
assembly	_	_	O
machine	_	_	O
is	_	_	O
available	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
12	_	_	B-LIMIT
hours	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
the	_	_	O
painting	_	_	O
machine	_	_	O
is	_	_	O
available	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
11	_	_	B-LIMIT
hours	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
vehicle	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
make	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Leeside	_	_	O
Designs	_	_	O
sells	_	_	O
office	_	_	B-VAR
and	_	_	O
dining	_	_	B-VAR
chairs	_	_	I-VAR
.	_	_	O
An	_	_	O
office	_	_	B-VAR
chair	_	_	I-VAR
costs	_	_	O
the	_	_	O
company	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
a	_	_	O
dining	_	_	B-VAR
chair	_	_	I-VAR
costs	_	_	O
the	_	_	O
company	_	_	O
$	_	_	O
250	_	_	B-PARAM
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
office	_	_	B-VAR
chair	_	_	I-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
120	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
dining	_	_	B-VAR
chair	_	_	I-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
180	_	_	B-PARAM
.	_	_	O
The	_	_	O
company	_	_	O
does	_	_	O
not	_	_	B-CONST_DIR
want	_	_	I-CONST_DIR
to	_	_	I-CONST_DIR
invest	_	_	I-CONST_DIR
more	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
$	_	_	O
20000	_	_	B-LIMIT
on	_	_	O
chairs	_	_	O
and	_	_	O
estimates	_	_	O
a	_	_	O
monthly	_	_	O
demand	_	_	O
of	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
130	_	_	B-LIMIT
total	_	_	O
chairs	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
chair	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
stock	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

John	_	_	O
is	_	_	O
an	_	_	O
artisan	_	_	O
and	_	_	O
he	_	_	O
makes	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
terracotta	_	_	O
pots	_	_	O
:	_	_	O
an	_	_	O
oval	_	_	B-VAR
pot	_	_	I-VAR
and	_	_	O
a	_	_	O
square	_	_	B-VAR
pot	_	_	I-VAR
.	_	_	O
Each	_	_	O
oval	_	_	B-VAR
pot	_	_	I-VAR
requires	_	_	O
40	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
shaping	_	_	O
time	_	_	O
and	_	_	O
50	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
baking	_	_	O
time	_	_	O
.	_	_	O
Each	_	_	O
square	_	_	B-VAR
pot	_	_	I-VAR
requires	_	_	O
35	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
shaping	_	_	O
time	_	_	O
and	_	_	O
80	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
baking	_	_	O
time	_	_	O
.	_	_	O
Per	_	_	O
week	_	_	O
,	_	_	O
there	_	_	O
are	_	_	O
2500	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
shaping	_	_	O
and	_	_	O
3800	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
baking	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
oval	_	_	B-VAR
pot	_	_	I-VAR
is	_	_	O
$	_	_	O
4.5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
square	_	_	B-VAR
pot	_	_	I-VAR
is	_	_	O
$	_	_	O
8	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
pots	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
he	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
tasty	_	_	O
burrito	_	_	O
is	_	_	O
to	_	_	O
be	_	_	O
made	_	_	O
from	_	_	O
units	_	_	O
of	_	_	O
beans	_	_	B-VAR
and	_	_	O
onions	_	_	B-VAR
and	_	_	O
is	_	_	O
to	_	_	O
contain	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
110	_	_	B-LIMIT
units	_	_	O
of	_	_	O
spice	_	_	O
and	_	_	O
80	_	_	B-LIMIT
units	_	_	O
of	_	_	O
flavor	_	_	O
.	_	_	O
Beans	_	_	B-VAR
cost	_	_	B-OBJ_NAME
$	_	_	O
6	_	_	B-PARAM
per	_	_	O
unit	_	_	O
and	_	_	O
onion	_	_	B-VAR
cost	_	_	B-OBJ_NAME
$	_	_	O
8	_	_	B-PARAM
per	_	_	O
unit	_	_	O
.	_	_	O
One	_	_	O
unit	_	_	O
of	_	_	O
beans	_	_	B-VAR
contains	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
spice	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
flavor	_	_	O
.	_	_	O
One	_	_	O
unit	_	_	O
of	_	_	O
onions	_	_	B-VAR
contains	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
spice	_	_	O
and	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
flavor	_	_	O
.	_	_	O
Formulate	_	_	O
this	_	_	O
as	_	_	O
an	_	_	O
LP	_	_	O
and	_	_	O
find	_	_	O
the	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
burrito	_	_	O
that	_	_	O
can	_	_	O
be	_	_	O
made	_	_	O
.	_	_	O

Daniel	_	_	O
has	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
liquid	_	_	O
supplementation	_	_	O
available	_	_	O
:	_	_	O
Zeta	_	_	B-VAR
and	_	_	O
Phi	_	_	B-VAR
.	_	_	O
After	_	_	O
consulting	_	_	O
with	_	_	O
a	_	_	O
doctor	_	_	O
,	_	_	O
he	_	_	O
finds	_	_	O
that	_	_	O
he	_	_	O
needs	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
25	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
iron	_	_	O
and	_	_	O
40	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
vitamin	_	_	O
A.	_	_	O
Zeta	_	_	B-VAR
supplementation	_	_	I-VAR
consists	_	_	O
of	_	_	O
15	_	_	B-PARAM
%	_	_	I-PARAM
iron	_	_	O
and	_	_	O
20	_	_	B-PARAM
%	_	_	I-PARAM
vitamin	_	_	O
A	_	_	O
while	_	_	O
Phi	_	_	B-VAR
supplementation	_	_	I-VAR
consists	_	_	O
of	_	_	O
20	_	_	B-PARAM
%	_	_	I-PARAM
iron	_	_	O
and	_	_	O
45	_	_	B-PARAM
%	_	_	I-PARAM
vitamin	_	_	O
A.	_	_	O
Zeta	_	_	B-VAR
supplementation	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
0.08	_	_	B-PARAM
per	_	_	O
gram	_	_	O
while	_	_	O
Phi	_	_	B-VAR
supplementation	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
0.18	_	_	B-PARAM
per	_	_	O
gram	_	_	O
.	_	_	O
How	_	_	O
much	_	_	O
of	_	_	O
each	_	_	O
supplementation	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
meet	_	_	O
his	_	_	O
requirements	_	_	O
and	_	_	O
minimize	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
?	_	_	O

Alex	_	_	O
is	_	_	O
making	_	_	O
a	_	_	O
special	_	_	O
vitamin	_	_	O
mix	_	_	O
using	_	_	O
two	_	_	O
drinks	_	_	O
:	_	_	O
orange	_	_	B-VAR
juice	_	_	I-VAR
and	_	_	O
apple	_	_	B-VAR
juice	_	_	I-VAR
.	_	_	O
The	_	_	O
vitamin	_	_	O
mix	_	_	O
must	_	_	O
contain	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
units	_	_	O
of	_	_	O
Vitamin	_	_	O
A	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
200	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamin	_	_	O
D	_	_	O
,	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
150	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamin	_	_	O
E.	_	_	O
A	_	_	O
cup	_	_	O
of	_	_	O
orange	_	_	B-VAR
juice	_	_	I-VAR
contains	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
Vitamin	_	_	O
A	_	_	O
,	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
Vitamin	_	_	O
D	_	_	O
,	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
Vitamin	_	_	O
E	_	_	O
,	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
Vitamin	_	_	B-OBJ_NAME
K.	_	_	I-OBJ_NAME
A	_	_	O
cup	_	_	O
of	_	_	O
apple	_	_	B-VAR
juice	_	_	I-VAR
contains	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
Vitamin	_	_	O
A	_	_	O
,	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
Vitamin	_	_	O
D	_	_	O
,	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
Vitamin	_	_	O
E	_	_	O
,	_	_	O
and	_	_	O
9	_	_	B-PARAM
units	_	_	O
of	_	_	O
Vitamin	_	_	B-OBJ_NAME
K.	_	_	I-OBJ_NAME
How	_	_	O
many	_	_	O
cups	_	_	O
of	_	_	O
each	_	_	O
drink	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
make	_	_	O
the	_	_	O
vitamin	_	_	O
mix	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
Vitamin	_	_	I-OBJ_NAME
K	_	_	I-OBJ_NAME
?	_	_	O

Sofia	_	_	O
Paint	_	_	O
store	_	_	O
mixes	_	_	O
two	_	_	O
brands	_	_	O
of	_	_	O
paint	_	_	O
,	_	_	O
Iota	_	_	B-VAR
and	_	_	O
Lambda	_	_	B-VAR
,	_	_	O
to	_	_	O
create	_	_	O
a	_	_	O
new	_	_	O
mixture	_	_	O
of	_	_	O
paint	_	_	O
.	_	_	O
A	_	_	O
can	_	_	O
of	_	_	O
Iota	_	_	B-VAR
paint	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
8	_	_	B-PARAM
and	_	_	O
a	_	_	O
can	_	_	O
of	_	_	O
Lambda	_	_	B-VAR
paint	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
12	_	_	B-PARAM
.	_	_	O
A	_	_	O
can	_	_	O
of	_	_	O
Iota	_	_	B-VAR
paint	_	_	I-VAR
contains	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
dye	_	_	O
,	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
thinner	_	_	O
,	_	_	O
and	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
oil	_	_	O
.	_	_	O
A	_	_	O
can	_	_	O
of	_	_	O
Lambda	_	_	B-VAR
paint	_	_	I-VAR
contains	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
dye	_	_	O
,	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
thinner	_	_	O
,	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
oil	_	_	O
.	_	_	O
The	_	_	O
minimum	_	_	B-CONST_DIR
requirements	_	_	O
of	_	_	O
dye	_	_	O
,	_	_	O
thinner	_	_	O
,	_	_	O
and	_	_	O
oil	_	_	O
for	_	_	O
the	_	_	O
new	_	_	O
mixture	_	_	O
are	_	_	O
10	_	_	B-LIMIT
units	_	_	O
,	_	_	O
12	_	_	B-LIMIT
units	_	_	O
,	_	_	O
and	_	_	O
15	_	_	B-LIMIT
units	_	_	O
,	_	_	O
respectively	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
cans	_	_	O
of	_	_	O
each	_	_	O
paint	_	_	O
brand	_	_	O
should	_	_	O
be	_	_	O
mixed	_	_	O
to	_	_	O
achieve	_	_	O
the	_	_	O
new	_	_	O
mixture	_	_	O
at	_	_	O
a	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
double	_	_	O
-	_	_	O
decker	_	_	O
bus	_	_	O
can	_	_	O
carry	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
50	_	_	B-LIMIT
passengers	_	_	O
.	_	_	O
It	_	_	O
has	_	_	O
two	_	_	O
seat	_	_	O
types	_	_	O
:	_	_	O
bottom	_	_	B-VAR
deck	_	_	I-VAR
seats	_	_	I-VAR
and	_	_	O
top	_	_	B-VAR
deck	_	_	I-VAR
seats	_	_	I-VAR
.	_	_	O
A	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
25	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
bottom	_	_	B-VAR
deck	_	_	I-VAR
seat	_	_	I-VAR
ticket	_	_	O
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
35	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
top	_	_	B-VAR
deck	_	_	I-VAR
seat	_	_	I-VAR
ticket	_	_	O
.	_	_	O
The	_	_	O
bus	_	_	O
factory	_	_	O
reserves	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
seats	_	_	O
as	_	_	O
bottom	_	_	B-VAR
deck	_	_	I-VAR
seats	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
2	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
many	_	_	O
passengers	_	_	O
prefer	_	_	O
to	_	_	O
travel	_	_	O
on	_	_	O
top	_	_	B-VAR
deck	_	_	I-VAR
seats	_	_	I-VAR
than	_	_	O
on	_	_	O
bottom	_	_	B-VAR
deck	_	_	I-VAR
seats	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
seats	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Delta	_	_	O
Electronics	_	_	O
sells	_	_	O
two	_	_	O
microphones	_	_	O
:	_	_	O
a	_	_	O
regular	_	_	B-VAR
one	_	_	O
and	_	_	O
a	_	_	O
premium	_	_	B-VAR
one	_	_	O
.	_	_	O
The	_	_	O
regular	_	_	B-VAR
microphone	_	_	I-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
75	_	_	B-PARAM
and	_	_	O
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
80	_	_	B-PARAM
.	_	_	O
The	_	_	O
premium	_	_	B-VAR
microphone	_	_	I-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
100	_	_	B-PARAM
and	_	_	O
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
95	_	_	B-PARAM
.	_	_	O
The	_	_	O
store	_	_	O
owner	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
30000	_	_	B-LIMIT
for	_	_	O
investing	_	_	O
in	_	_	O
microphone	_	_	O
inventory	_	_	O
and	_	_	O
estimates	_	_	O
a	_	_	O
total	_	_	O
monthly	_	_	O
demand	_	_	O
of	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
300	_	_	B-LIMIT
microphones	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
microphones	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
should	_	_	O
be	_	_	O
stocked	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Lucas	_	_	O
has	_	_	B-CONST_DIR
120	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
on	_	_	O
which	_	_	O
he	_	_	O
grows	_	_	O
carrots	_	_	B-VAR
and	_	_	O
onions	_	_	B-VAR
.	_	_	O
It	_	_	O
takes	_	_	O
1.5	_	_	B-PARAM
days	_	_	O
of	_	_	O
tractor	_	_	O
time	_	_	O
and	_	_	O
2.5	_	_	B-PARAM
days	_	_	O
of	_	_	O
hand	_	_	O
-	_	_	O
picking	_	_	O
time	_	_	O
per	_	_	O
acre	_	_	O
of	_	_	O
carrots	_	_	B-VAR
.	_	_	O
It	_	_	O
takes	_	_	O
2	_	_	B-PARAM
days	_	_	O
of	_	_	O
tractor	_	_	O
time	_	_	O
and	_	_	O
2	_	_	B-PARAM
days	_	_	O
of	_	_	O
hand	_	_	O
-	_	_	O
picking	_	_	O
time	_	_	O
per	_	_	O
acre	_	_	O
of	_	_	O
onions	_	_	B-VAR
.	_	_	O
In	_	_	O
a	_	_	O
year	_	_	O
,	_	_	O
there	_	_	O
are	_	_	O
120	_	_	B-LIMIT
days	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
tractor	_	_	O
use	_	_	O
and	_	_	O
200	_	_	B-LIMIT
days	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
hand	_	_	O
-	_	_	O
picking	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
carrots	_	_	B-VAR
is	_	_	O
$	_	_	O
75	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
onions	_	_	B-VAR
is	_	_	O
$	_	_	O
90	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
grown	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

James	_	_	O
is	_	_	O
following	_	_	O
a	_	_	O
fitness	_	_	O
plan	_	_	O
and	_	_	O
has	_	_	O
decided	_	_	O
to	_	_	O
mix	_	_	O
two	_	_	O
brands	_	_	O
of	_	_	O
protein	_	_	O
drinks	_	_	O
to	_	_	O
create	_	_	O
a	_	_	O
new	_	_	O
mixture	_	_	O
.	_	_	O
The	_	_	O
Delta	_	_	B-VAR
brand	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
2.5	_	_	B-PARAM
per	_	_	O
can	_	_	O
and	_	_	O
contains	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
carbs	_	_	O
,	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
The	_	_	O
Phi	_	_	B-VAR
brand	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
4	_	_	B-PARAM
per	_	_	O
can	_	_	O
and	_	_	O
contains	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
carbs	_	_	O
,	_	_	O
and	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
James	_	_	O
wants	_	_	O
to	_	_	O
create	_	_	O
a	_	_	O
mixture	_	_	O
having	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
80	_	_	B-LIMIT
units	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
50	_	_	B-LIMIT
units	_	_	O
of	_	_	O
carbs	_	_	O
,	_	_	O
and	_	_	O
65	_	_	B-LIMIT
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
cans	_	_	O
of	_	_	O
each	_	_	O
brand	_	_	O
of	_	_	O
drink	_	_	O
should	_	_	O
be	_	_	O
mixed	_	_	O
to	_	_	O
create	_	_	O
the	_	_	O
new	_	_	O
mixture	_	_	O
at	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
?	_	_	O

Nu	_	_	O
Designs	_	_	O
makes	_	_	O
bookcases	_	_	B-VAR
and	_	_	O
garden	_	_	B-VAR
chairs	_	_	I-VAR
.	_	_	O
Each	_	_	O
bookcase	_	_	B-VAR
requires	_	_	O
3	_	_	B-PARAM
hours	_	_	O
of	_	_	O
woodworking	_	_	O
,	_	_	O
2	_	_	B-PARAM
boxes	_	_	O
of	_	_	O
nails	_	_	O
,	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
varnish	_	_	O
.	_	_	O
Each	_	_	O
garden	_	_	B-VAR
chair	_	_	I-VAR
requires	_	_	O
2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
woodworking	_	_	O
,	_	_	O
4	_	_	B-PARAM
boxes	_	_	O
of	_	_	O
nails	_	_	O
,	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
varnish	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
80	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
woodworking	_	_	O
available	_	_	B-CONST_DIR
,	_	_	O
70	_	_	B-LIMIT
boxes	_	_	O
of	_	_	O
nails	_	_	O
available	_	_	B-CONST_DIR
,	_	_	O
and	_	_	O
90	_	_	B-LIMIT
units	_	_	O
of	_	_	O
varnish	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
If	_	_	O
each	_	_	O
bookcase	_	_	B-VAR
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
270	_	_	B-PARAM
and	_	_	O
each	_	_	O
garden	_	_	B-VAR
chair	_	_	I-VAR
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
350	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
factory	_	_	O
makes	_	_	O
dotted	_	_	B-VAR
paper	_	_	I-VAR
and	_	_	O
grid	_	_	B-VAR
paper	_	_	I-VAR
.	_	_	O
Both	_	_	O
have	_	_	O
to	_	_	O
go	_	_	O
through	_	_	O
a	_	_	O
cutting	_	_	O
machine	_	_	O
and	_	_	O
a	_	_	O
printing	_	_	O
machine	_	_	O
.	_	_	O
A	_	_	O
ream	_	_	O
of	_	_	O
dotted	_	_	B-VAR
paper	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
cutting	_	_	O
machine	_	_	O
and	_	_	O
5.5	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
printing	_	_	O
machine	_	_	O
.	_	_	O
A	_	_	O
ream	_	_	O
of	_	_	O
grid	_	_	B-VAR
paper	_	_	I-VAR
requires	_	_	O
1.5	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
cutting	_	_	O
machine	_	_	O
and	_	_	O
7	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
printing	_	_	O
machine	_	_	O
.	_	_	O
In	_	_	O
a	_	_	O
week	_	_	O
,	_	_	O
each	_	_	O
machine	_	_	O
is	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
3000	_	_	B-LIMIT
minutes	_	_	O
.	_	_	O
There	_	_	O
is	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
5.5	_	_	B-PARAM
per	_	_	O
ream	_	_	O
of	_	_	O
dotted	_	_	B-VAR
paper	_	_	I-VAR
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
11	_	_	B-PARAM
per	_	_	O
ream	_	_	O
of	_	_	O
grid	_	_	B-VAR
paper	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
reams	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
factory	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Daniel	_	_	O
and	_	_	O
David	_	_	O
are	_	_	O
running	_	_	O
a	_	_	O
bakery	_	_	O
store	_	_	O
to	_	_	O
sell	_	_	O
pancakes	_	_	B-VAR
and	_	_	O
bagels	_	_	B-VAR
.	_	_	O
Each	_	_	O
batch	_	_	O
of	_	_	O
pancakes	_	_	B-VAR
takes	_	_	O
25	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
Daniel	_	_	O
's	_	_	O
time	_	_	O
and	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
David	_	_	O
's	_	_	O
time	_	_	O
.	_	_	O
Each	_	_	O
batch	_	_	O
of	_	_	O
bagels	_	_	B-VAR
takes	_	_	O
9	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
Daniel	_	_	O
's	_	_	O
time	_	_	O
and	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
David	_	_	O
's	_	_	O
time	_	_	O
.	_	_	O
In	_	_	O
a	_	_	O
day	_	_	O
,	_	_	O
Daniel	_	_	O
has	_	_	O
150	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
and	_	_	O
David	_	_	O
has	_	_	O
350	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
batch	_	_	O
of	_	_	O
pancakes	_	_	B-VAR
is	_	_	O
$	_	_	O
25	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
batch	_	_	O
of	_	_	O
bagels	_	_	B-VAR
is	_	_	O
$	_	_	O
30	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
batches	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

William	_	_	O
is	_	_	O
a	_	_	O
potato	_	_	O
farmer	_	_	O
and	_	_	O
he	_	_	O
has	_	_	O
to	_	_	O
send	_	_	O
his	_	_	O
product	_	_	O
to	_	_	O
the	_	_	O
city	_	_	O
.	_	_	O
He	_	_	O
can	_	_	O
transport	_	_	O
his	_	_	O
potato	_	_	B-OBJ_NAME
packages	_	_	I-OBJ_NAME
by	_	_	O
regular	_	_	B-VAR
truck	_	_	I-VAR
which	_	_	O
can	_	_	O
take	_	_	O
70	_	_	B-PARAM
packages	_	_	B-OBJ_NAME
per	_	_	O
trip	_	_	O
or	_	_	O
by	_	_	O
refrigerated	_	_	B-VAR
truck	_	_	I-VAR
which	_	_	O
can	_	_	O
take	_	_	O
100	_	_	B-PARAM
packages	_	_	B-OBJ_NAME
per	_	_	O
trip	_	_	O
.	_	_	O
The	_	_	O
cost	_	_	O
per	_	_	O
regular	_	_	B-VAR
truck	_	_	I-VAR
trip	_	_	O
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	O
per	_	_	O
refrigerated	_	_	B-VAR
truck	_	_	I-VAR
trip	_	_	O
is	_	_	O
$	_	_	O
70	_	_	B-PARAM
.	_	_	O
He	_	_	O
wants	_	_	O
to	_	_	O
spend	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
5000	_	_	B-LIMIT
and	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
refrigerated	_	_	B-VAR
truck	_	_	I-VAR
trips	_	_	O
must	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
regular	_	_	B-VAR
truck	_	_	I-VAR
trips	_	_	O
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
potato	_	_	I-OBJ_NAME
packages	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
transported	_	_	O
.	_	_	O

Iota	_	_	O
Software	_	_	O
has	_	_	O
full	_	_	B-VAR
-	_	_	I-VAR
time	_	_	I-VAR
employees	_	_	I-VAR
earning	_	_	B-OBJ_NAME
$	_	_	O
800	_	_	B-PARAM
per	_	_	O
week	_	_	O
and	_	_	O
part	_	_	B-VAR
-	_	_	I-VAR
time	_	_	I-VAR
employees	_	_	I-VAR
earning	_	_	B-OBJ_NAME
$	_	_	O
400	_	_	B-PARAM
per	_	_	O
week	_	_	O
.	_	_	O
The	_	_	O
projects	_	_	O
require	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
60	_	_	B-LIMIT
employees	_	_	O
,	_	_	O
of	_	_	O
whom	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
40	_	_	B-LIMIT
have	_	_	O
to	_	_	O
be	_	_	O
full	_	_	B-VAR
-	_	_	I-VAR
time	_	_	I-VAR
employees	_	_	I-VAR
.	_	_	O
Due	_	_	O
to	_	_	O
corporate	_	_	O
law	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
full	_	_	B-VAR
-	_	_	I-VAR
time	_	_	I-VAR
employees	_	_	I-VAR
should	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
a	_	_	O
third	_	_	B-PARAM
of	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
part	_	_	B-VAR
-	_	_	I-VAR
time	_	_	I-VAR
employees	_	_	I-VAR
.	_	_	O
It	_	_	O
is	_	_	O
also	_	_	O
required	_	_	O
to	_	_	O
keep	_	_	O
the	_	_	O
weekly	_	_	B-OBJ_NAME
wage	_	_	I-OBJ_NAME
bill	_	_	I-OBJ_NAME
below	_	_	B-CONST_DIR
$	_	_	O
30000	_	_	B-LIMIT
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	B-OBJ_NAME
wage	_	_	I-OBJ_NAME
bill	_	_	I-OBJ_NAME
.	_	_	O

Nolan	_	_	O
has	_	_	O
to	_	_	O
allocate	_	_	O
his	_	_	O
farming	_	_	O
equipment	_	_	O
between	_	_	O
his	_	_	O
two	_	_	O
farms	_	_	O
,	_	_	O
a	_	_	O
pumpkin	_	_	B-VAR
farm	_	_	I-VAR
and	_	_	O
a	_	_	O
potato	_	_	B-VAR
farm	_	_	I-VAR
.	_	_	O
The	_	_	O
revenue	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
pumpkins	_	_	B-VAR
is	_	_	O
$	_	_	O
150	_	_	B-PARAM
and	_	_	O
the	_	_	O
revenue	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
potatoes	_	_	B-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
.	_	_	O
He	_	_	O
has	_	_	O
one	_	_	O
tractor	_	_	O
,	_	_	O
one	_	_	O
plow	_	_	O
,	_	_	O
and	_	_	O
one	_	_	O
combine	_	_	O
.	_	_	O
Each	_	_	O
equipment	_	_	O
can	_	_	B-CONST_DIR
be	_	_	I-CONST_DIR
used	_	_	I-CONST_DIR
for	_	_	I-CONST_DIR
12	_	_	B-LIMIT
hours	_	_	O
a	_	_	O
day	_	_	O
divided	_	_	O
in	_	_	O
any	_	_	O
way	_	_	O
between	_	_	O
his	_	_	O
two	_	_	O
farms	_	_	O
.	_	_	O
On	_	_	O
his	_	_	O
pumpkin	_	_	B-VAR
farm	_	_	I-VAR
,	_	_	O
harvesting	_	_	O
an	_	_	O
acre	_	_	O
of	_	_	O
pumpkins	_	_	B-VAR
requires	_	_	O
0.5	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
tractor	_	_	O
,	_	_	O
0.6	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
plow	_	_	O
,	_	_	O
and	_	_	O
0.4	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
combine	_	_	O
.	_	_	O
On	_	_	O
his	_	_	O
potato	_	_	B-VAR
farm	_	_	I-VAR
,	_	_	O
harvesting	_	_	O
an	_	_	O
acre	_	_	O
of	_	_	O
potatoes	_	_	B-VAR
requires	_	_	O
0.9	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
tractor	_	_	O
,	_	_	O
0.5	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
plow	_	_	O
,	_	_	O
and	_	_	O
0.3	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
combine	_	_	O
.	_	_	O
How	_	_	O
should	_	_	O
Nolan	_	_	O
allocate	_	_	O
his	_	_	O
equipment	_	_	O
between	_	_	O
his	_	_	O
farms	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
revenue	_	_	B-OBJ_NAME
?	_	_	O

Andrew	_	_	O
is	_	_	O
a	_	_	O
berry	_	_	O
farmer	_	_	O
and	_	_	O
he	_	_	O
has	_	_	O
two	_	_	O
farms	_	_	O
,	_	_	O
a	_	_	O
local	_	_	B-VAR
farm	_	_	I-VAR
and	_	_	O
a	_	_	O
foreign	_	_	B-VAR
farm	_	_	I-VAR
,	_	_	O
where	_	_	O
he	_	_	O
grows	_	_	O
raspberries	_	_	O
,	_	_	O
bilberries	_	_	O
,	_	_	O
and	_	_	O
strawberries	_	_	O
.	_	_	O
He	_	_	O
has	_	_	O
a	_	_	O
contract	_	_	O
to	_	_	O
provide	_	_	B-CONST_DIR
a	_	_	O
local	_	_	O
store	_	_	O
with	_	_	O
12	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
raspberries	_	_	O
,	_	_	O
10	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
bilberries	_	_	O
,	_	_	O
and	_	_	O
20	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
strawberries	_	_	O
.	_	_	O
At	_	_	O
his	_	_	O
local	_	_	B-VAR
farm	_	_	I-VAR
,	_	_	O
it	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
200	_	_	B-PARAM
to	_	_	O
operate	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
he	_	_	O
can	_	_	O
harvest	_	_	O
and	_	_	O
deliver	_	_	O
2.5	_	_	B-PARAM
kg	_	_	O
of	_	_	O
raspberries	_	_	O
,	_	_	O
3	_	_	B-PARAM
kg	_	_	O
of	_	_	O
bilberries	_	_	O
,	_	_	O
and	_	_	O
2	_	_	B-PARAM
kg	_	_	O
of	_	_	O
strawberries	_	_	O
in	_	_	O
a	_	_	O
day	_	_	O
.	_	_	O
At	_	_	O
his	_	_	O
foreign	_	_	B-VAR
farm	_	_	I-VAR
,	_	_	O
it	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
500	_	_	B-PARAM
to	_	_	O
operate	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
he	_	_	O
can	_	_	O
harvest	_	_	O
and	_	_	O
deliver	_	_	O
5	_	_	B-PARAM
kg	_	_	O
of	_	_	O
raspberries	_	_	O
,	_	_	O
4	_	_	B-PARAM
kg	_	_	O
of	_	_	O
bilberries	_	_	O
,	_	_	O
and	_	_	O
4	_	_	B-PARAM
kg	_	_	O
of	_	_	O
strawberries	_	_	O
in	_	_	O
a	_	_	O
day	_	_	O
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
to	_	_	O
meet	_	_	O
his	_	_	O
contract	_	_	O
while	_	_	O
minimizing	_	_	B-OBJ_DIR
his	_	_	O
cost	_	_	B-OBJ_NAME
.	_	_	O

Omega	_	_	O
Seafood	_	_	O
fishes	_	_	O
in	_	_	O
two	_	_	O
areas	_	_	O
,	_	_	O
the	_	_	O
Indian	_	_	B-VAR
and	_	_	O
Arctic	_	_	B-VAR
oceans	_	_	I-VAR
.	_	_	O
In	_	_	O
a	_	_	O
week	_	_	O
,	_	_	O
they	_	_	O
must	_	_	O
provide	_	_	B-CONST_DIR
20	_	_	B-LIMIT
tons	_	_	O
of	_	_	O
fish	_	_	O
,	_	_	O
12	_	_	B-LIMIT
tons	_	_	O
of	_	_	O
crab	_	_	O
,	_	_	O
and	_	_	O
10	_	_	B-LIMIT
tons	_	_	O
of	_	_	O
shrimp	_	_	O
.	_	_	O
It	_	_	O
costs	_	_	B-OBJ_NAME
the	_	_	O
company	_	_	O
$	_	_	O
6000	_	_	B-PARAM
per	_	_	O
day	_	_	O
to	_	_	O
operate	_	_	O
in	_	_	O
the	_	_	O
Indian	_	_	B-VAR
ocean	_	_	I-VAR
and	_	_	O
$	_	_	O
9000	_	_	B-PARAM
per	_	_	O
day	_	_	O
to	_	_	O
operate	_	_	O
in	_	_	O
the	_	_	O
Arctic	_	_	B-VAR
ocean	_	_	I-VAR
.	_	_	O
In	_	_	O
a	_	_	O
day	_	_	O
's	_	_	O
operation	_	_	O
in	_	_	O
the	_	_	O
Indian	_	_	B-VAR
ocean	_	_	I-VAR
,	_	_	O
the	_	_	O
company	_	_	O
can	_	_	O
catch	_	_	O
3.4	_	_	B-PARAM
tons	_	_	O
of	_	_	O
fish	_	_	O
,	_	_	O
2.2	_	_	B-PARAM
tons	_	_	O
of	_	_	O
crab	_	_	O
,	_	_	O
and	_	_	O
1.5	_	_	B-PARAM
tons	_	_	O
of	_	_	O
shrimp	_	_	O
.	_	_	O
In	_	_	O
a	_	_	O
day	_	_	O
's	_	_	O
operation	_	_	O
in	_	_	O
the	_	_	O
Arctic	_	_	B-VAR
ocean	_	_	I-VAR
,	_	_	O
the	_	_	O
company	_	_	O
can	_	_	O
catch	_	_	O
6	_	_	B-PARAM
tons	_	_	O
of	_	_	O
fish	_	_	O
,	_	_	O
5	_	_	B-PARAM
tons	_	_	O
of	_	_	O
crab	_	_	O
,	_	_	O
and	_	_	O
3	_	_	B-PARAM
tons	_	_	O
of	_	_	O
shrimp	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
days	_	_	O
a	_	_	O
week	_	_	O
should	_	_	O
fishing	_	_	O
be	_	_	O
done	_	_	O
in	_	_	O
each	_	_	O
ocean	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

Luke	_	_	O
is	_	_	O
a	_	_	O
carrot	_	_	O
farmer	_	_	O
and	_	_	O
he	_	_	O
has	_	_	B-CONST_DIR
150	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
on	_	_	O
which	_	_	O
he	_	_	O
grows	_	_	O
Danvers	_	_	B-VAR
carrots	_	_	I-VAR
and	_	_	O
Nantes	_	_	B-VAR
carrots	_	_	I-VAR
.	_	_	O
The	_	_	O
net	_	_	B-OBJ_NAME
revenue	_	_	I-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
Danvers	_	_	B-VAR
carrots	_	_	I-VAR
is	_	_	O
$	_	_	O
600	_	_	B-PARAM
and	_	_	O
the	_	_	O
net	_	_	B-OBJ_NAME
revenue	_	_	I-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
Nantes	_	_	B-VAR
carrots	_	_	I-VAR
is	_	_	O
$	_	_	O
300	_	_	B-PARAM
.	_	_	O
Each	_	_	O
acre	_	_	O
of	_	_	O
Danvers	_	_	B-VAR
carrots	_	_	I-VAR
requires	_	_	O
2.5	_	_	B-PARAM
days	_	_	O
worth	_	_	O
of	_	_	O
labor	_	_	O
and	_	_	O
$	_	_	O
100	_	_	B-PARAM
in	_	_	O
maintenance	_	_	O
costs	_	_	O
.	_	_	O
Each	_	_	O
acre	_	_	O
of	_	_	O
Nantes	_	_	B-VAR
carrots	_	_	I-VAR
requires	_	_	O
3.7	_	_	B-PARAM
days	_	_	O
worth	_	_	O
of	_	_	O
labor	_	_	O
and	_	_	O
$	_	_	O
200	_	_	B-PARAM
in	_	_	O
maintenance	_	_	O
costs	_	_	O
.	_	_	O
Luke	_	_	O
has	_	_	O
$	_	_	O
20000	_	_	B-LIMIT
available	_	_	B-CONST_DIR
to	_	_	O
spend	_	_	O
on	_	_	O
maintenance	_	_	O
costs	_	_	O
and	_	_	O
300	_	_	B-LIMIT
days	_	_	O
worth	_	_	O
of	_	_	O
labor	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
How	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
grown	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
net	_	_	B-OBJ_NAME
revenue	_	_	I-OBJ_NAME
?	_	_	O

Gabriel	_	_	O
has	_	_	O
lemons	_	_	B-VAR
and	_	_	O
pecans	_	_	B-VAR
to	_	_	O
eat	_	_	O
.	_	_	O
A	_	_	O
pound	_	_	O
of	_	_	O
lemons	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
12	_	_	B-PARAM
and	_	_	O
contains	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
calcium	_	_	O
,	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
potassium	_	_	O
,	_	_	O
and	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
zinc	_	_	O
per	_	_	O
pound	_	_	O
.	_	_	O
A	_	_	O
pound	_	_	O
of	_	_	O
pecans	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
10	_	_	B-PARAM
and	_	_	O
contains	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
calcium	_	_	O
,	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
potassium	_	_	O
,	_	_	O
and	_	_	O
9	_	_	B-PARAM
units	_	_	O
of	_	_	O
zinc	_	_	O
per	_	_	O
pound	_	_	O
.	_	_	O
There	_	_	O
is	_	_	O
nothing	_	_	O
else	_	_	O
available	_	_	O
to	_	_	O
eat	_	_	O
and	_	_	O
Gabriel	_	_	O
must	_	_	O
meet	_	_	O
his	_	_	O
daily	_	_	O
requirements	_	_	O
of	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
25	_	_	B-LIMIT
units	_	_	O
of	_	_	O
calcium	_	_	O
,	_	_	O
18	_	_	B-LIMIT
units	_	_	O
of	_	_	O
potassium	_	_	O
,	_	_	O
and	_	_	O
19	_	_	B-LIMIT
units	_	_	O
of	_	_	O
zinc	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
pounds	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
Gabriel	_	_	O
eat	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
cost	_	_	B-OBJ_NAME
?	_	_	O

Alpha	_	_	O
Nut	_	_	O
has	_	_	B-CONST_DIR
35	_	_	B-LIMIT
kilograms	_	_	O
of	_	_	O
almonds	_	_	O
and	_	_	O
20	_	_	B-LIMIT
kilograms	_	_	O
of	_	_	O
hazelnuts	_	_	O
.	_	_	O
They	_	_	O
sell	_	_	O
two	_	_	O
combos	_	_	O
of	_	_	O
these	_	_	O
nuts	_	_	O
:	_	_	O
Combo	_	_	B-VAR
X	_	_	I-VAR
and	_	_	O
Combo	_	_	B-VAR
Y.	_	_	I-VAR
Combo	_	_	B-VAR
X	_	_	I-VAR
is	_	_	O
70	_	_	B-PARAM
%	_	_	I-PARAM
almonds	_	_	O
and	_	_	O
30	_	_	B-PARAM
%	_	_	I-PARAM
hazelnuts	_	_	O
.	_	_	O
Combo	_	_	B-VAR
Y	_	_	I-VAR
is	_	_	O
35	_	_	B-PARAM
%	_	_	I-PARAM
almonds	_	_	O
and	_	_	O
65	_	_	B-PARAM
%	_	_	I-PARAM
hazelnuts	_	_	O
.	_	_	O
A	_	_	O
kilogram	_	_	O
of	_	_	O
Combo	_	_	B-VAR
X	_	_	I-VAR
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
35	_	_	B-PARAM
and	_	_	O
a	_	_	O
kilogram	_	_	O
of	_	_	O
Combo	_	_	B-VAR
Y	_	_	I-VAR
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
55	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
kilograms	_	_	O
of	_	_	O
each	_	_	O
combo	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Calcium	_	_	O
and	_	_	O
magnesium	_	_	O
are	_	_	O
found	_	_	O
in	_	_	O
pork	_	_	B-VAR
meat	_	_	I-VAR
and	_	_	O
shrimp	_	_	B-VAR
meat	_	_	I-VAR
.	_	_	O
A	_	_	O
serving	_	_	O
of	_	_	O
pork	_	_	B-VAR
meat	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
6.5	_	_	B-PARAM
and	_	_	O
contains	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
calcium	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
magnesium	_	_	O
.	_	_	O
A	_	_	O
serving	_	_	O
of	_	_	O
shrimp	_	_	B-VAR
meat	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
9	_	_	B-PARAM
and	_	_	O
contains	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
calcium	_	_	O
and	_	_	O
9	_	_	B-PARAM
units	_	_	O
of	_	_	O
magnesium	_	_	O
.	_	_	O
If	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
25	_	_	B-LIMIT
units	_	_	O
of	_	_	O
calcium	_	_	O
and	_	_	O
35	_	_	B-LIMIT
units	_	_	O
of	_	_	O
magnesium	_	_	O
must	_	_	O
be	_	_	O
consumed	_	_	O
daily	_	_	O
,	_	_	O
formulate	_	_	O
an	_	_	O
LP	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
.	_	_	O

Rho	_	_	O
Burrito	_	_	O
sell	_	_	O
two	_	_	O
burritos	_	_	O
:	_	_	O
a	_	_	O
Mexican	_	_	B-VAR
burrito	_	_	I-VAR
and	_	_	O
a	_	_	O
Korean	_	_	B-VAR
burrito	_	_	I-VAR
.	_	_	O
The	_	_	O
burritos	_	_	O
are	_	_	O
made	_	_	O
using	_	_	O
cheese	_	_	O
,	_	_	O
beans	_	_	O
,	_	_	O
and	_	_	O
onions	_	_	O
.	_	_	O
A	_	_	O
Mexican	_	_	B-VAR
burrito	_	_	I-VAR
requires	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
cheese	_	_	O
and	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
beans	_	_	O
.	_	_	O
A	_	_	O
Korean	_	_	B-VAR
burrito	_	_	I-VAR
requires	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
cheese	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
onions	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
70	_	_	B-LIMIT
units	_	_	O
of	_	_	O
cheese	_	_	O
available	_	_	B-CONST_DIR
,	_	_	O
60	_	_	B-LIMIT
units	_	_	O
of	_	_	O
beans	_	_	O
available	_	_	B-CONST_DIR
,	_	_	O
and	_	_	O
45	_	_	B-LIMIT
units	_	_	O
of	_	_	O
onions	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
Mexican	_	_	B-VAR
burrito	_	_	I-VAR
is	_	_	O
$	_	_	O
7	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
Korean	_	_	B-VAR
burrito	_	_	I-VAR
is	_	_	O
$	_	_	O
4.5	_	_	B-PARAM
.	_	_	O
Formulate	_	_	O
as	_	_	O
an	_	_	O
LP	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
.	_	_	O

Mia	_	_	O
Clothing	_	_	O
makes	_	_	O
fancy	_	_	O
skirts	_	_	B-VAR
and	_	_	O
coats	_	_	B-VAR
.	_	_	O
Both	_	_	O
of	_	_	O
these	_	_	O
items	_	_	O
require	_	_	O
use	_	_	O
of	_	_	O
a	_	_	O
sewing	_	_	O
machine	_	_	O
and	_	_	O
embroidery	_	_	O
machine	_	_	O
.	_	_	O
A	_	_	O
skirt	_	_	B-VAR
requires	_	_	O
3	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
sewing	_	_	O
machine	_	_	O
and	_	_	O
5	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
embroidery	_	_	O
machine	_	_	O
.	_	_	O
A	_	_	O
coat	_	_	B-VAR
requires	_	_	O
2	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
sewing	_	_	O
machine	_	_	O
and	_	_	O
3.5	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
embroidery	_	_	O
machine	_	_	O
.	_	_	O
In	_	_	O
a	_	_	O
week	_	_	O
,	_	_	O
there	_	_	O
are	_	_	O
25	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
on	_	_	O
the	_	_	O
sewing	_	_	O
machine	_	_	O
and	_	_	O
35	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
on	_	_	O
the	_	_	O
embroidery	_	_	O
machine	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
skirt	_	_	B-VAR
is	_	_	O
$	_	_	O
300	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
coat	_	_	B-VAR
is	_	_	O
$	_	_	O
500	_	_	B-PARAM
,	_	_	O
what	_	_	O
should	_	_	O
the	_	_	O
weekly	_	_	O
production	_	_	O
be	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
milk	_	_	O
company	_	_	O
makes	_	_	O
ice	_	_	B-VAR
cream	_	_	I-VAR
and	_	_	O
cheese	_	_	B-VAR
.	_	_	O
Two	_	_	O
different	_	_	O
teams	_	_	O
produce	_	_	O
ice	_	_	B-VAR
cream	_	_	I-VAR
and	_	_	O
cheese	_	_	B-VAR
.	_	_	O
The	_	_	O
ice	_	_	B-VAR
cream	_	_	I-VAR
team	_	_	O
has	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
daily	_	_	O
production	_	_	O
of	_	_	O
50	_	_	B-LIMIT
units	_	_	O
of	_	_	O
ice	_	_	B-VAR
cream	_	_	I-VAR
while	_	_	O
the	_	_	O
cheese	_	_	B-VAR
team	_	_	O
has	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
daily	_	_	O
production	_	_	O
of	_	_	O
80	_	_	B-LIMIT
units	_	_	O
of	_	_	O
cheese	_	_	B-VAR
.	_	_	O
However	_	_	O
,	_	_	O
both	_	_	O
items	_	_	O
require	_	_	O
time	_	_	O
on	_	_	O
a	_	_	O
shared	_	_	O
processing	_	_	O
machine	_	_	O
and	_	_	O
this	_	_	O
machine	_	_	O
can	_	_	O
process	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
units	_	_	O
of	_	_	O
total	_	_	O
units	_	_	O
of	_	_	O
items	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
unit	_	_	O
of	_	_	O
ice	_	_	B-VAR
cream	_	_	I-VAR
is	_	_	O
$	_	_	O
2.5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
unit	_	_	O
of	_	_	O
cheese	_	_	B-VAR
is	_	_	O
$	_	_	O
4	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
units	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
make	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profits	_	_	B-OBJ_NAME
?	_	_	O

Eta	_	_	O
Auto	_	_	O
makes	_	_	O
two	_	_	O
versions	_	_	O
of	_	_	O
the	_	_	O
same	_	_	O
car	_	_	O
,	_	_	O
a	_	_	O
hybrid	_	_	B-VAR
model	_	_	I-VAR
and	_	_	O
an	_	_	O
electric	_	_	B-VAR
model	_	_	I-VAR
.	_	_	O
They	_	_	O
make	_	_	O
y1	_	_	O
hybrid	_	_	B-VAR
models	_	_	I-VAR
per	_	_	O
day	_	_	O
and	_	_	O
y2	_	_	O
electric	_	_	B-VAR
models	_	_	I-VAR
per	_	_	O
day	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
hybrid	_	_	B-VAR
model	_	_	I-VAR
is	_	_	O
$	_	_	O
4500	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
electric	_	_	B-VAR
model	_	_	I-VAR
is	_	_	O
$	_	_	O
5500	_	_	B-PARAM
(	_	_	O
y1	_	_	O
and	_	_	O
y2	_	_	O
are	_	_	O
unknown	_	_	O
values	_	_	O
both	_	_	O
greater	_	_	O
than	_	_	O
or	_	_	O
equal	_	_	O
to	_	_	O
0	_	_	O
)	_	_	O
.	_	_	O
The	_	_	O
daily	_	_	O
demand	_	_	O
for	_	_	O
these	_	_	O
cars	_	_	O
is	_	_	O
limited	_	_	O
to	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
9	_	_	B-LIMIT
hybrid	_	_	B-VAR
models	_	_	I-VAR
and	_	_	O
5	_	_	B-LIMIT
electric	_	_	B-VAR
models	_	_	I-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
the	_	_	O
manufacturer	_	_	O
can	_	_	O
make	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
10	_	_	B-LIMIT
total	_	_	O
cars	_	_	O
a	_	_	O
day	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
cars	_	_	O
of	_	_	O
each	_	_	O
model	_	_	O
should	_	_	O
the	_	_	O
manufacturer	_	_	O
make	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Kappa	_	_	O
Medical	_	_	O
wants	_	_	O
to	_	_	O
mix	_	_	O
two	_	_	O
creams	_	_	O
to	_	_	O
create	_	_	O
a	_	_	O
mixture	_	_	O
that	_	_	O
contains	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
4	_	_	B-LIMIT
units	_	_	O
of	_	_	O
compound	_	_	O
X	_	_	O
and	_	_	O
8	_	_	B-LIMIT
units	_	_	O
of	_	_	O
compound	_	_	O
Y.	_	_	O
The	_	_	O
amount	_	_	O
of	_	_	O
compound	_	_	O
X	_	_	O
and	_	_	O
compound	_	_	O
Y	_	_	O
in	_	_	O
cream	_	_	B-VAR
Alpha	_	_	I-VAR
is	_	_	O
2	_	_	B-PARAM
units	_	_	O
/	_	_	O
mg	_	_	O
and	_	_	O
2.7	_	_	B-PARAM
units	_	_	O
/	_	_	O
mg	_	_	O
respectively	_	_	O
.	_	_	O
On	_	_	O
the	_	_	O
other	_	_	O
hand	_	_	O
,	_	_	O
the	_	_	O
amount	_	_	O
of	_	_	O
compound	_	_	O
X	_	_	O
and	_	_	O
compound	_	_	O
Y	_	_	O
in	_	_	O
cream	_	_	B-VAR
Beta	_	_	I-VAR
is	_	_	O
4.1	_	_	B-PARAM
units	_	_	O
/	_	_	O
mg	_	_	O
and	_	_	O
3.2	_	_	B-PARAM
units	_	_	O
/	_	_	O
mg	_	_	O
respectively	_	_	O
.	_	_	O
It	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
0.70	_	_	B-PARAM
per	_	_	O
mg	_	_	O
to	_	_	O
purchase	_	_	O
cream	_	_	B-VAR
Alpha	_	_	I-VAR
and	_	_	O
$	_	_	O
0.90	_	_	B-PARAM
per	_	_	O
mg	_	_	O
to	_	_	O
purchase	_	_	O
cream	_	_	B-VAR
Beta	_	_	I-VAR
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
cost	_	_	B-OBJ_NAME
of	_	_	O
such	_	_	O
a	_	_	O
mixture	_	_	O
.	_	_	O

Hudson	_	_	O
has	_	_	B-CONST_DIR
55	_	_	B-LIMIT
acres	_	_	O
to	_	_	O
grow	_	_	O
daisies	_	_	B-VAR
and	_	_	O
peonies	_	_	B-VAR
.	_	_	O
Hudson	_	_	O
must	_	_	O
use	_	_	O
plant	_	_	O
nutrition	_	_	O
to	_	_	O
feed	_	_	O
the	_	_	O
flowers	_	_	O
to	_	_	O
ensure	_	_	O
the	_	_	O
flowers	_	_	O
grow	_	_	O
.	_	_	O
Daisies	_	_	B-VAR
require	_	_	O
4.5	_	_	B-PARAM
kg	_	_	O
of	_	_	O
plant	_	_	O
nutrition	_	_	O
per	_	_	O
acre	_	_	O
while	_	_	O
peonies	_	_	B-VAR
require	_	_	O
7	_	_	B-PARAM
kg	_	_	O
of	_	_	O
plant	_	_	O
nutrition	_	_	O
per	_	_	O
acre	_	_	O
.	_	_	O
Due	_	_	O
to	_	_	O
the	_	_	O
high	_	_	O
cost	_	_	O
of	_	_	O
plant	_	_	O
nutrition	_	_	O
,	_	_	O
Hudson	_	_	O
wants	_	_	O
to	_	_	O
use	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
200	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
plant	_	_	O
nutrition	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
daisies	_	_	B-VAR
is	_	_	O
$	_	_	O
150	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
peonies	_	_	B-VAR
is	_	_	O
$	_	_	O
180	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
Hudson	_	_	O
grow	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Theta	_	_	O
Electronics	_	_	O
makes	_	_	O
two	_	_	O
phone	_	_	O
models	_	_	O
:	_	_	O
a	_	_	O
regular	_	_	B-VAR
model	_	_	I-VAR
and	_	_	O
a	_	_	O
premium	_	_	B-VAR
model	_	_	I-VAR
.	_	_	O
Each	_	_	O
regular	_	_	B-VAR
model	_	_	I-VAR
requires	_	_	O
70	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
assembly	_	_	O
and	_	_	O
25	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
software	_	_	O
verification	_	_	O
.	_	_	O
Each	_	_	O
premium	_	_	B-VAR
model	_	_	I-VAR
requires	_	_	O
100	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
assembly	_	_	O
and	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
software	_	_	O
verification	_	_	O
.	_	_	O
The	_	_	O
maximum	_	_	O
available	_	_	B-CONST_DIR
time	_	_	O
for	_	_	O
assembly	_	_	O
is	_	_	O
6000	_	_	B-LIMIT
minutes	_	_	O
and	_	_	O
the	_	_	O
maximum	_	_	O
available	_	_	B-CONST_DIR
time	_	_	O
for	_	_	O
software	_	_	O
verification	_	_	O
is	_	_	O
4000	_	_	B-LIMIT
minutes	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
company	_	_	O
makes	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
200	_	_	B-PARAM
per	_	_	O
regular	_	_	B-VAR
model	_	_	I-VAR
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
500	_	_	B-PARAM
per	_	_	O
premium	_	_	B-VAR
model	_	_	I-VAR
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Adrian	_	_	O
needs	_	_	O
to	_	_	O
gain	_	_	O
weight	_	_	O
for	_	_	O
a	_	_	O
role	_	_	O
and	_	_	O
decides	_	_	O
to	_	_	O
eat	_	_	O
only	_	_	O
bagels	_	_	B-VAR
and	_	_	O
burgers	_	_	B-VAR
.	_	_	O
He	_	_	O
wants	_	_	O
to	_	_	O
eat	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
2500	_	_	B-LIMIT
calories	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
500	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
fat	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
Each	_	_	O
bagel	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
4.5	_	_	B-PARAM
and	_	_	O
contains	_	_	O
250	_	_	B-PARAM
calories	_	_	O
and	_	_	O
15	_	_	B-PARAM
grams	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
Each	_	_	O
burger	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
12	_	_	B-PARAM
and	_	_	O
contains	_	_	O
800	_	_	B-PARAM
calories	_	_	O
and	_	_	O
23.5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
Adrian	_	_	O
eat	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

Owen	_	_	O
has	_	_	O
$	_	_	O
500,000	_	_	B-LIMIT
available	_	_	B-CONST_DIR
for	_	_	O
investment	_	_	O
.	_	_	O
He	_	_	O
wants	_	_	O
to	_	_	O
invest	_	_	O
in	_	_	O
the	_	_	O
fast	_	_	B-VAR
food	_	_	I-VAR
,	_	_	O
pharmaceutical	_	_	B-VAR
,	_	_	O
healthcare	_	_	B-VAR
,	_	_	O
and	_	_	O
green	_	_	B-VAR
energy	_	_	I-VAR
industries	_	_	I-VAR
.	_	_	O
The	_	_	O
annual	_	_	O
rate	_	_	O
of	_	_	O
return	_	_	B-OBJ_NAME
for	_	_	O
each	_	_	O
industry	_	_	O
is	_	_	O
known	_	_	O
to	_	_	O
be	_	_	O
:	_	_	O
fast	_	_	B-VAR
food	_	_	I-VAR
,	_	_	O
5.5	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
pharmaceutical	_	_	B-VAR
,	_	_	O
3.2	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
healthcare	_	_	B-VAR
,	_	_	O
7.5	_	_	B-PARAM
%	_	_	I-PARAM
;	_	_	O
green	_	_	B-VAR
energy	_	_	I-VAR
,	_	_	O
11.4	_	_	B-PARAM
%	_	_	I-PARAM
.	_	_	O
To	_	_	O
make	_	_	O
his	_	_	O
investments	_	_	O
more	_	_	O
spread	_	_	O
out	_	_	O
,	_	_	O
he	_	_	O
wants	_	_	O
to	_	_	O
ensure	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
green	_	_	B-VAR
energy	_	_	I-VAR
industry	_	_	I-VAR
does	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
fast	_	_	B-VAR
food	_	_	I-VAR
industry	_	_	I-VAR
.	_	_	O
Also	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
pharmaceutical	_	_	B-VAR
industry	_	_	I-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
healthcare	_	_	B-VAR
industry	_	_	I-VAR
.	_	_	O
Finally	_	_	O
,	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
35	_	_	B-LIMIT
%	_	_	I-LIMIT
can	_	_	O
be	_	_	O
invested	_	_	O
in	_	_	O
the	_	_	O
green	_	_	B-VAR
energy	_	_	I-VAR
industry	_	_	I-VAR
.	_	_	O
How	_	_	O
should	_	_	O
Owen	_	_	O
invest	_	_	O
his	_	_	O
money	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
return	_	_	B-OBJ_NAME
?	_	_	O

Mary	_	_	O
follows	_	_	O
a	_	_	O
new	_	_	O
daily	_	_	O
diet	_	_	O
for	_	_	O
which	_	_	O
she	_	_	O
needs	_	_	O
to	_	_	O
have	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
vitamin	_	_	O
A	_	_	O
,	_	_	O
500	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
vitamin	_	_	O
C	_	_	O
,	_	_	O
and	_	_	O
3000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
proteins	_	_	O
.	_	_	O
In	_	_	O
order	_	_	O
to	_	_	O
do	_	_	O
so	_	_	O
,	_	_	O
her	_	_	O
dietician	_	_	O
recommended	_	_	O
her	_	_	O
to	_	_	O
drink	_	_	O
a	_	_	O
protein	_	_	B-VAR
drink	_	_	I-VAR
or	_	_	O
fruit	_	_	B-VAR
snack	_	_	I-VAR
.	_	_	O
The	_	_	O
protein	_	_	B-VAR
drink	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
4	_	_	B-PARAM
per	_	_	O
serving	_	_	O
and	_	_	O
contains	_	_	O
45	_	_	B-PARAM
grams	_	_	O
of	_	_	O
vitamin	_	_	O
A	_	_	O
,	_	_	O
200	_	_	B-PARAM
grams	_	_	O
of	_	_	O
vitamin	_	_	O
C	_	_	O
,	_	_	O
and	_	_	O
300	_	_	B-PARAM
grams	_	_	O
of	_	_	O
proteins	_	_	O
.	_	_	O
Fruit	_	_	B-VAR
snack	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
12	_	_	B-PARAM
per	_	_	O
serving	_	_	O
and	_	_	O
contains	_	_	O
400	_	_	B-PARAM
grams	_	_	O
of	_	_	O
vitamin	_	_	O
A	_	_	O
,	_	_	O
600	_	_	B-PARAM
unit	_	_	O
of	_	_	O
vitamin	_	_	O
C	_	_	O
,	_	_	O
and	_	_	O
200	_	_	B-PARAM
grams	_	_	O
of	_	_	O
proteins	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
servings	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
Mary	_	_	O
buy	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
her	_	_	O
cost	_	_	B-OBJ_NAME
?	_	_	O

Organic	_	_	O
Farming	_	_	O
has	_	_	B-CONST_DIR
300	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
to	_	_	O
grow	_	_	O
daikons	_	_	B-VAR
and	_	_	O
fennels	_	_	B-VAR
.	_	_	O
Daikons	_	_	B-VAR
require	_	_	O
0.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
watering	_	_	O
and	_	_	O
$	_	_	O
70	_	_	B-PARAM
worth	_	_	O
of	_	_	O
compost	_	_	O
per	_	_	O
acre	_	_	O
.	_	_	O
Fennels	_	_	B-VAR
require	_	_	O
1.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
watering	_	_	O
and	_	_	O
$	_	_	O
50	_	_	B-PARAM
worth	_	_	O
of	_	_	O
compost	_	_	O
per	_	_	O
acre	_	_	O
.	_	_	O
The	_	_	O
farmer	_	_	O
has	_	_	O
500	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
watering	_	_	O
and	_	_	O
$	_	_	O
7400	_	_	B-LIMIT
available	_	_	B-CONST_DIR
to	_	_	O
spend	_	_	O
on	_	_	O
compost	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
revenue	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
daikons	_	_	B-VAR
is	_	_	O
$	_	_	O
300	_	_	B-PARAM
and	_	_	O
the	_	_	O
revenue	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
fennels	_	_	B-VAR
is	_	_	O
$	_	_	O
250	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
grow	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
revenue	_	_	B-OBJ_NAME
.	_	_	O

Pierre	_	_	O
is	_	_	O
working	_	_	O
on	_	_	O
his	_	_	O
e	_	_	O
-	_	_	O
commerce	_	_	O
dream	_	_	O
.	_	_	O
He	_	_	O
buys	_	_	O
sandals	_	_	B-VAR
and	_	_	O
slippers	_	_	B-VAR
for	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
$	_	_	O
20	_	_	B-PARAM
respectively	_	_	O
,	_	_	O
and	_	_	O
plans	_	_	O
to	_	_	O
re	_	_	O
-	_	_	O
sell	_	_	O
them	_	_	O
.	_	_	O
He	_	_	O
knows	_	_	O
that	_	_	O
,	_	_	O
for	_	_	O
this	_	_	O
summer	_	_	O
,	_	_	O
the	_	_	O
demand	_	_	O
for	_	_	O
sandals	_	_	B-VAR
is	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	I-PARAM
the	_	_	O
demand	_	_	O
for	_	_	O
the	_	_	O
slippers	_	_	B-VAR
.	_	_	O
Since	_	_	O
he	_	_	O
wants	_	_	O
to	_	_	O
start	_	_	O
small	_	_	O
,	_	_	O
Pierre	_	_	O
decides	_	_	O
to	_	_	O
invest	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
3000	_	_	B-LIMIT
buying	_	_	O
for	_	_	O
his	_	_	O
first	_	_	O
inventory	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
sandal	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
70	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
slipper	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
30	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
buy	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

Great	_	_	O
Sounds	_	_	O
Co	_	_	O
makes	_	_	O
headphones	_	_	B-VAR
and	_	_	O
earphones	_	_	B-VAR
.	_	_	O
Each	_	_	O
headphone	_	_	B-VAR
requires	_	_	O
30	_	_	B-PARAM
dollars	_	_	O
of	_	_	O
labor	_	_	O
to	_	_	O
make	_	_	O
whereas	_	_	O
each	_	_	O
earphone	_	_	B-VAR
requires	_	_	O
only	_	_	O
20	_	_	B-PARAM
dollars	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
each	_	_	O
headphone	_	_	B-VAR
requires	_	_	O
50	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
production	_	_	O
time	_	_	O
and	_	_	O
each	_	_	O
earphone	_	_	B-VAR
requires	_	_	O
40	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
production	_	_	O
time	_	_	O
.	_	_	O
The	_	_	O
manufacturer	_	_	O
has	_	_	O
at	_	_	O
most	_	_	O
2000	_	_	B-LIMIT
dollars	_	_	O
of	_	_	O
budget	_	_	B-CONST_DIR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
2500	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
production	_	_	O
time	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
headphone	_	_	B-VAR
is	_	_	O
$	_	_	O
350	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
earphone	_	_	B-VAR
is	_	_	O
$	_	_	O
120	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
product	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
boat	_	_	O
company	_	_	O
provides	_	_	O
transportation	_	_	O
service	_	_	O
for	_	_	O
both	_	_	O
vehicles	_	_	B-VAR
and	_	_	O
passengers	_	_	B-VAR
.	_	_	O
Due	_	_	O
to	_	_	O
capacity	_	_	O
limit	_	_	O
,	_	_	O
the	_	_	O
company	_	_	O
can	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
200	_	_	B-LIMIT
tickets	_	_	O
.	_	_	O
A	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
130	_	_	B-PARAM
is	_	_	O
made	_	_	O
for	_	_	O
each	_	_	O
vehicle	_	_	B-VAR
and	_	_	O
the	_	_	O
company	_	_	O
makes	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
60	_	_	B-PARAM
for	_	_	O
each	_	_	O
passenger	_	_	B-VAR
.	_	_	O
The	_	_	O
company	_	_	O
reserved	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
20	_	_	B-LIMIT
tickets	_	_	O
for	_	_	O
vehicles	_	_	B-VAR
.	_	_	O
However	_	_	O
,	_	_	O
because	_	_	O
most	_	_	O
people	_	_	O
do	_	_	O
n't	_	_	O
have	_	_	O
cars	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
4	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
many	_	_	O
tickets	_	_	O
are	_	_	O
sold	_	_	O
for	_	_	O
passenger	_	_	B-VAR
tickets	_	_	I-VAR
than	_	_	O
vehicle	_	_	B-VAR
tickets	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
ticket	_	_	O
type	_	_	O
should	_	_	O
be	_	_	O
sold	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Amazing	_	_	O
Arts	_	_	O
makes	_	_	O
large	_	_	B-VAR
and	_	_	O
small	_	_	B-VAR
artworks	_	_	I-VAR
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
200	_	_	B-LIMIT
units	_	_	O
of	_	_	O
paint	_	_	O
,	_	_	O
100	_	_	B-LIMIT
units	_	_	O
of	_	_	O
glitter	_	_	O
,	_	_	O
and	_	_	O
80	_	_	B-LIMIT
units	_	_	O
of	_	_	O
glue	_	_	O
.	_	_	O
To	_	_	O
make	_	_	O
a	_	_	O
large	_	_	B-VAR
artwork	_	_	I-VAR
requires	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
paint	_	_	O
,	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
glitter	_	_	O
,	_	_	O
and	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
glue	_	_	O
.	_	_	O
To	_	_	O
make	_	_	O
a	_	_	O
small	_	_	B-VAR
artwork	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
paint	_	_	O
,	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
glitter	_	_	O
,	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
glue	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
units	_	_	O
of	_	_	O
large	_	_	B-VAR
artworks	_	_	I-VAR
and	_	_	O
10	_	_	B-LIMIT
units	_	_	O
of	_	_	O
small	_	_	B-VAR
artworks	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
large	_	_	B-VAR
artwork	_	_	I-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
small	_	_	B-VAR
artwork	_	_	I-VAR
is	_	_	O
$	_	_	O
75	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
artwork	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
fragrance	_	_	O
shop	_	_	O
makes	_	_	O
a	_	_	O
mixture	_	_	O
of	_	_	O
perfume	_	_	O
using	_	_	O
essential	_	_	B-VAR
oils	_	_	I-VAR
and	_	_	O
fruit	_	_	B-VAR
scents	_	_	I-VAR
.	_	_	O
A	_	_	O
unit	_	_	O
of	_	_	O
essential	_	_	B-VAR
oil	_	_	I-VAR
contains	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
aromatic	_	_	O
notes	_	_	O
and	_	_	O
lasts	_	_	O
up	_	_	O
to	_	_	O
9	_	_	B-LIMIT
hours	_	_	O
.	_	_	O
A	_	_	O
unit	_	_	O
of	_	_	O
fruit	_	_	B-VAR
scent	_	_	I-VAR
has	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
aromatic	_	_	O
notes	_	_	O
but	_	_	O
lasts	_	_	O
only	_	_	O
for	_	_	O
4	_	_	B-PARAM
hours	_	_	O
.	_	_	O
The	_	_	O
shop	_	_	O
wants	_	_	O
to	_	_	O
make	_	_	O
sure	_	_	O
that	_	_	O
the	_	_	O
mixture	_	_	O
contains	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
6	_	_	B-LIMIT
units	_	_	O
of	_	_	O
aromatic	_	_	O
notes	_	_	O
and	_	_	O
lasts	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
for	_	_	O
7	_	_	B-LIMIT
hours	_	_	O
.	_	_	O
The	_	_	O
mixture	_	_	O
can	_	_	O
also	_	_	O
contain	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
8	_	_	B-LIMIT
units	_	_	O
of	_	_	O
aromatic	_	_	O
notes	_	_	O
.	_	_	O
If	_	_	O
a	_	_	O
unit	_	_	O
of	_	_	O
essential	_	_	B-VAR
oil	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
3.50	_	_	B-PARAM
and	_	_	O
a	_	_	O
unit	_	_	O
of	_	_	O
fruit	_	_	B-VAR
scent	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
2	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
units	_	_	O
of	_	_	O
each	_	_	O
ingredient	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
of	_	_	O
the	_	_	O
mixture	_	_	O
?	_	_	O

A	_	_	O
wood	_	_	O
factory	_	_	O
produces	_	_	O
lumbers	_	_	B-VAR
and	_	_	O
plywood	_	_	B-VAR
using	_	_	O
workers	_	_	O
and	_	_	O
machines	_	_	O
.	_	_	O
The	_	_	O
factory	_	_	O
has	_	_	O
a	_	_	O
total	_	_	B-CONST_DIR
of	_	_	O
2500	_	_	B-LIMIT
worker	_	_	O
-	_	_	O
hours	_	_	O
and	_	_	O
4000	_	_	B-LIMIT
machine	_	_	O
-	_	_	O
hours	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
Each	_	_	O
lumber	_	_	B-VAR
takes	_	_	O
3	_	_	B-PARAM
worker	_	_	O
-	_	_	O
hours	_	_	O
and	_	_	O
8	_	_	B-PARAM
works	_	_	O
of	_	_	O
machine	_	_	O
-	_	_	O
hours	_	_	O
.	_	_	O
On	_	_	O
the	_	_	O
other	_	_	O
hand	_	_	O
,	_	_	O
each	_	_	O
plywood	_	_	B-VAR
requires	_	_	O
2	_	_	B-PARAM
worker	_	_	O
-	_	_	O
hours	_	_	O
and	_	_	O
12	_	_	B-PARAM
machine	_	_	O
-	_	_	O
hours	_	_	O
.	_	_	O
The	_	_	O
factory	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
200	_	_	B-LIMIT
lumbers	_	_	B-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
300	_	_	B-LIMIT
plywood	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
lumber	_	_	B-VAR
is	_	_	O
$	_	_	O
10	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
plywood	_	_	B-VAR
is	_	_	O
$	_	_	O
35	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Gary	_	_	O
eats	_	_	O
only	_	_	O
noodles	_	_	B-VAR
and	_	_	O
cakes	_	_	B-VAR
for	_	_	O
a	_	_	O
diet	_	_	O
.	_	_	O
A	_	_	O
serving	_	_	O
of	_	_	O
noodles	_	_	B-VAR
contains	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
proteins	_	_	O
and	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
minerals	_	_	O
.	_	_	O
A	_	_	O
serving	_	_	O
of	_	_	O
cake	_	_	B-VAR
contains	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
proteins	_	_	O
and	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
minerals	_	_	O
.	_	_	O
He	_	_	O
wants	_	_	O
to	_	_	O
receive	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
units	_	_	O
of	_	_	O
proteins	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
units	_	_	O
of	_	_	O
minerals	_	_	O
.	_	_	O
If	_	_	O
noodles	_	_	B-VAR
cost	_	_	B-OBJ_NAME
$	_	_	O
3	_	_	B-PARAM
per	_	_	O
serving	_	_	O
and	_	_	O
each	_	_	O
cake	_	_	B-VAR
cost	_	_	B-OBJ_NAME
$	_	_	O
5	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
servings	_	_	O
of	_	_	O
each	_	_	O
food	_	_	O
should	_	_	O
Gary	_	_	O
eat	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
cost	_	_	B-OBJ_NAME
?	_	_	O

Fancy	_	_	O
Clothing	_	_	O
Co	_	_	O
makes	_	_	O
red	_	_	B-VAR
shirts	_	_	I-VAR
and	_	_	O
green	_	_	B-VAR
shirts	_	_	I-VAR
.	_	_	O
A	_	_	O
red	_	_	B-VAR
shirt	_	_	I-VAR
requires	_	_	O
2	_	_	B-PARAM
unit	_	_	O
of	_	_	O
dye	_	_	O
,	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	O
,	_	_	O
and	_	_	O
20	_	_	B-PARAM
worker	_	_	O
minutes	_	_	O
.	_	_	O
A	_	_	O
green	_	_	B-VAR
shirt	_	_	I-VAR
requires	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
dye	_	_	O
,	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	O
,	_	_	O
and	_	_	O
25	_	_	B-PARAM
worker	_	_	O
minutes	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
only	_	_	O
has	_	_	O
1500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
dye	_	_	O
,	_	_	O
3000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
water	_	_	O
,	_	_	O
and	_	_	O
8000	_	_	B-LIMIT
worker	_	_	O
minutes	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
red	_	_	B-VAR
shirt	_	_	I-VAR
is	_	_	O
$	_	_	O
20	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
green	_	_	B-VAR
shirt	_	_	I-VAR
is	_	_	O
$	_	_	O
35	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

WFH	_	_	O
factory	_	_	O
makes	_	_	O
standing	_	_	B-VAR
desks	_	_	I-VAR
and	_	_	O
office	_	_	B-VAR
chairs	_	_	I-VAR
using	_	_	O
a	_	_	O
special	_	_	O
machine	_	_	O
.	_	_	O
This	_	_	O
machine	_	_	O
must	_	_	O
be	_	_	O
operated	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
2000	_	_	B-LIMIT
minutes	_	_	O
per	_	_	O
week	_	_	O
.	_	_	O
Each	_	_	O
standing	_	_	B-VAR
desk	_	_	I-VAR
takes	_	_	O
60	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
machine	_	_	O
while	_	_	O
each	_	_	O
office	_	_	B-VAR
chair	_	_	I-VAR
takes	_	_	O
35	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
machine	_	_	O
.	_	_	O
The	_	_	O
factory	_	_	O
must	_	_	O
make	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
100	_	_	B-LIMIT
items	_	_	O
total	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
for	_	_	O
producing	_	_	O
a	_	_	O
standing	_	_	B-VAR
desk	_	_	I-VAR
is	_	_	O
$	_	_	O
500	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
for	_	_	O
producing	_	_	O
a	_	_	O
office	_	_	B-VAR
chair	_	_	I-VAR
is	_	_	O
$	_	_	O
230	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

ABC	_	_	O
Toys	_	_	O
Co	_	_	O
makes	_	_	O
RC	_	_	B-VAR
drones	_	_	I-VAR
and	_	_	O
model	_	_	B-VAR
cars	_	_	I-VAR
using	_	_	O
wood	_	_	O
and	_	_	O
paint	_	_	O
.	_	_	O
A	_	_	O
RC	_	_	B-VAR
drone	_	_	I-VAR
requires	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
wood	_	_	O
and	_	_	O
30	_	_	B-PARAM
units	_	_	O
of	_	_	O
paint	_	_	O
.	_	_	O
A	_	_	O
model	_	_	B-VAR
car	_	_	I-VAR
requires	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
wood	_	_	O
and	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
paint	_	_	O
.	_	_	O
The	_	_	O
hobbyist	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
200	_	_	B-LIMIT
units	_	_	O
of	_	_	O
wood	_	_	O
and	_	_	O
900	_	_	B-LIMIT
units	_	_	O
of	_	_	O
paint	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
RC	_	_	B-VAR
drone	_	_	I-VAR
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
model	_	_	B-VAR
car	_	_	I-VAR
is	_	_	O
$	_	_	O
90	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
toy	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

You	_	_	O
are	_	_	O
buying	_	_	O
vehicles	_	_	O
to	_	_	O
transport	_	_	O
foods	_	_	O
and	_	_	O
will	_	_	O
keep	_	_	O
them	_	_	O
in	_	_	O
your	_	_	O
parking	_	_	O
lot	_	_	O
.	_	_	O
A	_	_	O
small	_	_	B-VAR
vehicle	_	_	I-VAR
costs	_	_	O
$	_	_	O
7000	_	_	B-PARAM
,	_	_	O
takes	_	_	O
1	_	_	B-PARAM
parking	_	_	O
spot	_	_	O
,	_	_	O
and	_	_	O
can	_	_	O
carry	_	_	O
10	_	_	B-PARAM
boxes	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
foods	_	_	I-OBJ_NAME
.	_	_	O
A	_	_	O
large	_	_	B-VAR
vehicle	_	_	I-VAR
costs	_	_	O
$	_	_	O
14000	_	_	B-PARAM
,	_	_	O
takes	_	_	O
2	_	_	B-PARAM
parking	_	_	O
spots	_	_	O
,	_	_	O
and	_	_	O
can	_	_	O
carry	_	_	O
25	_	_	B-PARAM
boxes	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
foods	_	_	I-OBJ_NAME
.	_	_	O
You	_	_	O
have	_	_	O
a	_	_	O
$	_	_	O
200000	_	_	B-LIMIT
limit	_	_	B-CONST_DIR
and	_	_	O
have	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
parking	_	_	O
spots	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
vehicle	_	_	O
should	_	_	O
be	_	_	O
purchased	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
boxes	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
foods	_	_	I-OBJ_NAME
you	_	_	O
can	_	_	O
carry	_	_	O
?	_	_	O
