-DOCSTART-	_	_	O

Bold	_	_	O
Tycoon	_	_	O
wants	_	_	O
to	_	_	O
put	_	_	O
his	_	_	O
$	_	_	O
10,000	_	_	B-LIMIT
to	_	_	O
work	_	_	O
and	_	_	O
decides	_	_	O
to	_	_	O
invest	_	_	B-CONST_DIR
his	_	_	O
money	_	_	O
in	_	_	O
GICs	_	_	B-VAR
and	_	_	O
index	_	_	B-VAR
ETF	_	_	I-VAR
.	_	_	O
GICs	_	_	B-VAR
yields	_	_	O
a	_	_	O
2	_	_	B-PARAM
%	_	_	I-PARAM
return	_	_	B-OBJ_NAME
whereas	_	_	O
index	_	_	B-VAR
ETF	_	_	I-VAR
yields	_	_	O
an	_	_	O
average	_	_	O
return	_	_	B-OBJ_NAME
of	_	_	O
7.5	_	_	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
4,000	_	_	B-LIMIT
in	_	_	O
index	_	_	B-VAR
ETF	_	_	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
30	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
his	_	_	O
money	_	_	O
to	_	_	O
be	_	_	O
safely	_	_	O
invested	_	_	O
in	_	_	O
GICs	_	_	B-VAR
.	_	_	O
Help	_	_	O
Bold	_	_	O
Tycoon	_	_	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
cell	_	_	O
-	_	_	O
phone	_	_	O
company	_	_	O
makes	_	_	O
foldable	_	_	B-VAR
and	_	_	O
regular	_	_	B-VAR
cell	_	_	O
-	_	_	O
phones	_	_	O
in	_	_	O
a	_	_	O
factory	_	_	O
that	_	_	O
is	_	_	O
divided	_	_	O
into	_	_	O
a	_	_	O
hardware	_	_	O
and	_	_	O
software	_	_	O
section	_	_	O
.	_	_	O
The	_	_	O
hardware	_	_	O
section	_	_	O
must	_	_	O
work	_	_	O
10	_	_	B-PARAM
hours	_	_	O
on	_	_	O
each	_	_	O
foldable	_	_	B-VAR
cell	_	_	O
-	_	_	O
phone	_	_	O
but	_	_	O
only	_	_	O
3	_	_	B-PARAM
hours	_	_	O
on	_	_	O
each	_	_	O
regular	_	_	B-VAR
one	_	_	O
.	_	_	O
The	_	_	O
software	_	_	O
section	_	_	O
must	_	_	O
work	_	_	O
3	_	_	B-PARAM
hours	_	_	O
for	_	_	O
each	_	_	O
cell	_	_	O
-	_	_	O
phone	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
from	_	_	O
the	_	_	O
foldable	_	_	B-VAR
cell	_	_	O
-	_	_	O
phone	_	_	O
is	_	_	O
$	_	_	O
500	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
from	_	_	O
the	_	_	O
regular	_	_	B-VAR
cell	_	_	O
-	_	_	O
phone	_	_	O
is	_	_	O
$	_	_	O
300	_	_	B-PARAM
.	_	_	O
Due	_	_	O
to	_	_	O
a	_	_	O
recent	_	_	O
strike	_	_	O
,	_	_	O
the	_	_	O
hardware	_	_	O
section	_	_	O
only	_	_	O
has	_	_	O
200	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
per	_	_	O
week	_	_	O
and	_	_	O
the	_	_	O
software	_	_	O
section	_	_	O
only	_	_	O
has	_	_	O
150	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
per	_	_	O
week	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
phone	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
produce	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
paint	_	_	O
manufacturer	_	_	O
produces	_	_	B-CONST_DIR
300	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
dye	_	_	O
and	_	_	O
200	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
filler	_	_	O
each	_	_	O
week	_	_	O
.	_	_	O
By	_	_	O
using	_	_	O
different	_	_	O
combinations	_	_	O
,	_	_	O
they	_	_	O
can	_	_	O
produce	_	_	O
three	_	_	O
different	_	_	O
paint	_	_	O
products	_	_	O
for	_	_	O
sale	_	_	O
:	_	_	O
Low	_	_	B-VAR
Quality	_	_	I-VAR
,	_	_	O
Regular	_	_	B-VAR
Quality	_	_	I-VAR
,	_	_	O
and	_	_	O
Premium	_	_	B-VAR
Quality	_	_	I-VAR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
kg	_	_	O
for	_	_	O
selling	_	_	O
the	_	_	O
paint	_	_	O
is	_	_	O
$	_	_	O
100	_	_	B-PARAM
,	_	_	O
$	_	_	O
200	_	_	B-PARAM
,	_	_	O
$	_	_	O
230	_	_	B-PARAM
for	_	_	O
the	_	_	O
low	_	_	B-VAR
quality	_	_	I-VAR
,	_	_	O
regular	_	_	B-VAR
quality	_	_	I-VAR
,	_	_	O
and	_	_	O
premium	_	_	B-VAR
quality	_	_	I-VAR
respectively	_	_	O
.	_	_	O
To	_	_	O
produce	_	_	O
1	_	_	O
kg	_	_	O
of	_	_	O
low	_	_	B-VAR
quality	_	_	I-VAR
paint	_	_	I-VAR
requires	_	_	O
6	_	_	B-PARAM
kg	_	_	O
of	_	_	O
dye	_	_	O
and	_	_	O
20	_	_	B-PARAM
kg	_	_	O
of	_	_	O
filler	_	_	O
.	_	_	O
To	_	_	O
produce	_	_	O
1	_	_	O
kg	_	_	O
of	_	_	O
regular	_	_	B-VAR
quality	_	_	I-VAR
paint	_	_	I-VAR
requires	_	_	O
10	_	_	B-PARAM
kg	_	_	O
of	_	_	O
dye	_	_	O
and	_	_	O
10	_	_	B-PARAM
kg	_	_	O
of	_	_	O
filler	_	_	O
.	_	_	O
To	_	_	O
produce	_	_	O
1	_	_	O
kg	_	_	O
of	_	_	O
premium	_	_	B-VAR
quality	_	_	I-VAR
paint	_	_	I-VAR
require	_	_	O
15	_	_	B-PARAM
kg	_	_	O
of	_	_	O
dye	_	_	O
and	_	_	O
2	_	_	B-PARAM
kg	_	_	O
of	_	_	O
dye	_	_	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

David	_	_	O
likes	_	_	O
to	_	_	O
mix	_	_	O
his	_	_	O
two	_	_	O
post	_	_	O
workout	_	_	O
drinks	_	_	O
:	_	_	O
coconut	_	_	B-VAR
water	_	_	I-VAR
and	_	_	O
blue	_	_	B-VAR
energade	_	_	I-VAR
.	_	_	O
Coconut	_	_	B-VAR
water	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
3	_	_	B-PARAM
per	_	_	O
bottle	_	_	O
,	_	_	O
contains	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
potassium	_	_	O
,	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
magnesium	_	_	O
,	_	_	O
and	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
calcium	_	_	O
.	_	_	O
Blue	_	_	B-VAR
energade	_	_	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
potassium	_	_	O
,	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
magnesium	_	_	O
,	_	_	O
and	_	_	O
4	_	_	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
15	_	_	B-LIMIT
units	_	_	O
of	_	_	O
potassium	_	_	O
,	_	_	O
10	_	_	B-LIMIT
units	_	_	O
of	_	_	O
magnesium	_	_	O
,	_	_	O
and	_	_	O
20	_	_	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

George	_	_	O
has	_	_	B-CONST_DIR
120	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
farmland	_	_	O
on	_	_	O
which	_	_	O
to	_	_	O
grow	_	_	O
strawberries	_	_	B-VAR
and	_	_	O
watermelons	_	_	B-VAR
Both	_	_	O
fruits	_	_	O
have	_	_	O
to	_	_	O
be	_	_	O
watered	_	_	O
and	_	_	O
sprayed	_	_	O
with	_	_	O
bug	_	_	O
repellant	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
150	_	_	B-LIMIT
days	_	_	O
per	_	_	O
year	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
watering	_	_	O
and	_	_	O
100	_	_	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
0.5	_	_	B-PARAM
days	_	_	O
to	_	_	O
water	_	_	O
an	_	_	O
acre	_	_	O
of	_	_	O
strawberries	_	_	B-VAR
and	_	_	O
1	_	_	B-PARAM
day	_	_	O
to	_	_	O
spray	_	_	O
an	_	_	O
acre	_	_	O
of	_	_	O
strawberries	_	_	B-VAR
.	_	_	O
It	_	_	O
takes	_	_	O
0.2	_	_	B-PARAM
days	_	_	O
to	_	_	O
water	_	_	O
an	_	_	O
acre	_	_	O
of	_	_	O
watermelons	_	_	B-VAR
and	_	_	O
2	_	_	B-PARAM
days	_	_	O
to	_	_	O
spray	_	_	O
an	_	_	O
acre	_	_	O
of	_	_	O
watermelons	_	_	B-VAR
.	_	_	O
George	_	_	O
earns	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
200	_	_	B-PARAM
per	_	_	O
acre	_	_	O
of	_	_	O
strawberries	_	_	B-VAR
and	_	_	O
$	_	_	O
500	_	_	B-PARAM
per	_	_	O
acre	_	_	O
of	_	_	O
watermelons	_	_	B-VAR
.	_	_	O
How	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
fruit	_	_	O
should	_	_	O
be	_	_	O
planted	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
factory	_	_	O
in	_	_	O
India	_	_	O
produces	_	_	O
rice	_	_	B-VAR
and	_	_	O
corn	_	_	B-VAR
.	_	_	O
To	_	_	O
make	_	_	O
one	_	_	O
kilogram	_	_	O
of	_	_	O
rice	_	_	B-VAR
requires	_	_	O
2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
human	_	_	O
labor	_	_	O
,	_	_	O
3	_	_	B-PARAM
hours	_	_	O
of	_	_	O
machine	_	_	O
work	_	_	O
,	_	_	O
and	_	_	O
4	_	_	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
corn	_	_	B-VAR
requires	_	_	O
1	_	_	B-PARAM
hour	_	_	O
of	_	_	O
human	_	_	O
labor	_	_	O
,	_	_	O
5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
machine	_	_	O
work	_	_	O
,	_	_	O
and	_	_	O
1	_	_	B-PARAM
hour	_	_	O
of	_	_	O
resting	_	_	O
under	_	_	O
the	_	_	O
sun	_	_	O
.	_	_	O
The	_	_	O
factory	_	_	O
only	_	_	O
has	_	_	O
100	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
human	_	_	O
labor	_	_	O
,	_	_	O
200	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
machine	_	_	O
labor	_	_	O
,	_	_	O
and	_	_	O
75	_	_	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
rice	_	_	B-VAR
is	_	_	O
$	_	_	O
20	_	_	B-PARAM
and	_	_	O
the	_	_	O
net	_	_	B-OBJ_NAME
profit	_	_	I-OBJ_NAME
per	_	_	O
kilogram	_	_	O
of	_	_	O
corn	_	_	B-VAR
is	_	_	O
$	_	_	O
25	_	_	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

Two	_	_	O
brothers	_	_	O
,	_	_	O
John	_	_	O
and	_	_	O
William	_	_	O
,	_	_	O
run	_	_	O
a	_	_	O
stand	_	_	O
selling	_	_	O
lemonade	_	_	B-VAR
and	_	_	O
brownies	_	_	B-VAR
.	_	_	O
A	_	_	O
pitcher	_	_	O
of	_	_	O
lemonade	_	_	B-VAR
takes	_	_	O
0.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
John	_	_	O
's	_	_	O
time	_	_	O
along	_	_	O
with	_	_	O
0.2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
William	_	_	O
's	_	_	O
time	_	_	O
.	_	_	O
A	_	_	O
batch	_	_	O
of	_	_	O
brownies	_	_	B-VAR
take	_	_	O
1	_	_	B-PARAM
hour	_	_	O
of	_	_	O
John	_	_	O
's	_	_	O
time	_	_	O
and	_	_	O
0.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
William	_	_	O
's	_	_	O
time	_	_	O
.	_	_	O
John	_	_	O
has	_	_	O
10	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
each	_	_	O
day	_	_	O
,	_	_	O
but	_	_	O
since	_	_	O
William	_	_	O
has	_	_	O
hockey	_	_	O
lessons	_	_	O
,	_	_	O
he	_	_	O
only	_	_	O
has	_	_	O
8	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
each	_	_	O
day	_	_	O
.	_	_	O
They	_	_	O
get	_	_	O
$	_	_	O
20	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
per	_	_	O
pitcher	_	_	O
of	_	_	O
lemonade	_	_	B-VAR
,	_	_	O
and	_	_	O
$	_	_	O
15	_	_	B-PARAM
per	_	_	O
batch	_	_	O
of	_	_	O
brownies	_	_	B-VAR
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
.	_	_	O

The	_	_	O
Vision	_	_	O
Corporation	_	_	O
manufactures	_	_	O
two	_	_	O
models	_	_	O
of	_	_	O
monitors	_	_	O
:	_	_	O
Aleph	_	_	B-VAR
3	_	_	I-VAR
and	_	_	O
Gilgamesh	_	_	B-VAR
Supreme	_	_	I-VAR
.	_	_	O
They	_	_	O
share	_	_	O
a	_	_	O
similar	_	_	O
manufacturing	_	_	O
process	_	_	O
in	_	_	O
that	_	_	O
they	_	_	O
both	_	_	O
require	_	_	O
a	_	_	O
certain	_	_	O
amount	_	_	O
of	_	_	O
assembly	_	_	O
and	_	_	O
packaging	_	_	O
.	_	_	O
Each	_	_	O
Aleph	_	_	B-VAR
3	_	_	I-VAR
monitor	_	_	O
takes	_	_	O
2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
assembly	_	_	O
and	_	_	O
each	_	_	O
Gilgamesh	_	_	B-VAR
Supreme	_	_	I-VAR
requires	_	_	O
2.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
assembly	_	_	O
.	_	_	O
They	_	_	O
both	_	_	O
require	_	_	O
0.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
packaging	_	_	O
time	_	_	O
per	_	_	O
unit	_	_	O
.	_	_	O
During	_	_	O
the	_	_	O
next	_	_	O
season	_	_	O
,	_	_	O
5000	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
assembly	_	_	O
time	_	_	O
are	_	_	O
available	_	_	B-CONST_DIR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
2500	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
packaging	_	_	O
time	_	_	O
may	_	_	O
be	_	_	O
used	_	_	O
.	_	_	O
Each	_	_	O
Aleph	_	_	B-VAR
3	_	_	I-VAR
sold	_	_	O
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
1500	_	_	B-PARAM
.	_	_	O
Each	_	_	O
Gilgamesh	_	_	B-VAR
Supreme	_	_	I-VAR
sold	_	_	O
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
2500	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
.	_	_	O
Formulate	_	_	O
and	_	_	O
solve	_	_	O
this	_	_	O
LP	_	_	O
problem	_	_	O
and	_	_	O
find	_	_	O
the	_	_	O
best	_	_	O
combination	_	_	O
of	_	_	O
monitors	_	_	O
that	_	_	O
yields	_	_	O
the	_	_	O
highest	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
clothing	_	_	O
factory	_	_	O
makes	_	_	O
t	_	_	B-VAR
-	_	_	I-VAR
shirts	_	_	I-VAR
and	_	_	O
hoodies	_	_	B-VAR
with	_	_	O
images	_	_	O
of	_	_	O
super	_	_	O
heroes	_	_	O
on	_	_	O
them	_	_	O
using	_	_	O
a	_	_	O
printing	_	_	O
machine	_	_	O
.	_	_	O
Due	_	_	O
to	_	_	O
the	_	_	O
popularity	_	_	O
of	_	_	O
super	_	_	O
heroes	_	_	O
,	_	_	O
the	_	_	O
company	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1000	_	_	B-LIMIT
t	_	_	B-VAR
-	_	_	I-VAR
shirts	_	_	I-VAR
or	_	_	O
hoodies	_	_	B-VAR
,	_	_	O
in	_	_	O
any	_	_	O
combination	_	_	O
,	_	_	O
per	_	_	O
week	_	_	O
.	_	_	O
Also	_	_	O
,	_	_	O
in	_	_	O
one	_	_	O
week	_	_	O
,	_	_	O
the	_	_	O
printing	_	_	O
machine	_	_	O
must	_	_	O
be	_	_	O
kept	_	_	O
running	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
60	_	_	B-LIMIT
hours	_	_	O
.	_	_	O
A	_	_	O
t	_	_	B-VAR
-	_	_	I-VAR
shirt	_	_	I-VAR
takes	_	_	O
0.2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
printing	_	_	O
time	_	_	O
and	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
10	_	_	B-PARAM
.	_	_	O
A	_	_	O
hoodie	_	_	B-VAR
take	_	_	O
0.3	_	_	B-PARAM
hours	_	_	O
of	_	_	O
printing	_	_	O
time	_	_	O
and	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
20	_	_	B-PARAM
.	_	_	O
Formulate	_	_	O
this	_	_	O
problem	_	_	O
so	_	_	O
as	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
total	_	_	O
production	_	_	O
costs	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
fashion	_	_	O
company	_	_	O
produces	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
nail	_	_	O
paints	_	_	O
,	_	_	O
gel	_	_	B-VAR
and	_	_	O
acrylic	_	_	B-VAR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
unit	_	_	O
of	_	_	O
gel	_	_	B-VAR
is	_	_	O
$	_	_	O
80	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
unit	_	_	O
of	_	_	O
acrylic	_	_	B-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
.	_	_	O
It	_	_	O
takes	_	_	O
4	_	_	B-PARAM
hours	_	_	O
to	_	_	O
produce	_	_	O
the	_	_	O
raw	_	_	O
materials	_	_	O
for	_	_	O
one	_	_	O
unit	_	_	O
of	_	_	O
gel	_	_	B-VAR
,	_	_	O
3	_	_	B-PARAM
hour	_	_	O
to	_	_	O
mix	_	_	O
and	_	_	O
6	_	_	B-PARAM
hours	_	_	O
in	_	_	O
packing	_	_	O
.	_	_	O
It	_	_	O
takes	_	_	O
2	_	_	B-PARAM
hours	_	_	O
to	_	_	O
produce	_	_	O
the	_	_	O
raw	_	_	O
materials	_	_	O
for	_	_	O
one	_	_	O
unit	_	_	O
of	_	_	O
acrylic	_	_	B-VAR
,	_	_	O
5	_	_	B-PARAM
hour	_	_	O
to	_	_	O
mix	_	_	O
and	_	_	O
2.3	_	_	B-PARAM
hours	_	_	O
in	_	_	O
packing	_	_	O
.	_	_	O
Per	_	_	O
month	_	_	O
,	_	_	O
290	_	_	B-LIMIT
hours	_	_	O
are	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
preparing	_	_	O
the	_	_	O
raw	_	_	O
materials	_	_	O
,	_	_	O
480	_	_	B-LIMIT
hours	_	_	O
for	_	_	O
mixing	_	_	O
and	_	_	O
510	_	_	B-LIMIT
hours	_	_	O
for	_	_	O
packing	_	_	O
the	_	_	O
nail	_	_	O
paints	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
nail	_	_	O
paint	_	_	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

The	_	_	O
Chips	_	_	O
Alloy	_	_	O
company	_	_	O
produces	_	_	B-CONST_DIR
150	_	_	B-LIMIT
tons	_	_	O
of	_	_	O
iron	_	_	O
ore	_	_	O
and	_	_	O
35	_	_	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
different	_	_	O
alloy	_	_	O
grades	_	_	O
:	_	_	O
Standard	_	_	B-VAR
,	_	_	O
Plus	_	_	B-VAR
or	_	_	O
Premium	_	_	B-VAR
.	_	_	O
To	_	_	O
produce	_	_	O
1	_	_	O
ton	_	_	O
of	_	_	O
the	_	_	O
Standard	_	_	B-VAR
grade	_	_	I-VAR
alloy	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
tons	_	_	O
of	_	_	O
iron	_	_	O
ore	_	_	O
and	_	_	O
1	_	_	B-PARAM
ton	_	_	O
of	_	_	O
zinc	_	_	O
ore	_	_	O
.	_	_	O
To	_	_	O
produce	_	_	O
1	_	_	O
ton	_	_	O
of	_	_	O
the	_	_	O
Plus	_	_	B-VAR
grade	_	_	I-VAR
alloy	_	_	I-VAR
requires	_	_	O
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
Finally	_	_	O
,	_	_	O
to	_	_	O
produce	_	_	O
1	_	_	O
ton	_	_	O
of	_	_	O
the	_	_	O
Premium	_	_	B-VAR
grade	_	_	I-VAR
alloy	_	_	I-VAR
requires	_	_	O
6	_	_	B-PARAM
tons	_	_	O
of	_	_	O
iron	_	_	O
ore	_	_	O
and	_	_	O
3	_	_	B-PARAM
tons	_	_	O
of	_	_	O
zinc	_	_	O
ore	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
ton	_	_	O
from	_	_	O
selling	_	_	O
the	_	_	O
alloys	_	_	O
are	_	_	O
$	_	_	O
1500	_	_	B-PARAM
,	_	_	O
$	_	_	O
2500	_	_	B-PARAM
and	_	_	O
$	_	_	O
5500	_	_	B-PARAM
for	_	_	O
the	_	_	O
Standard	_	_	B-VAR
,	_	_	O
Plus	_	_	B-VAR
,	_	_	O
and	_	_	O
Premium	_	_	B-VAR
grades	_	_	O
respectively	_	_	O
.	_	_	O
How	_	_	O
much	_	_	O
of	_	_	O
each	_	_	O
alloy	_	_	O
grade	_	_	O
should	_	_	O
be	_	_	O
produced	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
spicy	_	_	O
paste	_	_	O
is	_	_	O
to	_	_	O
be	_	_	O
made	_	_	O
from	_	_	O
units	_	_	O
of	_	_	O
peppers	_	_	B-VAR
and	_	_	O
tomatoes	_	_	B-VAR
and	_	_	O
is	_	_	O
to	_	_	O
contain	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
130	_	_	B-LIMIT
units	_	_	O
of	_	_	O
spice	_	_	O
and	_	_	O
90	_	_	B-LIMIT
units	_	_	O
of	_	_	O
flavor	_	_	O
.	_	_	O
Peppers	_	_	B-VAR
cost	_	_	B-OBJ_NAME
$	_	_	O
8	_	_	B-PARAM
per	_	_	O
unit	_	_	O
and	_	_	O
tomatoes	_	_	B-VAR
cost	_	_	B-OBJ_NAME
$	_	_	O
5	_	_	B-PARAM
per	_	_	O
unit	_	_	O
.	_	_	O
One	_	_	O
unit	_	_	O
of	_	_	O
peppers	_	_	B-VAR
contains	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
spice	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
flavor	_	_	O
.	_	_	O
One	_	_	O
unit	_	_	O
of	_	_	O
tomatoes	_	_	B-VAR
contains	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
spice	_	_	O
and	_	_	O
8	_	_	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
spicy	_	_	O
paste	_	_	O
that	_	_	O
can	_	_	O
be	_	_	O
made	_	_	O
.	_	_	O

A	_	_	O
train	_	_	O
can	_	_	O
carry	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
500	_	_	B-LIMIT
passengers	_	_	O
.	_	_	O
It	_	_	O
has	_	_	O
two	_	_	O
seat	_	_	O
types	_	_	O
:	_	_	O
AC	_	_	B-VAR
seats	_	_	I-VAR
,	_	_	O
and	_	_	O
non	_	_	B-VAR
-	_	_	I-VAR
AC	_	_	I-VAR
seats	_	_	I-VAR
(	_	_	O
AC	_	_	O
is	_	_	O
air	_	_	O
conditioned	_	_	O
)	_	_	O
.	_	_	O
A	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
50	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
AC	_	_	B-VAR
seat	_	_	I-VAR
ticket	_	_	O
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
30	_	_	B-PARAM
is	_	_	O
made	_	_	O
on	_	_	O
each	_	_	O
non	_	_	B-VAR
-	_	_	I-VAR
AC	_	_	I-VAR
seat	_	_	I-VAR
ticket	_	_	O
.	_	_	O
The	_	_	O
train	_	_	O
company	_	_	O
reserves	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
seats	_	_	O
as	_	_	O
AC	_	_	B-VAR
seats	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
2	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
passengers	_	_	O
prefer	_	_	O
to	_	_	O
travel	_	_	O
on	_	_	O
non	_	_	B-VAR
-	_	_	I-VAR
AC	_	_	I-VAR
seats	_	_	I-VAR
than	_	_	O
on	_	_	O
AC	_	_	B-VAR
seats	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
seat	_	_	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
What	_	_	O
is	_	_	O
that	_	_	O
profit	_	_	O
?	_	_	O

A	_	_	O
kitchen	_	_	O
prepares	_	_	O
diced	_	_	B-VAR
onions	_	_	I-VAR
and	_	_	O
carrots	_	_	B-VAR
each	_	_	O
involving	_	_	O
both	_	_	O
peeling	_	_	O
and	_	_	O
cutting	_	_	O
.	_	_	O
To	_	_	O
prepare	_	_	O
a	_	_	O
container	_	_	O
of	_	_	O
diced	_	_	B-VAR
onions	_	_	I-VAR
takes	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
peeling	_	_	O
and	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
cutting	_	_	O
.	_	_	O
To	_	_	O
prepare	_	_	O
a	_	_	O
container	_	_	O
of	_	_	O
diced	_	_	B-VAR
carrots	_	_	I-VAR
takes	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
peeling	_	_	O
and	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
cutting	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
2000	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
peeling	_	_	O
time	_	_	O
and	_	_	O
2500	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
cutting	_	_	O
time	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
container	_	_	O
of	_	_	O
diced	_	_	B-VAR
onions	_	_	I-VAR
is	_	_	O
$	_	_	O
8	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
container	_	_	O
of	_	_	O
diced	_	_	B-VAR
carrots	_	_	I-VAR
is	_	_	O
$	_	_	O
6	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
containers	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
prepared	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
suit	_	_	O
store	_	_	O
makes	_	_	O
2	_	_	B-VAR
-	_	_	I-VAR
piece	_	_	I-VAR
and	_	_	O
3	_	_	B-VAR
-	_	_	I-VAR
piece	_	_	I-VAR
suits	_	_	I-VAR
.	_	_	O
To	_	_	O
make	_	_	O
a	_	_	O
2	_	_	B-VAR
-	_	_	I-VAR
piece	_	_	I-VAR
suit	_	_	I-VAR
requires	_	_	O
1	_	_	B-PARAM
hour	_	_	O
of	_	_	O
measuring	_	_	O
and	_	_	O
4	_	_	B-PARAM
hours	_	_	O
of	_	_	O
stitching	_	_	O
.	_	_	O
To	_	_	O
make	_	_	O
a	_	_	O
3	_	_	B-VAR
-	_	_	I-VAR
piece	_	_	I-VAR
suit	_	_	I-VAR
requires	_	_	O
2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
measuring	_	_	O
and	_	_	O
5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
stitching	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
150	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
measuring	_	_	O
time	_	_	O
and	_	_	O
300	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
stitching	_	_	O
time	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
In	_	_	O
order	_	_	O
to	_	_	O
stay	_	_	O
in	_	_	O
business	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
40	_	_	B-LIMIT
2	_	_	B-VAR
-	_	_	I-VAR
piece	_	_	I-VAR
suites	_	_	I-VAR
should	_	_	O
be	_	_	O
made	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
2	_	_	B-VAR
-	_	_	I-VAR
piece	_	_	I-VAR
suit	_	_	I-VAR
is	_	_	O
$	_	_	O
600	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
3	_	_	B-VAR
-	_	_	I-VAR
piece	_	_	I-VAR
suit	_	_	I-VAR
is	_	_	O
$	_	_	O
800	_	_	B-PARAM
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
furniture	_	_	O
store	_	_	O
only	_	_	O
stocks	_	_	O
and	_	_	O
sells	_	_	O
dining	_	_	B-VAR
tables	_	_	I-VAR
and	_	_	O
chairs	_	_	B-VAR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
dining	_	_	B-VAR
table	_	_	I-VAR
is	_	_	O
$	_	_	O
350	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
chair	_	_	B-VAR
is	_	_	O
$	_	_	O
75	_	_	B-PARAM
.	_	_	O
There	_	_	O
is	_	_	O
500	_	_	B-LIMIT
sq	_	_	O
ft	_	_	O
of	_	_	O
space	_	_	O
available	_	_	B-CONST_DIR
and	_	_	O
a	_	_	O
dining	_	_	B-VAR
table	_	_	I-VAR
requires	_	_	O
8	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
of	_	_	O
floor	_	_	O
space	_	_	O
while	_	_	O
a	_	_	O
chair	_	_	B-VAR
requires	_	_	O
2	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
.	_	_	O
Because	_	_	O
chairs	_	_	B-VAR
sell	_	_	O
in	_	_	O
larger	_	_	O
quantities	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
70	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
all	_	_	O
furniture	_	_	O
in	_	_	O
the	_	_	O
store	_	_	O
must	_	_	O
be	_	_	O
chairs	_	_	B-VAR
.	_	_	O
In	_	_	O
terms	_	_	O
of	_	_	O
capital	_	_	O
,	_	_	O
a	_	_	O
dining	_	_	B-VAR
table	_	_	I-VAR
ties	_	_	O
up	_	_	O
$	_	_	O
1000	_	_	B-PARAM
in	_	_	O
capital	_	_	O
and	_	_	O
a	_	_	O
chair	_	_	B-VAR
ties	_	_	O
up	_	_	O
$	_	_	O
150	_	_	B-PARAM
in	_	_	O
capital	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
wants	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
20000	_	_	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

A	_	_	O
coconut	_	_	O
seller	_	_	O
has	_	_	O
to	_	_	O
transport	_	_	O
coconuts	_	_	O
using	_	_	O
either	_	_	O
rickshaws	_	_	B-VAR
or	_	_	O
ox	_	_	B-VAR
carts	_	_	I-VAR
.	_	_	O
The	_	_	O
rickshaws	_	_	B-VAR
can	_	_	O
take	_	_	O
50	_	_	B-PARAM
coconuts	_	_	B-OBJ_NAME
each	_	_	O
and	_	_	O
cost	_	_	O
$	_	_	O
10	_	_	B-PARAM
per	_	_	O
trip	_	_	O
.	_	_	O
The	_	_	O
ox	_	_	B-VAR
carts	_	_	I-VAR
can	_	_	O
take	_	_	O
30	_	_	B-PARAM
coconuts	_	_	B-OBJ_NAME
each	_	_	O
and	_	_	O
cost	_	_	O
$	_	_	O
8	_	_	B-PARAM
per	_	_	O
trip	_	_	O
.	_	_	O
The	_	_	O
seller	_	_	O
has	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
200	_	_	B-LIMIT
to	_	_	O
spend	_	_	O
on	_	_	O
transporting	_	_	O
the	_	_	O
coconuts	_	_	O
.	_	_	O
Due	_	_	O
to	_	_	O
pollution	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
rickshaws	_	_	B-VAR
must	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
ox	_	_	B-VAR
carts	_	_	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
coconuts	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
transported	_	_	O
.	_	_	O

A	_	_	O
company	_	_	O
wants	_	_	O
to	_	_	O
advertise	_	_	O
its	_	_	O
product	_	_	O
.	_	_	O
They	_	_	O
want	_	_	O
to	_	_	O
use	_	_	O
three	_	_	O
types	_	_	O
of	_	_	O
ads	_	_	O
:	_	_	O
magazine	_	_	B-VAR
ads	_	_	I-VAR
,	_	_	O
flyers	_	_	B-VAR
,	_	_	O
and	_	_	O
billboard	_	_	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
magazine	_	_	B-VAR
ad	_	_	I-VAR
costs	_	_	O
$	_	_	O
1000	_	_	B-PARAM
and	_	_	O
attracts	_	_	O
10000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
A	_	_	O
flyer	_	_	B-VAR
costs	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
attracts	_	_	O
5000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
A	_	_	O
billboard	_	_	B-VAR
ad	_	_	I-VAR
costs	_	_	O
$	_	_	O
7000	_	_	B-PARAM
and	_	_	O
attracts	_	_	O
25000	_	_	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
flyers	_	_	B-VAR
from	_	_	O
a	_	_	O
single	_	_	O
company	_	_	O
to	_	_	O
8	_	_	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
billboard	_	_	B-VAR
ads	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
15	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
ads	_	_	O
should	_	_	O
be	_	_	O
magazine	_	_	B-VAR
ads	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
weekly	_	_	O
budget	_	_	B-CONST_DIR
is	_	_	O
$	_	_	O
50000	_	_	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	_	_	O
of	_	_	O
viewers	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
bakery	_	_	O
sells	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
cakes	_	_	O
.	_	_	O
They	_	_	O
sell	_	_	O
a	_	_	O
chocolate	_	_	B-VAR
cake	_	_	I-VAR
and	_	_	O
a	_	_	O
vanilla	_	_	B-VAR
cake	_	_	I-VAR
.	_	_	O
Let	_	_	O
's	_	_	O
say	_	_	O
they	_	_	O
make	_	_	O
x1	_	_	O
chocolate	_	_	B-VAR
cakes	_	_	I-VAR
,	_	_	O
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
10	_	_	B-PARAM
each	_	_	O
,	_	_	O
and	_	_	O
x2	_	_	O
vanilla	_	_	B-VAR
cakes	_	_	I-VAR
,	_	_	O
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
11	_	_	B-PARAM
each	_	_	O
(	_	_	O
x1	_	_	O
and	_	_	O
x2	_	_	O
are	_	_	O
unknowns	_	_	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
cakes	_	_	O
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
50	_	_	B-LIMIT
chocolate	_	_	B-VAR
cakes	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
vanilla	_	_	B-VAR
cakes	_	_	I-VAR
.	_	_	O
The	_	_	O
bakery	_	_	O
is	_	_	O
short	_	_	O
staffed	_	_	O
and	_	_	O
can	_	_	O
make	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
50	_	_	B-LIMIT
cakes	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
How	_	_	O
much	_	_	O
of	_	_	O
each	_	_	O
cake	_	_	O
should	_	_	O
the	_	_	O
bakery	_	_	O
make	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
meat	_	_	O
processing	_	_	O
plant	_	_	O
has	_	_	O
a	_	_	O
machine	_	_	O
that	_	_	O
makes	_	_	O
ham	_	_	B-VAR
and	_	_	O
bacon	_	_	B-VAR
.	_	_	O
Each	_	_	O
kg	_	_	O
of	_	_	O
ham	_	_	B-VAR
takes	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
machine	_	_	O
time	_	_	O
and	_	_	O
each	_	_	O
kg	_	_	O
of	_	_	O
bacon	_	_	B-VAR
takes	_	_	O
8	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
machine	_	_	O
time	_	_	O
.	_	_	O
In	_	_	O
a	_	_	O
week	_	_	O
the	_	_	O
machine	_	_	O
is	_	_	O
only	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
2000	_	_	B-LIMIT
minutes	_	_	O
.	_	_	O
The	_	_	O
plant	_	_	O
can	_	_	O
also	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
200	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
ham	_	_	B-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
220	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
bacon	_	_	B-VAR
per	_	_	O
week	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
kg	_	_	O
of	_	_	O
ham	_	_	B-VAR
is	_	_	O
$	_	_	O
20	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
kg	_	_	O
of	_	_	O
bacon	_	_	B-VAR
is	_	_	O
$	_	_	O
12	_	_	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
factory	_	_	O
makes	_	_	O
bike	_	_	B-VAR
tires	_	_	I-VAR
and	_	_	O
car	_	_	B-VAR
tires	_	_	I-VAR
.	_	_	O
Bike	_	_	B-VAR
tires	_	_	I-VAR
take	_	_	O
4	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
manufacturing	_	_	O
machine	_	_	O
and	_	_	O
2	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
fill	_	_	O
with	_	_	O
air	_	_	O
.	_	_	O
Car	_	_	B-VAR
tires	_	_	I-VAR
take	_	_	O
6	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
manufacturing	_	_	O
machine	_	_	O
and	_	_	O
3.5	_	_	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
600	_	_	B-LIMIT
minutes	_	_	O
and	_	_	O
they	_	_	O
have	_	_	O
400	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
filling	_	_	O
the	_	_	O
tires	_	_	O
with	_	_	O
air	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
bike	_	_	B-VAR
tire	_	_	I-VAR
is	_	_	O
$	_	_	O
12	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
car	_	_	B-VAR
tire	_	_	I-VAR
is	_	_	O
$	_	_	O
20	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
tire	_	_	O
should	_	_	O
the	_	_	O
factory	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
software	_	_	O
company	_	_	O
has	_	_	O
UI	_	_	B-VAR
designers	_	_	I-VAR
earning	_	_	B-OBJ_NAME
$	_	_	O
2500	_	_	B-PARAM
per	_	_	O
week	_	_	O
and	_	_	O
software	_	_	B-VAR
engineers	_	_	I-VAR
earning	_	_	B-OBJ_NAME
$	_	_	O
2000	_	_	B-PARAM
per	_	_	O
week	_	_	O
.	_	_	O
The	_	_	O
contracts	_	_	O
with	_	_	O
companies	_	_	O
to	_	_	O
provide	_	_	O
cloud	_	_	O
services	_	_	O
require	_	_	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
10	_	_	B-LIMIT
must	_	_	O
be	_	_	O
software	_	_	B-VAR
engineers	_	_	I-VAR
.	_	_	O
To	_	_	O
make	_	_	O
sure	_	_	O
there	_	_	O
is	_	_	O
enough	_	_	O
experience	_	_	O
on	_	_	O
the	_	_	O
team	_	_	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
a	_	_	O
third	_	_	B-PARAM
of	_	_	O
the	_	_	O
number	_	_	O
to	_	_	O
UI	_	_	B-VAR
designers	_	_	I-VAR
.	_	_	O
The	_	_	O
company	_	_	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
200000	_	_	B-LIMIT
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
problem	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	B-OBJ_NAME
wage	_	_	I-OBJ_NAME
bill	_	_	I-OBJ_NAME
.	_	_	O

An	_	_	O
electronics	_	_	O
company	_	_	O
makes	_	_	O
economical	_	_	B-VAR
and	_	_	O
premium	_	_	B-VAR
mobile	_	_	I-VAR
phones	_	_	O
in	_	_	O
a	_	_	O
factory	_	_	O
that	_	_	O
is	_	_	O
divided	_	_	O
into	_	_	O
a	_	_	O
hardware	_	_	O
and	_	_	O
software	_	_	O
section	_	_	O
.	_	_	O
The	_	_	O
hardware	_	_	O
section	_	_	O
must	_	_	O
work	_	_	O
5	_	_	B-PARAM
hours	_	_	O
on	_	_	O
each	_	_	O
economical	_	_	B-VAR
mobile	_	_	I-VAR
phone	_	_	I-VAR
but	_	_	O
12	_	_	B-PARAM
hours	_	_	O
on	_	_	O
each	_	_	O
premium	_	_	B-VAR
one	_	_	I-VAR
.	_	_	O
The	_	_	O
software	_	_	O
section	_	_	O
must	_	_	O
work	_	_	O
3	_	_	B-PARAM
hours	_	_	O
for	_	_	O
each	_	_	O
mobile	_	_	O
phone	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
from	_	_	O
the	_	_	O
economical	_	_	B-VAR
mobile	_	_	I-VAR
phone	_	_	I-VAR
is	_	_	O
$	_	_	O
150	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
from	_	_	O
the	_	_	O
premium	_	_	B-VAR
mobile	_	_	I-VAR
phone	_	_	I-VAR
is	_	_	O
$	_	_	O
400	_	_	B-PARAM
.	_	_	O
Due	_	_	O
to	_	_	O
a	_	_	O
recent	_	_	O
strike	_	_	O
,	_	_	O
the	_	_	O
hardware	_	_	O
section	_	_	O
only	_	_	O
has	_	_	O
150	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
per	_	_	O
week	_	_	O
and	_	_	O
the	_	_	O
software	_	_	O
section	_	_	O
only	_	_	O
has	_	_	O
100	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
per	_	_	O
week	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
phone	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
produce	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
company	_	_	O
makes	_	_	O
raincoats	_	_	B-VAR
and	_	_	O
umbrellas	_	_	B-VAR
with	_	_	O
images	_	_	O
of	_	_	O
Latin	_	_	O
alphabet	_	_	O
on	_	_	O
them	_	_	O
using	_	_	O
a	_	_	O
printing	_	_	O
machine	_	_	O
.	_	_	O
Due	_	_	O
to	_	_	O
the	_	_	O
popularity	_	_	O
of	_	_	O
Latin	_	_	O
alphabet	_	_	O
,	_	_	O
the	_	_	O
company	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1200	_	_	B-LIMIT
raincoats	_	_	B-VAR
or	_	_	O
umbrellas	_	_	B-VAR
,	_	_	O
in	_	_	O
any	_	_	O
combination	_	_	O
,	_	_	O
per	_	_	O
week	_	_	O
.	_	_	O
Also	_	_	O
,	_	_	O
in	_	_	O
one	_	_	O
week	_	_	O
,	_	_	O
the	_	_	O
printing	_	_	O
machine	_	_	O
must	_	_	O
be	_	_	O
kept	_	_	O
running	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
70	_	_	B-LIMIT
hours	_	_	O
.	_	_	O
A	_	_	O
raincoat	_	_	B-VAR
takes	_	_	O
0.3	_	_	B-PARAM
hours	_	_	O
of	_	_	O
printing	_	_	O
time	_	_	O
and	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
7	_	_	B-PARAM
.	_	_	O
An	_	_	O
umbrella	_	_	B-VAR
takes	_	_	O
0.5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
printing	_	_	O
time	_	_	O
and	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
12	_	_	B-PARAM
.	_	_	O
Formulate	_	_	O
this	_	_	O
problem	_	_	O
so	_	_	O
as	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
total	_	_	O
production	_	_	O
costs	_	_	B-OBJ_NAME
.	_	_	O

There	_	_	O
are	_	_	O
two	_	_	O
methods	_	_	O
of	_	_	O
extracting	_	_	O
a	_	_	O
chemical	_	_	B-OBJ_NAME
element	_	_	I-OBJ_NAME
,	_	_	O
method	_	_	B-VAR
X	_	_	I-VAR
and	_	_	O
method	_	_	B-VAR
Y.	_	_	I-VAR
Method	_	_	B-VAR
X	_	_	I-VAR
requires	_	_	O
5	_	_	B-PARAM
atomic	_	_	O
units	_	_	O
(	_	_	O
au	_	_	O
)	_	_	O
of	_	_	O
aluminum	_	_	O
,	_	_	O
1	_	_	B-PARAM
au	_	_	O
of	_	_	O
oxygen	_	_	O
,	_	_	O
and	_	_	O
can	_	_	O
extract	_	_	O
0.5	_	_	B-PARAM
au	_	_	O
of	_	_	O
the	_	_	O
desired	_	_	B-OBJ_NAME
chemical	_	_	I-OBJ_NAME
element	_	_	I-OBJ_NAME
.	_	_	O
Method	_	_	B-VAR
Y	_	_	I-VAR
requires	_	_	O
6	_	_	B-PARAM
au	_	_	O
of	_	_	O
aluminum	_	_	O
,	_	_	O
2	_	_	B-PARAM
au	_	_	O
of	_	_	O
oxygen	_	_	O
,	_	_	O
and	_	_	O
can	_	_	O
extract	_	_	O
0.7	_	_	B-PARAM
au	_	_	O
of	_	_	O
the	_	_	O
desired	_	_	B-OBJ_NAME
chemical	_	_	I-OBJ_NAME
element	_	_	I-OBJ_NAME
.	_	_	O
There	_	_	O
are	_	_	O
650	_	_	B-LIMIT
au	_	_	O
of	_	_	O
aluminum	_	_	O
,	_	_	O
and	_	_	O
425	_	_	B-LIMIT
au	_	_	O
of	_	_	O
oxygen	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
What	_	_	O
is	_	_	O
the	_	_	O
best	_	_	O
combination	_	_	O
of	_	_	O
these	_	_	O
two	_	_	O
methods	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
desired	_	_	I-OBJ_NAME
chemical	_	_	I-OBJ_NAME
element	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
tutoring	_	_	O
company	_	_	O
hires	_	_	O
full	_	_	B-VAR
-	_	_	I-VAR
time	_	_	I-VAR
tutors	_	_	I-VAR
and	_	_	O
supplements	_	_	O
with	_	_	O
assistant	_	_	B-VAR
tutors	_	_	I-VAR
from	_	_	O
a	_	_	O
nearby	_	_	O
high	_	_	O
school	_	_	O
.	_	_	O
Every	_	_	O
day	_	_	O
,	_	_	O
full	_	_	B-VAR
-	_	_	I-VAR
time	_	_	I-VAR
tutors	_	_	I-VAR
work	_	_	O
8	_	_	B-PARAM
hours	_	_	O
and	_	_	O
get	_	_	O
paid	_	_	O
$	_	_	O
650	_	_	B-PARAM
while	_	_	O
assistant	_	_	B-VAR
tutors	_	_	I-VAR
work	_	_	O
4	_	_	B-PARAM
hours	_	_	O
and	_	_	O
get	_	_	O
paid	_	_	O
$	_	_	O
120	_	_	B-PARAM
.	_	_	O
During	_	_	O
Christmas	_	_	O
break	_	_	O
,	_	_	O
the	_	_	O
tutoring	_	_	O
company	_	_	O
expects	_	_	O
more	_	_	O
interest	_	_	O
and	_	_	O
plans	_	_	O
to	_	_	O
require	_	_	B-CONST_DIR
1200	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
teaching	_	_	O
availability	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
tutoring	_	_	O
company	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
55000	_	_	B-LIMIT
,	_	_	O
how	_	_	O
many	_	_	O
tutors	_	_	B-VAR
and	_	_	O
assistant	_	_	B-VAR
tutors	_	_	I-VAR
should	_	_	O
be	_	_	O
hired	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
staff	_	_	I-OBJ_NAME
?	_	_	O

An	_	_	O
arcade	_	_	O
is	_	_	O
implementing	_	_	O
two	_	_	O
systems	_	_	O
,	_	_	O
a	_	_	O
card	_	_	B-VAR
-	_	_	I-VAR
based	_	_	I-VAR
system	_	_	I-VAR
and	_	_	O
a	_	_	O
coin	_	_	B-VAR
-	_	_	I-VAR
based	_	_	I-VAR
system	_	_	I-VAR
.	_	_	O
A	_	_	O
card	_	_	B-VAR
-	_	_	I-VAR
based	_	_	I-VAR
system	_	_	I-VAR
can	_	_	O
accept	_	_	O
60	_	_	B-PARAM
guests	_	_	O
per	_	_	O
hour	_	_	O
.	_	_	O
Conversely	_	_	O
,	_	_	O
a	_	_	O
coin	_	_	B-VAR
-	_	_	I-VAR
based	_	_	I-VAR
system	_	_	I-VAR
can	_	_	O
only	_	_	O
accept	_	_	O
45	_	_	B-LIMIT
guests	_	_	O
per	_	_	O
hour	_	_	O
.	_	_	O
The	_	_	O
card	_	_	B-VAR
-	_	_	I-VAR
based	_	_	I-VAR
machine	_	_	I-VAR
needs	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
electricity	_	_	O
every	_	_	O
hour	_	_	O
while	_	_	O
the	_	_	O
coin	_	_	B-VAR
-	_	_	I-VAR
based	_	_	I-VAR
machine	_	_	I-VAR
needs	_	_	O
only	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
electricity	_	_	O
every	_	_	O
hour	_	_	O
.	_	_	O
The	_	_	O
arcade	_	_	O
needs	_	_	O
to	_	_	O
be	_	_	O
able	_	_	O
to	_	_	O
accept	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1500	_	_	B-LIMIT
guests	_	_	O
per	_	_	O
hour	_	_	O
but	_	_	O
only	_	_	B-CONST_DIR
has	_	_	O
access	_	_	O
to	_	_	O
145	_	_	B-LIMIT
units	_	_	O
of	_	_	O
electricity	_	_	O
every	_	_	O
hour	_	_	O
.	_	_	O
Since	_	_	O
most	_	_	O
guests	_	_	O
prefer	_	_	O
to	_	_	O
use	_	_	O
cards	_	_	O
,	_	_	O
there	_	_	O
must	_	_	B-CONST_DIR
be	_	_	I-CONST_DIR
more	_	_	I-CONST_DIR
card	_	_	B-VAR
-	_	_	I-VAR
based	_	_	I-VAR
than	_	_	O
coin	_	_	B-VAR
-	_	_	I-VAR
based	_	_	I-VAR
machines	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
machine	_	_	O
should	_	_	O
be	_	_	O
kept	_	_	O
in	_	_	O
the	_	_	O
arcade	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
machines	_	_	I-OBJ_NAME
in	_	_	O
the	_	_	O
arcade	_	_	O
?	_	_	O

A	_	_	O
popular	_	_	O
coffee	_	_	O
shop	_	_	O
has	_	_	O
coffee	_	_	B-VAR
and	_	_	O
cappuccinos	_	_	B-VAR
.	_	_	O
Each	_	_	O
coffee	_	_	B-VAR
requires	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
milk	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	B-OBJ_NAME
.	_	_	O
Each	_	_	O
cappuccino	_	_	B-VAR
requires	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
cream	_	_	O
and	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
coffee	_	_	O
shop	_	_	O
purchases	_	_	O
a	_	_	O
total	_	_	B-CONST_DIR
of	_	_	O
3300	_	_	B-LIMIT
units	_	_	O
of	_	_	O
milk	_	_	O
and	_	_	O
2600	_	_	B-LIMIT
units	_	_	O
of	_	_	O
cream	_	_	O
.	_	_	O
Regulars	_	_	O
like	_	_	O
the	_	_	O
coffee	_	_	B-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
thirty	_	_	B-LIMIT
percent	_	_	I-LIMIT
of	_	_	O
drinks	_	_	O
must	_	_	O
be	_	_	O
coffee	_	_	B-VAR
.	_	_	O
However	_	_	O
,	_	_	O
cappuccinos	_	_	B-VAR
make	_	_	O
more	_	_	O
profit	_	_	O
,	_	_	O
and	_	_	O
the	_	_	O
owner	_	_	O
wants	_	_	O
to	_	_	O
sell	_	_	O
more	_	_	B-CONST_DIR
cappuccino	_	_	B-VAR
than	_	_	O
coffee	_	_	B-VAR
.	_	_	O
Since	_	_	O
the	_	_	O
town	_	_	O
is	_	_	O
in	_	_	O
a	_	_	O
water	_	_	O
shortage	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
drink	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
water	_	_	I-OBJ_NAME
needed	_	_	O
?	_	_	O

A	_	_	O
children	_	_	O
clothing	_	_	O
manufacturer	_	_	O
can	_	_	O
either	_	_	O
implement	_	_	O
small	_	_	B-VAR
or	_	_	O
large	_	_	B-VAR
production	_	_	I-VAR
lines	_	_	I-VAR
.	_	_	O
A	_	_	O
small	_	_	B-VAR
production	_	_	I-VAR
line	_	_	I-VAR
is	_	_	O
capable	_	_	O
of	_	_	O
creating	_	_	O
150	_	_	B-LIMIT
sets	_	_	O
of	_	_	O
clothing	_	_	O
every	_	_	O
day	_	_	O
and	_	_	O
takes	_	_	O
12	_	_	B-PARAM
employees	_	_	O
to	_	_	O
run	_	_	O
.	_	_	O
Conversely	_	_	O
,	_	_	O
the	_	_	O
children	_	_	O
clothing	_	_	O
manufacturer	_	_	O
may	_	_	O
implement	_	_	O
a	_	_	O
large	_	_	B-VAR
production	_	_	I-VAR
line	_	_	I-VAR
which	_	_	O
requires	_	_	O
26	_	_	B-PARAM
employees	_	_	O
to	_	_	O
create	_	_	O
500	_	_	B-PARAM
sets	_	_	O
of	_	_	O
clothing	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
There	_	_	B-CONST_DIR
are	_	_	I-CONST_DIR
435	_	_	B-LIMIT
employees	_	_	O
and	_	_	O
the	_	_	O
manufacturer	_	_	O
must	_	_	O
meet	_	_	O
the	_	_	O
demand	_	_	O
of	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
6300	_	_	B-LIMIT
sets	_	_	O
of	_	_	O
children	_	_	O
clothing	_	_	O
every	_	_	O
day	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
production	_	_	B-OBJ_NAME
line	_	_	I-OBJ_NAME
type	_	_	O
should	_	_	O
be	_	_	O
put	_	_	O
in	_	_	O
place	_	_	O
to	_	_	O
decrease	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
production	_	_	I-OBJ_NAME
lines	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
lumber	_	_	O
company	_	_	O
owns	_	_	O
and	_	_	O
can	_	_	O
use	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
450	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
where	_	_	O
they	_	_	O
can	_	_	O
transport	_	_	O
the	_	_	O
lumber	_	_	B-OBJ_NAME
out	_	_	O
using	_	_	O
large	_	_	B-VAR
and	_	_	O
small	_	_	B-VAR
logging	_	_	I-VAR
trucks	_	_	I-VAR
.	_	_	O
Per	_	_	O
acre	_	_	O
of	_	_	O
land	_	_	O
,	_	_	O
small	_	_	B-VAR
logging	_	_	I-VAR
trucks	_	_	I-VAR
can	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
transport	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
wood	_	_	B-OBJ_NAME
.	_	_	O
Per	_	_	O
acre	_	_	O
of	_	_	O
land	_	_	O
,	_	_	O
a	_	_	O
large	_	_	B-VAR
logging	_	_	I-VAR
truck	_	_	I-VAR
can	_	_	O
transport	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
wood	_	_	B-OBJ_NAME
.	_	_	O
However	_	_	O
,	_	_	O
a	_	_	O
small	_	_	B-VAR
logging	_	_	I-VAR
truck	_	_	I-VAR
produces	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
carbon	_	_	O
dioxide	_	_	O
and	_	_	O
requires	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
gasoline	_	_	O
per	_	_	O
acre	_	_	O
.	_	_	O
A	_	_	O
large	_	_	B-VAR
logging	_	_	I-VAR
truck	_	_	I-VAR
produces	_	_	O
25	_	_	B-PARAM
units	_	_	O
of	_	_	O
carbon	_	_	O
dioxide	_	_	O
and	_	_	O
requires	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
gasoline	_	_	O
per	_	_	O
acre	_	_	O
.	_	_	O
The	_	_	O
lumbering	_	_	O
company	_	_	O
has	_	_	O
access	_	_	B-CONST_DIR
to	_	_	O
3200	_	_	B-LIMIT
units	_	_	O
of	_	_	O
gasoline	_	_	O
and	_	_	O
the	_	_	O
company	_	_	O
has	_	_	O
vowed	_	_	O
to	_	_	O
limiting	_	_	B-CONST_DIR
pollution	_	_	O
to	_	_	O
5200	_	_	B-LIMIT
units	_	_	O
of	_	_	O
carbon	_	_	O
dioxide	_	_	O
.	_	_	O
How	_	_	O
should	_	_	O
the	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
logging	_	_	O
trucks	_	_	O
be	_	_	O
distributed	_	_	O
to	_	_	O
stay	_	_	O
within	_	_	O
the	_	_	O
limits	_	_	O
of	_	_	O
carbon	_	_	O
dioxide	_	_	O
while	_	_	O
maximizing	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
wood	_	_	I-OBJ_NAME
transported	_	_	O
?	_	_	O

A	_	_	O
tea	_	_	O
shop	_	_	O
brews	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
teas	_	_	O
;	_	_	O
black	_	_	B-VAR
and	_	_	O
green	_	_	B-VAR
tea	_	_	I-VAR
.	_	_	O
Brewing	_	_	O
black	_	_	B-VAR
tea	_	_	I-VAR
takes	_	_	O
2	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
and	_	_	O
green	_	_	B-VAR
tea	_	_	I-VAR
3	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
.	_	_	O
It	_	_	O
takes	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
tea	_	_	O
leaves	_	_	O
and	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
filtered	_	_	O
hot	_	_	O
water	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
cup	_	_	O
of	_	_	O
black	_	_	B-VAR
tea	_	_	I-VAR
.	_	_	O
It	_	_	O
takes	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
tea	_	_	O
leaves	_	_	O
and	_	_	O
18	_	_	B-PARAM
units	_	_	O
of	_	_	O
filtered	_	_	O
hot	_	_	O
water	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
cup	_	_	O
of	_	_	O
green	_	_	B-VAR
tea	_	_	I-VAR
.	_	_	O
The	_	_	O
owner	_	_	O
of	_	_	O
the	_	_	O
tea	_	_	O
shop	_	_	O
has	_	_	O
a	_	_	O
deal	_	_	O
with	_	_	O
her	_	_	O
distributer	_	_	O
to	_	_	O
acquire	_	_	B-CONST_DIR
700	_	_	B-LIMIT
units	_	_	O
of	_	_	O
tea	_	_	O
leaves	_	_	O
and	_	_	O
700	_	_	B-LIMIT
units	_	_	O
of	_	_	O
filtered	_	_	O
hot	_	_	O
water	_	_	O
every	_	_	O
week	_	_	O
.	_	_	O
The	_	_	O
tea	_	_	O
shop	_	_	O
also	_	_	O
has	_	_	O
a	_	_	O
repeating	_	_	O
customer	_	_	O
in	_	_	O
a	_	_	O
Japanese	_	_	O
restaurant	_	_	O
to	_	_	O
brew	_	_	O
green	_	_	B-VAR
tea	_	_	I-VAR
for	_	_	O
them	_	_	O
.	_	_	O
Therefore	_	_	O
,	_	_	O
the	_	_	O
shop	_	_	O
must	_	_	O
brew	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
four	_	_	B-PARAM
times	_	_	O
more	_	_	O
green	_	_	B-VAR
tea	_	_	I-VAR
than	_	_	O
black	_	_	B-VAR
tea	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
tea	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
time	_	_	I-OBJ_NAME
spent	_	_	I-OBJ_NAME
brewing	_	_	I-OBJ_NAME
tea	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
photography	_	_	O
firm	_	_	O
is	_	_	O
planning	_	_	O
to	_	_	O
open	_	_	O
different	_	_	O
stores	_	_	B-OBJ_NAME
to	_	_	O
expand	_	_	O
their	_	_	O
reach	_	_	O
to	_	_	O
customers	_	_	O
.	_	_	O
They	_	_	O
can	_	_	O
open	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
stores	_	_	O
;	_	_	O
film	_	_	B-VAR
-	_	_	I-VAR
based	_	_	I-VAR
and	_	_	O
electrical	_	_	B-VAR
-	_	_	I-VAR
based	_	_	I-VAR
stores	_	_	I-VAR
.	_	_	O
Since	_	_	O
film	_	_	B-VAR
-	_	_	I-VAR
based	_	_	I-VAR
stores	_	_	I-VAR
take	_	_	O
longer	_	_	O
to	_	_	O
process	_	_	O
,	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
two	_	_	B-PARAM
times	_	_	O
more	_	_	O
electrical	_	_	B-VAR
-	_	_	I-VAR
based	_	_	I-VAR
stores	_	_	I-VAR
than	_	_	O
film	_	_	B-VAR
-	_	_	I-VAR
based	_	_	I-VAR
stores	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
management	_	_	O
expects	_	_	O
film	_	_	B-VAR
-	_	_	I-VAR
based	_	_	I-VAR
stores	_	_	I-VAR
to	_	_	O
become	_	_	O
more	_	_	O
popular	_	_	O
and	_	_	O
requires	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
film	_	_	B-VAR
-	_	_	I-VAR
based	_	_	I-VAR
stores	_	_	I-VAR
to	_	_	O
be	_	_	O
opened	_	_	O
.	_	_	O
Film	_	_	B-VAR
-	_	_	I-VAR
based	_	_	I-VAR
stores	_	_	I-VAR
can	_	_	O
on	_	_	O
average	_	_	O
process	_	_	O
2	_	_	B-PARAM
orders	_	_	O
every	_	_	O
hour	_	_	O
while	_	_	O
an	_	_	O
electrical	_	_	B-VAR
-	_	_	I-VAR
based	_	_	I-VAR
store	_	_	I-VAR
can	_	_	O
process	_	_	O
on	_	_	O
average	_	_	O
four	_	_	B-PARAM
orders	_	_	O
every	_	_	O
hour	_	_	O
.	_	_	O
Film	_	_	B-VAR
-	_	_	I-VAR
based	_	_	I-VAR
stores	_	_	I-VAR
requires	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
electricity	_	_	O
every	_	_	O
hour	_	_	O
while	_	_	O
the	_	_	O
electric	_	_	B-VAR
-	_	_	I-VAR
based	_	_	I-VAR
stores	_	_	I-VAR
take	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
electricity	_	_	O
every	_	_	O
hour	_	_	O
.	_	_	O
Further	_	_	O
,	_	_	O
the	_	_	O
photography	_	_	O
firm	_	_	O
wants	_	_	O
to	_	_	O
be	_	_	O
able	_	_	O
to	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
170	_	_	B-LIMIT
orders	_	_	O
per	_	_	O
hour	_	_	O
and	_	_	O
use	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
600	_	_	B-LIMIT
units	_	_	O
of	_	_	O
electricity	_	_	O
every	_	_	O
hour	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
store	_	_	B-OBJ_NAME
should	_	_	O
be	_	_	O
opened	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
stores	_	_	I-OBJ_NAME
?	_	_	O

An	_	_	O
ice	_	_	O
cream	_	_	O
company	_	_	O
sells	_	_	O
ice	_	_	B-OBJ_NAME
cream	_	_	I-OBJ_NAME
as	_	_	O
cones	_	_	B-VAR
and	_	_	O
tubs	_	_	B-VAR
.	_	_	O
A	_	_	O
cone	_	_	B-VAR
of	_	_	I-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
contains	_	_	O
3	_	_	B-PARAM
oz	_	_	O
of	_	_	O
ice	_	_	O
cream	_	_	O
while	_	_	O
a	_	_	O
tub	_	_	B-VAR
contains	_	_	O
24	_	_	B-PARAM
oz	_	_	O
of	_	_	O
ice	_	_	O
cream	_	_	O
.	_	_	O
Due	_	_	O
to	_	_	O
the	_	_	O
recent	_	_	O
wave	_	_	O
of	_	_	O
heat	_	_	O
and	_	_	O
a	_	_	O
recent	_	_	O
promotion	_	_	O
,	_	_	O
the	_	_	O
company	_	_	O
expects	_	_	O
to	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
2	_	_	B-PARAM
times	_	_	I-PARAM
more	_	_	O
cones	_	_	B-VAR
than	_	_	O
tubs	_	_	B-VAR
of	_	_	I-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
to	_	_	O
reduce	_	_	O
labour	_	_	O
time	_	_	O
and	_	_	O
looking	_	_	O
at	_	_	O
previous	_	_	O
sales	_	_	O
,	_	_	O
management	_	_	O
decided	_	_	O
to	_	_	O
require	_	_	O
stores	_	_	O
to	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
create	_	_	O
30	_	_	B-LIMIT
tubs	_	_	B-VAR
of	_	_	I-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
company	_	_	O
has	_	_	O
the	_	_	O
capacity	_	_	B-CONST_DIR
to	_	_	O
make	_	_	O
5000	_	_	B-LIMIT
oz	_	_	O
of	_	_	O
ice	_	_	O
cream	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
orders	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
sales	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
ice	_	_	I-OBJ_NAME
cream	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
grocery	_	_	O
store	_	_	O
sushi	_	_	O
supplier	_	_	O
makes	_	_	O
sushi	_	_	O
in	_	_	O
bulk	_	_	O
and	_	_	O
can	_	_	O
purchase	_	_	O
either	_	_	O
an	_	_	O
all	_	_	B-VAR
-	_	_	I-VAR
in	_	_	I-VAR
-	_	_	I-VAR
one	_	_	I-VAR
manufacturing	_	_	I-VAR
line	_	_	O
or	_	_	O
a	_	_	O
decoupled	_	_	B-VAR
manufacturing	_	_	I-VAR
line	_	_	I-VAR
.	_	_	O
The	_	_	O
all	_	_	B-VAR
-	_	_	I-VAR
in	_	_	I-VAR
-	_	_	I-VAR
one	_	_	I-VAR
manufacturing	_	_	I-VAR
line	_	_	I-VAR
is	_	_	O
more	_	_	O
efficient	_	_	O
and	_	_	O
can	_	_	O
output	_	_	O
10000	_	_	B-LIMIT
orders	_	_	O
per	_	_	O
day	_	_	O
while	_	_	O
the	_	_	O
decoupled	_	_	B-VAR
manufacturing	_	_	I-VAR
line	_	_	I-VAR
can	_	_	O
output	_	_	O
7000	_	_	B-LIMIT
items	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
The	_	_	O
all	_	_	B-VAR
-	_	_	I-VAR
in	_	_	I-VAR
-	_	_	I-VAR
one	_	_	I-VAR
manufacturing	_	_	I-VAR
line	_	_	I-VAR
requires	_	_	O
5	_	_	B-PARAM
workers	_	_	O
per	_	_	O
day	_	_	O
while	_	_	O
the	_	_	O
decoupled	_	_	B-VAR
manufacturing	_	_	I-VAR
line	_	_	I-VAR
requires	_	_	O
10	_	_	B-PARAM
workers	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
The	_	_	O
grocery	_	_	O
store	_	_	O
sushi	_	_	O
supplier	_	_	O
must	_	_	O
be	_	_	O
able	_	_	O
to	_	_	O
satisfy	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
150000	_	_	B-LIMIT
orders	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
has	_	_	O
allocated	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
to	_	_	O
hire	_	_	O
135	_	_	B-LIMIT
workers	_	_	O
.	_	_	O
Since	_	_	O
the	_	_	O
decoupled	_	_	B-VAR
manufacturing	_	_	I-VAR
line	_	_	I-VAR
is	_	_	O
less	_	_	O
efficient	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
35	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
production	_	_	O
can	_	_	O
be	_	_	O
decoupled	_	_	B-VAR
manufacturing	_	_	I-VAR
lines	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
there	_	_	O
are	_	_	O
some	_	_	O
legacy	_	_	O
factories	_	_	O
remaining	_	_	O
that	_	_	O
already	_	_	O
have	_	_	O
decoupled	_	_	B-VAR
manufacturing	_	_	I-VAR
lines	_	_	I-VAR
and	_	_	O
about	_	_	O
10	_	_	O
%	_	_	O
of	_	_	O
workers	_	_	O
are	_	_	O
trained	_	_	O
on	_	_	O
these	_	_	O
older	_	_	O
methods	_	_	O
.	_	_	O
Therefore	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
%	_	_	I-LIMIT
must	_	_	O
be	_	_	O
decoupled	_	_	B-VAR
manufacturing	_	_	I-VAR
lines	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
manufacturing	_	_	B-OBJ_NAME
line	_	_	I-OBJ_NAME
should	_	_	O
the	_	_	O
sushi	_	_	O
supplier	_	_	O
plan	_	_	O
for	_	_	O
to	_	_	O
reduce	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
manufacturing	_	_	I-OBJ_NAME
lines	_	_	I-OBJ_NAME
?	_	_	O

Banking	_	_	O
firm	_	_	O
ABC	_	_	O
can	_	_	O
build	_	_	O
remote	_	_	B-VAR
and	_	_	O
urban	_	_	B-VAR
branches	_	_	I-VAR
to	_	_	O
expand	_	_	O
their	_	_	O
reach	_	_	O
to	_	_	O
customers	_	_	O
.	_	_	O
A	_	_	O
remote	_	_	B-VAR
branch	_	_	I-VAR
expects	_	_	O
5	_	_	B-LIMIT
new	_	_	O
account	_	_	O
registrations	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
requires	_	_	O
2	_	_	B-PARAM
registration	_	_	O
experts	_	_	O
.	_	_	O
An	_	_	O
urban	_	_	B-VAR
branch	_	_	I-VAR
generally	_	_	O
opens	_	_	O
accounts	_	_	O
for	_	_	O
12	_	_	B-LIMIT
new	_	_	O
account	_	_	O
registrations	_	_	O
every	_	_	O
day	_	_	O
and	_	_	O
requires	_	_	O
7	_	_	B-PARAM
registration	_	_	O
experts	_	_	O
.	_	_	O
The	_	_	O
bank	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
550	_	_	B-LIMIT
registration	_	_	O
experts	_	_	O
and	_	_	O
wants	_	_	O
to	_	_	O
open	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1200	_	_	B-LIMIT
new	_	_	O
accounts	_	_	O
every	_	_	O
day	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
branch	_	_	B-OBJ_NAME
should	_	_	O
banking	_	_	O
firm	_	_	O
ABC	_	_	O
open	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
branches	_	_	I-OBJ_NAME
needed	_	_	O
?	_	_	O

A	_	_	O
strawberry	_	_	O
farmer	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
225	_	_	B-LIMIT
hectares	_	_	O
of	_	_	O
land	_	_	O
and	_	_	O
she	_	_	O
needs	_	_	O
to	_	_	O
harvest	_	_	O
the	_	_	O
strawberries	_	_	B-OBJ_NAME
either	_	_	O
through	_	_	O
employees	_	_	B-VAR
or	_	_	O
U	_	_	B-VAR
-	_	_	I-VAR
pick	_	_	I-VAR
.	_	_	O
For	_	_	O
each	_	_	O
hectare	_	_	O
of	_	_	O
land	_	_	O
,	_	_	O
employees	_	_	B-VAR
can	_	_	O
hand	_	_	O
-	_	_	O
pick	_	_	O
60	_	_	B-PARAM
lbs	_	_	O
of	_	_	O
strawberries	_	_	B-OBJ_NAME
which	_	_	O
creates	_	_	O
5	_	_	B-PARAM
lbs	_	_	O
of	_	_	O
waste	_	_	O
,	_	_	O
and	_	_	O
takes	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
.	_	_	O
Conversely	_	_	O
,	_	_	O
for	_	_	O
each	_	_	O
hectare	_	_	O
of	_	_	O
land	_	_	O
,	_	_	O
opening	_	_	O
the	_	_	O
farm	_	_	O
for	_	_	O
U	_	_	B-VAR
-	_	_	I-VAR
pick	_	_	I-VAR
can	_	_	O
pick	_	_	O
45	_	_	B-PARAM
lbs	_	_	O
of	_	_	O
strawberries	_	_	B-OBJ_NAME
which	_	_	O
creates	_	_	O
20	_	_	B-PARAM
lbs	_	_	O
of	_	_	O
waste	_	_	O
,	_	_	O
but	_	_	O
only	_	_	O
takes	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
.	_	_	O
The	_	_	O
farmer	_	_	O
has	_	_	O
a	_	_	O
maximum	_	_	O
amount	_	_	O
of	_	_	O
people	_	_	O
allowed	_	_	O
on	_	_	O
the	_	_	O
field	_	_	O
at	_	_	O
all	_	_	O
times	_	_	O
and	_	_	O
due	_	_	O
to	_	_	O
the	_	_	O
restriction	_	_	O
of	_	_	O
trying	_	_	O
to	_	_	O
sell	_	_	O
the	_	_	O
product	_	_	O
while	_	_	O
it	_	_	O
is	_	_	O
still	_	_	O
fresh	_	_	O
,	_	_	O
expects	_	_	O
that	_	_	O
at	_	_	O
maximum	_	_	O
capacity	_	_	O
she	_	_	O
only	_	_	O
has	_	_	O
8000	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
picking	_	_	O
.	_	_	O
Additionally	_	_	O
,	_	_	O
there	_	_	O
can	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
6400	_	_	B-LIMIT
lbs	_	_	O
of	_	_	O
waste	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
hectares	_	_	O
should	_	_	O
be	_	_	O
allocated	_	_	O
to	_	_	O
each	_	_	O
harvesting	_	_	O
technique	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
strawberries	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
picked	_	_	O
?	_	_	O

A	_	_	O
butcher	_	_	O
sells	_	_	O
marinated	_	_	B-VAR
wild	_	_	I-VAR
boar	_	_	I-VAR
and	_	_	O
processed	_	_	B-VAR
lamb	_	_	I-VAR
chops	_	_	I-VAR
.	_	_	O
Each	_	_	O
portion	_	_	O
of	_	_	O
marinated	_	_	B-VAR
wild	_	_	I-VAR
boar	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
preparation	_	_	O
and	_	_	O
6	_	_	B-PARAM
ounces	_	_	O
of	_	_	O
meat	_	_	O
.	_	_	O
One	_	_	O
portion	_	_	O
of	_	_	O
processed	_	_	B-VAR
lamb	_	_	I-VAR
chops	_	_	I-VAR
requires	_	_	O
1	_	_	B-PARAM
minute	_	_	O
of	_	_	O
preparation	_	_	O
and	_	_	O
7	_	_	B-PARAM
ounces	_	_	O
of	_	_	O
meat	_	_	O
.	_	_	O
Since	_	_	O
processed	_	_	B-VAR
lamb	_	_	I-VAR
chops	_	_	I-VAR
are	_	_	O
more	_	_	O
popular	_	_	O
and	_	_	O
common	_	_	O
,	_	_	O
the	_	_	O
butcher	_	_	O
plans	_	_	O
to	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-PARAM
as	_	_	O
many	_	_	O
processed	_	_	B-VAR
lamb	_	_	I-VAR
chops	_	_	I-VAR
as	_	_	O
marinated	_	_	B-VAR
wild	_	_	I-VAR
boars	_	_	I-VAR
.	_	_	O
The	_	_	O
butcher	_	_	O
has	_	_	O
a	_	_	O
small	_	_	O
staff	_	_	O
and	_	_	O
only	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
250	_	_	B-LIMIT
collective	_	_	O
minutes	_	_	O
every	_	_	O
week	_	_	O
to	_	_	O
preparing	_	_	O
these	_	_	O
two	_	_	O
items	_	_	O
and	_	_	O
only	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
1375	_	_	B-LIMIT
ounces	_	_	O
of	_	_	O
meat	_	_	O
.	_	_	O
If	_	_	O
a	_	_	O
portion	_	_	O
of	_	_	O
marinated	_	_	B-VAR
wild	_	_	I-VAR
boar	_	_	I-VAR
sells	_	_	O
for	_	_	O
a	_	_	O
revenue	_	_	B-OBJ_NAME
of	_	_	O
6	_	_	B-PARAM
dollars	_	_	O
whereas	_	_	O
a	_	_	O
portion	_	_	O
of	_	_	O
processed	_	_	B-VAR
lamb	_	_	I-VAR
chops	_	_	I-VAR
sells	_	_	O
for	_	_	O
a	_	_	O
revenue	_	_	B-OBJ_NAME
of	_	_	O
4	_	_	B-PARAM
dollars	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
butcher	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
their	_	_	O
revenue	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
vending	_	_	O
machine	_	_	O
supplier	_	_	O
is	_	_	O
purchasing	_	_	O
vending	_	_	O
machines	_	_	O
and	_	_	O
they	_	_	O
can	_	_	O
buy	_	_	O
a	_	_	O
double	_	_	B-VAR
-	_	_	I-VAR
load	_	_	I-VAR
or	_	_	O
single	_	_	B-VAR
-	_	_	I-VAR
load	_	_	I-VAR
model	_	_	I-VAR
.	_	_	O
A	_	_	O
double	_	_	B-VAR
-	_	_	I-VAR
load	_	_	I-VAR
vending	_	_	I-VAR
machine	_	_	I-VAR
sells	_	_	O
400	_	_	B-PARAM
items	_	_	O
whereas	_	_	O
a	_	_	O
single	_	_	B-VAR
-	_	_	I-VAR
load	_	_	I-VAR
machine	_	_	I-VAR
sells	_	_	O
325	_	_	B-PARAM
items	_	_	O
.	_	_	O
The	_	_	O
double	_	_	B-VAR
-	_	_	I-VAR
load	_	_	I-VAR
machine	_	_	I-VAR
needs	_	_	O
to	_	_	O
be	_	_	O
re	_	_	O
-	_	_	O
stocked	_	_	O
five	_	_	B-PARAM
times	_	_	B-OBJ_NAME
every	_	_	I-OBJ_NAME
month	_	_	I-OBJ_NAME
and	_	_	O
uses	_	_	O
30	_	_	B-PARAM
units	_	_	O
of	_	_	O
electricity	_	_	O
every	_	_	O
month	_	_	O
.	_	_	O
The	_	_	O
single	_	_	B-VAR
-	_	_	I-VAR
load	_	_	I-VAR
machine	_	_	I-VAR
needs	_	_	O
to	_	_	O
be	_	_	O
re	_	_	O
-	_	_	O
stocked	_	_	O
two	_	_	B-PARAM
times	_	_	B-OBJ_NAME
every	_	_	I-OBJ_NAME
month	_	_	I-OBJ_NAME
and	_	_	O
uses	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
electricity	_	_	O
every	_	_	O
month	_	_	O
.	_	_	O
Since	_	_	O
the	_	_	O
single	_	_	B-VAR
-	_	_	I-VAR
load	_	_	I-VAR
machine	_	_	I-VAR
is	_	_	O
smaller	_	_	O
and	_	_	O
easier	_	_	O
to	_	_	O
fit	_	_	O
,	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
single	_	_	B-VAR
-	_	_	I-VAR
load	_	_	I-VAR
models	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
due	_	_	O
to	_	_	O
the	_	_	O
storage	_	_	O
capacity	_	_	O
,	_	_	O
management	_	_	O
prefers	_	_	O
to	_	_	O
have	_	_	B-CONST_DIR
twice	_	_	B-PARAM
as	_	_	O
many	_	_	O
double	_	_	B-VAR
-	_	_	I-VAR
loads	_	_	I-VAR
than	_	_	O
single	_	_	B-VAR
-	_	_	I-VAR
load	_	_	I-VAR
machines	_	_	I-VAR
.	_	_	O
Further	_	_	O
,	_	_	O
the	_	_	O
supplier	_	_	O
needs	_	_	O
to	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10000	_	_	B-LIMIT
items	_	_	O
every	_	_	O
month	_	_	O
,	_	_	O
and	_	_	O
can	_	_	O
use	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
600	_	_	B-LIMIT
units	_	_	O
of	_	_	O
electricity	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
vending	_	_	O
machine	_	_	O
type	_	_	O
should	_	_	O
the	_	_	O
supplier	_	_	O
purchase	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
times	_	_	I-OBJ_NAME
restocked	_	_	I-OBJ_NAME
?	_	_	O

Professor	_	_	O
ABC	_	_	O
sells	_	_	O
his	_	_	O
economics	_	_	O
textbook	_	_	O
as	_	_	O
paperback	_	_	B-VAR
or	_	_	O
hardcover	_	_	B-VAR
versions	_	_	I-VAR
.	_	_	O
Paperback	_	_	B-VAR
books	_	_	I-VAR
yield	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
150	_	_	B-PARAM
USD	_	_	O
whereas	_	_	O
hardcover	_	_	B-VAR
versions	_	_	I-VAR
yield	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
200	_	_	B-PARAM
USD	_	_	O
.	_	_	O
Since	_	_	O
hardcover	_	_	B-VAR
versions	_	_	I-VAR
are	_	_	O
more	_	_	O
sturdy	_	_	O
and	_	_	O
contain	_	_	O
some	_	_	O
extra	_	_	O
supplementary	_	_	O
materials	_	_	O
,	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
many	_	_	O
hardcover	_	_	B-VAR
than	_	_	O
paperback	_	_	B-VAR
textbooks	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
because	_	_	O
paperback	_	_	B-VAR
books	_	_	I-VAR
are	_	_	O
less	_	_	O
expensive	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
paperback	_	_	B-VAR
versions	_	_	I-VAR
must	_	_	O
be	_	_	O
created	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
professor	_	_	O
sells	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1000	_	_	B-LIMIT
textbooks	_	_	O
every	_	_	O
year	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
version	_	_	O
should	_	_	O
he	_	_	O
request	_	_	O
the	_	_	O
publisher	_	_	O
to	_	_	O
print	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

Architects	_	_	O
ABC	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
one	_	_	B-LIMIT
hundred	_	_	I-LIMIT
thousand	_	_	I-LIMIT
dollars	_	_	O
to	_	_	O
spend	_	_	O
every	_	_	O
week	_	_	O
on	_	_	O
their	_	_	O
employees	_	_	O
.	_	_	O
They	_	_	O
hire	_	_	O
architects	_	_	B-VAR
and	_	_	O
drafters	_	_	B-VAR
to	_	_	O
help	_	_	O
with	_	_	O
their	_	_	O
clients	_	_	O
’	_	_	O
projects	_	_	O
.	_	_	O
An	_	_	O
architect	_	_	B-VAR
averages	_	_	O
3000	_	_	B-PARAM
dollars	_	_	O
every	_	_	O
week	_	_	O
and	_	_	O
can	_	_	O
complete	_	_	O
2	_	_	B-PARAM
projects	_	_	B-OBJ_NAME
every	_	_	O
week	_	_	O
.	_	_	O
A	_	_	O
drafter	_	_	B-VAR
does	_	_	O
not	_	_	O
have	_	_	O
all	_	_	O
the	_	_	O
certifications	_	_	O
and	_	_	O
requires	_	_	O
an	_	_	O
architect	_	_	O
for	_	_	O
supervision	_	_	O
at	_	_	O
all	_	_	O
times	_	_	O
.	_	_	O
Therefore	_	_	O
,	_	_	O
there	_	_	O
must	_	_	B-CONST_DIR
be	_	_	I-CONST_DIR
more	_	_	I-CONST_DIR
architects	_	_	B-VAR
than	_	_	O
drafters	_	_	B-VAR
.	_	_	O
Additionally	_	_	O
,	_	_	O
a	_	_	O
drafter	_	_	B-VAR
averages	_	_	O
1200	_	_	B-PARAM
dollars	_	_	O
every	_	_	O
week	_	_	O
and	_	_	O
completes	_	_	O
1	_	_	B-PARAM
project	_	_	B-OBJ_NAME
every	_	_	O
week	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
architects	_	_	O
and	_	_	O
drafters	_	_	O
should	_	_	O
be	_	_	O
contracted	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
projects	_	_	I-OBJ_NAME
completed	_	_	I-OBJ_NAME
every	_	_	O
week	_	_	O
?	_	_	O

A	_	_	O
restaurant	_	_	O
chain	_	_	O
can	_	_	O
make	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
meals	_	_	O
,	_	_	O
a	_	_	O
steak	_	_	B-VAR
or	_	_	O
vegetarian	_	_	B-VAR
meal	_	_	I-VAR
.	_	_	O
The	_	_	O
steak	_	_	B-VAR
meal	_	_	I-VAR
makes	_	_	O
$	_	_	O
18	_	_	B-PARAM
profit	_	_	O
each	_	_	O
and	_	_	O
it	_	_	O
takes	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
for	_	_	O
a	_	_	O
chef	_	_	O
to	_	_	O
make	_	_	O
.	_	_	O
A	_	_	O
vegetarian	_	_	B-VAR
meal	_	_	I-VAR
makes	_	_	O
$	_	_	O
9	_	_	B-PARAM
profit	_	_	O
each	_	_	O
and	_	_	O
takes	_	_	O
2	_	_	B-PARAM
minutes	_	_	O
for	_	_	O
a	_	_	O
chef	_	_	O
make	_	_	O
.	_	_	O
The	_	_	O
restaurant	_	_	O
chain	_	_	O
needs	_	_	O
to	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
$	_	_	O
500	_	_	B-LIMIT
profit	_	_	O
every	_	_	O
day	_	_	O
and	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
1000	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
chef	_	_	O
involvement	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
meal	_	_	O
should	_	_	O
the	_	_	O
restaurant	_	_	O
try	_	_	O
to	_	_	O
push	_	_	O
through	_	_	O
the	_	_	O
waiting	_	_	O
staff	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
meals	_	_	I-OBJ_NAME
they	_	_	O
need	_	_	O
to	_	_	O
make	_	_	O
?	_	_	O

An	_	_	O
extremely	_	_	O
large	_	_	O
mall	_	_	O
needs	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
transportation	_	_	O
methods	_	_	O
for	_	_	O
customers	_	_	O
to	_	_	O
move	_	_	O
up	_	_	O
and	_	_	O
down	_	_	O
floors	_	_	O
.	_	_	O
They	_	_	O
can	_	_	O
either	_	_	O
purchase	_	_	O
an	_	_	O
escalator	_	_	B-VAR
or	_	_	O
an	_	_	O
elevator	_	_	B-VAR
.	_	_	O
Due	_	_	O
to	_	_	O
space	_	_	O
limitations	_	_	O
,	_	_	O
there	_	_	O
must	_	_	B-LIMIT
be	_	_	I-LIMIT
more	_	_	I-LIMIT
escalators	_	_	B-VAR
than	_	_	O
elevators	_	_	B-VAR
,	_	_	O
but	_	_	O
for	_	_	O
convenience	_	_	O
,	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
elevators	_	_	B-VAR
.	_	_	O
An	_	_	O
elevator	_	_	B-VAR
can	_	_	O
transport	_	_	O
1000	_	_	B-PARAM
customers	_	_	B-OBJ_NAME
every	_	_	O
day	_	_	O
and	_	_	O
uses	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
electricity	_	_	O
in	_	_	O
that	_	_	O
time	_	_	O
span	_	_	O
.	_	_	O
An	_	_	O
escalator	_	_	B-VAR
can	_	_	O
transport	_	_	O
2400	_	_	B-PARAM
customers	_	_	B-OBJ_NAME
every	_	_	O
day	_	_	O
and	_	_	O
uses	_	_	O
9	_	_	B-PARAM
units	_	_	O
of	_	_	O
electricity	_	_	O
in	_	_	O
that	_	_	O
time	_	_	O
span	_	_	O
.	_	_	O
The	_	_	O
mall	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
800	_	_	B-LIMIT
units	_	_	O
of	_	_	O
electricity	_	_	O
every	_	_	O
day	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
transportation	_	_	O
method	_	_	O
should	_	_	O
the	_	_	O
mall	_	_	O
install	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
customers	_	_	I-OBJ_NAME
they	_	_	O
can	_	_	O
transport	_	_	O
every	_	_	O
day	_	_	O
?	_	_	O

A	_	_	O
chemist	_	_	O
is	_	_	O
performing	_	_	O
novel	_	_	O
research	_	_	O
to	_	_	O
create	_	_	O
element	_	_	B-OBJ_NAME
A	_	_	I-OBJ_NAME
using	_	_	O
two	_	_	O
known	_	_	O
methods	_	_	O
:	_	_	O
the	_	_	O
gamma	_	_	B-VAR
experiment	_	_	I-VAR
and	_	_	O
the	_	_	O
omega	_	_	B-VAR
experiment	_	_	I-VAR
.	_	_	O
The	_	_	O
gamma	_	_	B-VAR
experiment	_	_	I-VAR
creates	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
element	_	_	B-OBJ_NAME
A	_	_	I-OBJ_NAME
and	_	_	O
uses	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
electricity	_	_	O
,	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
copper	_	_	O
,	_	_	O
and	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
.	_	_	O
The	_	_	O
omega	_	_	B-VAR
experiment	_	_	I-VAR
creates	_	_	O
16	_	_	B-PARAM
units	_	_	O
of	_	_	O
element	_	_	B-OBJ_NAME
A	_	_	I-OBJ_NAME
and	_	_	O
uses	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
electricity	_	_	O
,	_	_	O
9	_	_	B-PARAM
units	_	_	O
of	_	_	O
copper	_	_	O
,	_	_	O
and	_	_	O
1	_	_	B-PARAM
minutes	_	_	O
.	_	_	O
The	_	_	O
chemist	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
1000	_	_	B-LIMIT
minutes	_	_	O
,	_	_	O
4200	_	_	B-LIMIT
units	_	_	O
of	_	_	O
copper	_	_	O
,	_	_	O
and	_	_	O
1100	_	_	B-LIMIT
units	_	_	O
of	_	_	O
electricity	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
experiment	_	_	O
should	_	_	O
the	_	_	O
chemist	_	_	O
perform	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
amount	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
element	_	_	I-OBJ_NAME
A	_	_	I-OBJ_NAME
produced	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
furniture	_	_	O
store	_	_	O
builds	_	_	O
and	_	_	O
sells	_	_	O
sofas	_	_	B-VAR
and	_	_	O
beds	_	_	B-VAR
.	_	_	O
Each	_	_	O
sofa	_	_	B-VAR
costs	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
wood	_	_	O
and	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
time	_	_	O
while	_	_	O
each	_	_	O
bed	_	_	B-VAR
costs	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
wood	_	_	O
and	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
time	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
620	_	_	B-LIMIT
units	_	_	O
of	_	_	O
wood	_	_	O
and	_	_	O
1055	_	_	B-LIMIT
units	_	_	O
of	_	_	O
time	_	_	O
.	_	_	O
Each	_	_	O
bed	_	_	B-VAR
takes	_	_	O
an	_	_	O
additional	_	_	O
5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
shipping	_	_	B-OBJ_NAME
time	_	_	I-OBJ_NAME
while	_	_	O
each	_	_	O
sofa	_	_	B-VAR
takes	_	_	O
3	_	_	B-PARAM
hours	_	_	O
of	_	_	O
shipping	_	_	B-OBJ_NAME
time	_	_	I-OBJ_NAME
.	_	_	O
Since	_	_	O
there	_	_	O
are	_	_	O
usually	_	_	O
more	_	_	O
sofas	_	_	B-VAR
than	_	_	O
beds	_	_	B-VAR
,	_	_	O
the	_	_	O
store	_	_	O
aims	_	_	B-CONST_DIR
to	_	_	I-CONST_DIR
build	_	_	I-CONST_DIR
twice	_	_	B-PARAM
as	_	_	O
many	_	_	O
sofas	_	_	B-VAR
than	_	_	O
beds	_	_	B-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
store	_	_	O
make	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
shipping	_	_	I-OBJ_NAME
time	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
dental	_	_	O
firm	_	_	O
hires	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
employees	_	_	O
:	_	_	O
dentists	_	_	B-VAR
and	_	_	O
oral	_	_	B-VAR
hygienists	_	_	I-VAR
.	_	_	O
Dentists	_	_	B-VAR
work	_	_	O
12	_	_	B-PARAM
hours	_	_	O
every	_	_	O
shift	_	_	O
and	_	_	O
oral	_	_	B-VAR
hygienists	_	_	I-VAR
work	_	_	O
5	_	_	B-PARAM
hours	_	_	O
every	_	_	O
shift	_	_	O
.	_	_	O
Additionally	_	_	O
,	_	_	O
dentists	_	_	B-VAR
are	_	_	O
paid	_	_	O
$	_	_	O
900	_	_	B-PARAM
per	_	_	O
shift	_	_	O
while	_	_	O
oral	_	_	B-VAR
hygienists	_	_	I-VAR
are	_	_	O
paid	_	_	O
$	_	_	O
250	_	_	B-PARAM
per	_	_	O
shift	_	_	O
.	_	_	O
It	_	_	O
is	_	_	O
close	_	_	O
to	_	_	O
Halloween	_	_	O
and	_	_	O
the	_	_	O
dental	_	_	O
firm	_	_	O
expects	_	_	O
more	_	_	O
patients	_	_	O
coming	_	_	O
in	_	_	O
.	_	_	O
They	_	_	O
require	_	_	B-CONST_DIR
1000	_	_	B-PARAM
hours	_	_	O
of	_	_	O
labour	_	_	O
.	_	_	O
There	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
shifts	_	_	O
of	_	_	O
dentist	_	_	O
to	_	_	O
keep	_	_	O
the	_	_	O
office	_	_	O
running	_	_	O
.	_	_	O
If	_	_	O
there	_	_	O
is	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
65000	_	_	B-LIMIT
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
employee	_	_	O
should	_	_	O
the	_	_	O
firm	_	_	O
schedule	_	_	O
to	_	_	O
work	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
shifts	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
supermarket	_	_	O
can	_	_	O
purchase	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
refrigerators	_	_	O
to	_	_	O
properly	_	_	O
store	_	_	O
their	_	_	O
food	_	_	O
,	_	_	O
refrigerator	_	_	B-VAR
ABC	_	_	I-VAR
and	_	_	O
refrigerator	_	_	B-VAR
XYZ	_	_	I-VAR
,	_	_	O
and	_	_	O
they	_	_	O
have	_	_	O
different	_	_	O
specifications	_	_	O
to	_	_	O
consider	_	_	O
.	_	_	O
Refrigerator	_	_	B-VAR
ABC	_	_	I-VAR
is	_	_	O
larger	_	_	O
and	_	_	O
can	_	_	O
store	_	_	O
120	_	_	B-PARAM
items	_	_	O
but	_	_	O
uses	_	_	O
3	_	_	B-PARAM
kWh	_	_	O
.	_	_	O
Refrigerator	_	_	B-VAR
XYZ	_	_	I-VAR
is	_	_	O
smaller	_	_	O
more	_	_	O
efficient	_	_	O
and	_	_	O
can	_	_	O
store	_	_	O
80	_	_	B-PARAM
items	_	_	O
but	_	_	O
uses	_	_	O
1	_	_	B-PARAM
kWh	_	_	O
.	_	_	O
Due	_	_	O
to	_	_	O
soaring	_	_	O
electric	_	_	O
prices	_	_	O
,	_	_	O
the	_	_	O
store	_	_	O
is	_	_	O
limited	_	_	O
to	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
55	_	_	B-LIMIT
kWh	_	_	O
but	_	_	O
must	_	_	O
store	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1500	_	_	B-LIMIT
items	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
must	_	_	O
have	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
8	_	_	B-LIMIT
refrigerator	_	_	B-VAR
ABC	_	_	I-VAR
’s	_	_	O
and	_	_	O
5	_	_	B-LIMIT
refrigerator	_	_	B-VAR
XYZ	_	_	I-VAR
’s	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
refrigerator	_	_	O
should	_	_	O
the	_	_	O
supermarket	_	_	O
purchase	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
refrigerators	_	_	I-OBJ_NAME
needed	_	_	O
?	_	_	O

A	_	_	O
commercial	_	_	O
fishing	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
200	_	_	B-LIMIT
square	_	_	O
kilometers	_	_	O
of	_	_	O
water	_	_	O
that	_	_	O
they	_	_	O
can	_	_	O
fish	_	_	O
from	_	_	O
.	_	_	O
They	_	_	O
can	_	_	O
either	_	_	O
allocate	_	_	O
a	_	_	O
square	_	_	O
kilometer	_	_	O
for	_	_	O
fish	_	_	B-VAR
farming	_	_	I-VAR
or	_	_	O
trawling	_	_	B-VAR
.	_	_	O
For	_	_	O
each	_	_	O
square	_	_	O
kilometer	_	_	O
of	_	_	O
ocean	_	_	O
,	_	_	O
fish	_	_	B-VAR
farming	_	_	I-VAR
causes	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
pollution	_	_	O
and	_	_	O
nets	_	_	O
4	_	_	B-PARAM
tons	_	_	O
of	_	_	O
fish	_	_	B-OBJ_NAME
and	_	_	O
requires	_	_	O
6	_	_	B-PARAM
workers	_	_	O
every	_	_	O
day	_	_	O
.	_	_	O
For	_	_	O
each	_	_	O
square	_	_	O
kilometer	_	_	O
of	_	_	O
ocean	_	_	O
,	_	_	O
trawling	_	_	B-VAR
causes	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
pollution	_	_	O
,	_	_	O
nets	_	_	O
3	_	_	B-PARAM
tons	_	_	O
of	_	_	O
fish	_	_	B-OBJ_NAME
and	_	_	O
requires	_	_	O
2	_	_	B-PARAM
workers	_	_	O
every	_	_	O
day	_	_	O
.	_	_	O
Due	_	_	O
to	_	_	O
environmental	_	_	O
regulations	_	_	O
,	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
1700	_	_	B-LIMIT
units	_	_	O
of	_	_	O
pollution	_	_	O
and	_	_	O
the	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
500	_	_	B-LIMIT
workers	_	_	O
daily	_	_	O
.	_	_	O
Find	_	_	O
the	_	_	O
proportion	_	_	O
of	_	_	O
lands	_	_	O
that	_	_	O
use	_	_	O
each	_	_	O
fishing	_	_	O
technique	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
daily	_	_	B-OBJ_NAME
yield	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
fish	_	_	I-OBJ_NAME
.	_	_	O

A	_	_	O
woman	_	_	O
with	_	_	O
vitamin	_	_	O
deficiency	_	_	O
is	_	_	O
taking	_	_	O
supplements	_	_	O
from	_	_	O
two	_	_	O
brands	_	_	O
,	_	_	O
super	_	_	B-VAR
vitamin	_	_	I-VAR
XYZ	_	_	I-VAR
and	_	_	O
vitamin	_	_	B-VAR
ABC	_	_	I-VAR
.	_	_	O
Super	_	_	B-VAR
vitamin	_	_	I-VAR
XYZ	_	_	I-VAR
contains	_	_	O
2	_	_	B-PARAM
mg	_	_	O
of	_	_	O
vitamin	_	_	O
,	_	_	O
5	_	_	B-PARAM
mg	_	_	O
of	_	_	O
fiber	_	_	O
,	_	_	O
and	_	_	O
causes	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
drowsiness	_	_	B-OBJ_NAME
per	_	_	O
serving	_	_	O
.	_	_	O
Vitamin	_	_	B-VAR
ABC	_	_	I-VAR
contains	_	_	O
1.5	_	_	B-PARAM
mg	_	_	O
of	_	_	O
vitamin	_	_	O
,	_	_	O
3	_	_	B-PARAM
mg	_	_	O
of	_	_	O
fiber	_	_	O
,	_	_	O
and	_	_	O
causes	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
drowsiness	_	_	B-OBJ_NAME
per	_	_	O
serving	_	_	O
.	_	_	O
The	_	_	O
woman	_	_	O
wants	_	_	O
to	_	_	O
get	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
mg	_	_	O
of	_	_	O
vitamin	_	_	O
and	_	_	O
55	_	_	B-LIMIT
mg	_	_	O
of	_	_	O
fiber	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
40	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
supplements	_	_	O
taken	_	_	O
from	_	_	O
super	_	_	B-VAR
vitamin	_	_	I-VAR
XYZ	_	_	I-VAR
and	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-LIMIT
servings	_	_	O
of	_	_	O
super	_	_	B-VAR
vitamin	_	_	I-VAR
XYZ	_	_	I-VAR
because	_	_	O
it	_	_	O
is	_	_	O
expiring	_	_	O
soon	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
servings	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
she	_	_	O
take	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
her	_	_	O
total	_	_	B-OBJ_NAME
drowsiness	_	_	I-OBJ_NAME
.	_	_	O

A	_	_	O
physics	_	_	O
class	_	_	O
is	_	_	O
performing	_	_	O
a	_	_	O
volcano	_	_	O
experiment	_	_	O
using	_	_	O
two	_	_	O
mixtures	_	_	O
,	_	_	O
mixture	_	_	B-VAR
A	_	_	I-VAR
and	_	_	O
mixture	_	_	B-VAR
B.	_	_	I-VAR
Mixture	_	_	B-VAR
A	_	_	I-VAR
uses	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
baking	_	_	O
soda	_	_	O
,	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
vinegar	_	_	O
,	_	_	O
and	_	_	O
produces	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
eruption	_	_	B-OBJ_NAME
.	_	_	O
Mixture	_	_	B-VAR
B	_	_	I-VAR
uses	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
baking	_	_	O
soda	_	_	O
,	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
vinegar	_	_	O
,	_	_	O
and	_	_	O
produces	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
eruption	_	_	B-OBJ_NAME
.	_	_	O
However	_	_	O
,	_	_	O
mixture	_	_	B-VAR
A	_	_	I-VAR
generates	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
garbage	_	_	O
and	_	_	O
mixture	_	_	B-VAR
B	_	_	I-VAR
generates	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
garbage	_	_	O
.	_	_	O
The	_	_	O
physics	_	_	O
class	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
200	_	_	B-LIMIT
units	_	_	O
of	_	_	O
baking	_	_	O
soda	_	_	O
and	_	_	O
300	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vinegar	_	_	O
.	_	_	O
If	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
60	_	_	B-LIMIT
units	_	_	O
of	_	_	O
garbage	_	_	O
can	_	_	O
be	_	_	O
generated	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
mixture	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
eruption	_	_	I-OBJ_NAME
produced	_	_	O
?	_	_	O

An	_	_	O
athlete	_	_	O
drinks	_	_	O
protein	_	_	O
shakes	_	_	O
in	_	_	O
the	_	_	O
morning	_	_	O
before	_	_	O
a	_	_	O
workout	_	_	O
and	_	_	O
is	_	_	O
planning	_	_	O
for	_	_	O
the	_	_	O
coming	_	_	O
month	_	_	O
.	_	_	O
She	_	_	O
has	_	_	O
two	_	_	O
selections	_	_	O
of	_	_	O
protein	_	_	O
shakes	_	_	O
,	_	_	O
chocolate	_	_	B-VAR
powder	_	_	I-VAR
or	_	_	O
vanilla	_	_	B-VAR
powder	_	_	I-VAR
shakes	_	_	I-VAR
.	_	_	O
Each	_	_	O
scoop	_	_	O
of	_	_	O
chocolate	_	_	B-VAR
powder	_	_	I-VAR
protein	_	_	I-VAR
shake	_	_	I-VAR
contains	_	_	O
20	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	B-OBJ_NAME
and	_	_	O
4	_	_	B-PARAM
grams	_	_	O
of	_	_	O
sugar	_	_	O
.	_	_	O
Each	_	_	O
scoop	_	_	O
of	_	_	O
vanilla	_	_	B-VAR
powder	_	_	I-VAR
protein	_	_	I-VAR
shake	_	_	I-VAR
contains	_	_	O
18	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	B-OBJ_NAME
and	_	_	O
7	_	_	B-PARAM
grams	_	_	O
of	_	_	O
sugar	_	_	O
.	_	_	O
Since	_	_	O
she	_	_	O
prefers	_	_	O
the	_	_	O
vanilla	_	_	O
flavour	_	_	O
,	_	_	O
she	_	_	O
would	_	_	O
like	_	_	O
to	_	_	O
drink	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-PARAM
as	_	_	O
many	_	_	O
vanilla	_	_	B-VAR
powder	_	_	I-VAR
shakes	_	_	O
as	_	_	O
chocolate	_	_	B-VAR
powder	_	_	I-VAR
shakes	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
she	_	_	O
must	_	_	O
also	_	_	O
drink	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
2	_	_	B-LIMIT
scoops	_	_	O
of	_	_	O
the	_	_	O
chocolate	_	_	B-VAR
powder	_	_	I-VAR
shake	_	_	I-VAR
.	_	_	O
To	_	_	O
avoid	_	_	O
high	_	_	O
blood	_	_	O
glucose	_	_	O
levels	_	_	O
,	_	_	O
she	_	_	O
is	_	_	O
limiting	_	_	O
her	_	_	O
consumption	_	_	O
to	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
500	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
sugar	_	_	O
over	_	_	O
this	_	_	O
period	_	_	O
of	_	_	O
time	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
protein	_	_	O
shake	_	_	O
should	_	_	O
the	_	_	O
athlete	_	_	O
drink	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
her	_	_	O
total	_	_	B-OBJ_NAME
protein	_	_	I-OBJ_NAME
intake	_	_	O
over	_	_	O
this	_	_	O
period	_	_	O
of	_	_	O
time	_	_	O
?	_	_	O

A	_	_	O
water	_	_	O
purification	_	_	O
station	_	_	O
has	_	_	O
a	_	_	O
large	_	_	B-VAR
plant	_	_	I-VAR
and	_	_	O
a	_	_	O
small	_	_	B-VAR
plant	_	_	I-VAR
.	_	_	O
The	_	_	O
large	_	_	B-VAR
plant	_	_	I-VAR
purifies	_	_	O
30	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	O
per	_	_	O
hour	_	_	B-OBJ_NAME
and	_	_	O
produces	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
by	_	_	O
-	_	_	O
product	_	_	O
per	_	_	O
hour	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
small	_	_	B-VAR
plant	_	_	I-VAR
purifies	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	O
per	_	_	O
hour	_	_	B-OBJ_NAME
and	_	_	O
produces	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
by	_	_	O
-	_	_	O
product	_	_	O
per	_	_	O
hour	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
large	_	_	B-VAR
plant	_	_	I-VAR
requires	_	_	O
15	_	_	B-PARAM
filters	_	_	O
while	_	_	O
the	_	_	O
small	_	_	B-VAR
plant	_	_	I-VAR
requires	_	_	O
12	_	_	B-PARAM
filters	_	_	O
per	_	_	O
hour	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
water	_	_	O
purification	_	_	O
station	_	_	O
only	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
1200	_	_	B-LIMIT
filters	_	_	O
right	_	_	O
now	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
station	_	_	O
must	_	_	O
purify	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1200	_	_	B-LIMIT
units	_	_	O
of	_	_	O
water	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
by	_	_	O
-	_	_	O
product	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
hours	_	_	B-OBJ_NAME
should	_	_	O
each	_	_	O
plant	_	_	O
be	_	_	O
run	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
time	_	_	B-OBJ_NAME
needed	_	_	O
?	_	_	O

A	_	_	O
dietician	_	_	O
recommends	_	_	O
his	_	_	O
patient	_	_	O
drink	_	_	O
more	_	_	O
juice	_	_	B-VAR
and	_	_	O
vitamin	_	_	B-VAR
-	_	_	I-VAR
added	_	_	I-VAR
milk	_	_	I-VAR
to	_	_	O
increase	_	_	O
her	_	_	O
vitamin	_	_	O
and	_	_	O
hydration	_	_	O
intake	_	_	O
.	_	_	O
Each	_	_	O
cup	_	_	O
of	_	_	O
juice	_	_	B-VAR
contains	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamins	_	_	O
and	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
hydration	_	_	O
.	_	_	O
Each	_	_	O
vitamin	_	_	B-VAR
-	_	_	I-VAR
added	_	_	I-VAR
milk	_	_	I-VAR
contains	_	_	O
14	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamins	_	_	O
and	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
hydration	_	_	O
.	_	_	O
The	_	_	O
patient	_	_	O
needs	_	_	O
to	_	_	O
consume	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
180	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamins	_	_	O
and	_	_	O
140	_	_	B-LIMIT
units	_	_	O
of	_	_	O
hydration	_	_	O
.	_	_	O
Since	_	_	O
the	_	_	O
patient	_	_	O
is	_	_	O
slightly	_	_	O
lactose	_	_	O
-	_	_	O
intolerant	_	_	O
,	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
10	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
all	_	_	O
cups	_	_	O
of	_	_	O
drinks	_	_	O
be	_	_	O
vitamin	_	_	B-VAR
-	_	_	I-VAR
added	_	_	I-VAR
milk	_	_	I-VAR
.	_	_	O
If	_	_	O
each	_	_	O
cup	_	_	O
of	_	_	O
vitamin	_	_	B-VAR
-	_	_	I-VAR
added	_	_	I-VAR
milk	_	_	I-VAR
contains	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
sugar	_	_	B-OBJ_NAME
and	_	_	O
each	_	_	O
cup	_	_	O
of	_	_	O
juice	_	_	B-VAR
contains	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
sugar	_	_	B-OBJ_NAME
,	_	_	O
how	_	_	O
many	_	_	O
cups	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
she	_	_	O
drink	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
her	_	_	O
sugar	_	_	B-OBJ_NAME
intake	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
TCM	_	_	O
company	_	_	O
makes	_	_	O
powdered	_	_	O
medicine	_	_	O
in	_	_	O
two	_	_	O
different	_	_	O
packages	_	_	O
,	_	_	O
a	_	_	O
regular	_	_	B-VAR
package	_	_	I-VAR
and	_	_	O
premium	_	_	B-VAR
package	_	_	I-VAR
,	_	_	O
to	_	_	O
sell	_	_	O
to	_	_	O
TCM	_	_	O
doctors	_	_	O
.	_	_	O
The	_	_	O
regular	_	_	B-VAR
package	_	_	I-VAR
requires	_	_	O
100	_	_	B-PARAM
g	_	_	O
of	_	_	O
medicinal	_	_	O
herbs	_	_	O
and	_	_	O
30	_	_	B-PARAM
seconds	_	_	O
of	_	_	O
drying	_	_	O
.	_	_	O
A	_	_	O
premium	_	_	B-VAR
package	_	_	I-VAR
requires	_	_	O
130	_	_	B-PARAM
units	_	_	O
of	_	_	O
medicinal	_	_	O
herbs	_	_	O
and	_	_	O
60	_	_	B-PARAM
seconds	_	_	O
of	_	_	O
drying	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
9000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
medicinal	_	_	O
herbs	_	_	O
and	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
3500	_	_	B-LIMIT
seconds	_	_	O
in	_	_	O
the	_	_	O
drying	_	_	O
machine	_	_	O
.	_	_	O
Since	_	_	O
the	_	_	O
premium	_	_	B-VAR
package	_	_	I-VAR
sells	_	_	O
better	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
regular	_	_	B-VAR
packages	_	_	I-VAR
must	_	_	O
be	_	_	O
less	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
premium	_	_	B-VAR
packages	_	_	I-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
the	_	_	O
company	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
15	_	_	B-LIMIT
regular	_	_	B-VAR
packages	_	_	I-VAR
.	_	_	O
If	_	_	O
a	_	_	O
regular	_	_	B-VAR
package	_	_	I-VAR
can	_	_	O
treat	_	_	O
2	_	_	B-PARAM
people	_	_	B-OBJ_NAME
and	_	_	O
a	_	_	O
premium	_	_	B-VAR
batch	_	_	I-VAR
can	_	_	O
treat	_	_	O
3	_	_	B-PARAM
people	_	_	B-OBJ_NAME
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
package	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
people	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
treated	_	_	O
?	_	_	O

A	_	_	O
hospital	_	_	O
gives	_	_	O
pupil	_	_	O
dilation	_	_	O
drops	_	_	O
using	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
dilation	_	_	O
drops	_	_	O
,	_	_	O
fast	_	_	B-VAR
-	_	_	I-VAR
acting	_	_	I-VAR
eye	_	_	I-VAR
drops	_	_	I-VAR
and	_	_	O
slow	_	_	B-VAR
-	_	_	I-VAR
acting	_	_	I-VAR
eye	_	_	I-VAR
drops	_	_	I-VAR
.	_	_	O
The	_	_	O
fast	_	_	B-VAR
-	_	_	I-VAR
acting	_	_	I-VAR
eye	_	_	I-VAR
drops	_	_	I-VAR
take	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
per	_	_	O
patient	_	_	B-OBJ_NAME
to	_	_	O
adjust	_	_	O
the	_	_	O
patient	_	_	O
’s	_	_	O
pupils	_	_	O
while	_	_	O
the	_	_	O
slow	_	_	B-VAR
-	_	_	I-VAR
acting	_	_	I-VAR
eye	_	_	I-VAR
drops	_	_	I-VAR
take	_	_	O
25	_	_	B-PARAM
minutes	_	_	O
per	_	_	O
patient	_	_	B-OBJ_NAME
.	_	_	O
Since	_	_	O
the	_	_	O
fast	_	_	B-VAR
-	_	_	I-VAR
acting	_	_	I-VAR
eye	_	_	I-VAR
drops	_	_	I-VAR
are	_	_	O
more	_	_	O
expensive	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-PARAM
as	_	_	O
many	_	_	O
patients	_	_	B-OBJ_NAME
must	_	_	O
be	_	_	O
dilated	_	_	O
using	_	_	O
the	_	_	O
slow	_	_	B-VAR
-	_	_	I-VAR
acting	_	_	I-VAR
eye	_	_	I-VAR
drops	_	_	I-VAR
than	_	_	O
the	_	_	O
fast	_	_	B-VAR
-	_	_	I-VAR
acting	_	_	I-VAR
eye	_	_	I-VAR
drops	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
25	_	_	B-LIMIT
patients	_	_	B-OBJ_NAME
must	_	_	O
be	_	_	O
dilated	_	_	O
with	_	_	O
the	_	_	O
fast	_	_	B-VAR
-	_	_	I-VAR
acting	_	_	I-VAR
eye	_	_	I-VAR
drops	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
clinic	_	_	O
is	_	_	O
open	_	_	B-CONST_DIR
for	_	_	I-CONST_DIR
15000	_	_	B-LIMIT
minutes	_	_	O
,	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
patients	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
dilated	_	_	O
.	_	_	O

A	_	_	O
patient	_	_	O
lacking	_	_	O
sleep	_	_	O
can	_	_	O
take	_	_	O
two	_	_	O
drowsiness	_	_	O
medications	_	_	O
,	_	_	O
sleeping	_	_	B-VAR
pills	_	_	I-VAR
,	_	_	O
and	_	_	O
sleep	_	_	B-VAR
supplement	_	_	I-VAR
.	_	_	O
Per	_	_	O
serving	_	_	O
,	_	_	O
sleeping	_	_	B-VAR
pills	_	_	I-VAR
increase	_	_	O
sleepiness	_	_	O
by	_	_	O
2	_	_	B-PARAM
units	_	_	O
and	_	_	O
introduces	_	_	O
0.6	_	_	B-PARAM
units	_	_	O
of	_	_	O
discomfort	_	_	O
.	_	_	O
Per	_	_	O
serving	_	_	O
,	_	_	O
sleep	_	_	B-VAR
supplement	_	_	I-VAR
increases	_	_	O
sleepiness	_	_	O
by	_	_	O
3.5	_	_	B-PARAM
units	_	_	O
and	_	_	O
introduces	_	_	O
0.3	_	_	B-PARAM
units	_	_	O
of	_	_	O
discomfort	_	_	O
.	_	_	O
Furthermore	_	_	O
,	_	_	O
pills	_	_	B-VAR
contain	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
sugar	_	_	B-OBJ_NAME
while	_	_	O
sleep	_	_	B-VAR
supplement	_	_	I-VAR
contains	_	_	O
2.5	_	_	B-PARAM
units	_	_	O
of	_	_	O
sugar	_	_	B-OBJ_NAME
per	_	_	O
serving	_	_	O
.	_	_	O
The	_	_	O
patient	_	_	O
needs	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
units	_	_	O
of	_	_	O
sleepiness	_	_	O
and	_	_	O
can	_	_	O
take	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
2.5	_	_	B-LIMIT
units	_	_	O
of	_	_	O
discomfort	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
servings	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
patient	_	_	O
take	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
sugar	_	_	B-OBJ_NAME
intake	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
nutritionist	_	_	O
recommends	_	_	O
that	_	_	O
a	_	_	O
child	_	_	O
eat	_	_	O
fruits	_	_	B-VAR
and	_	_	O
drink	_	_	O
juice	_	_	B-VAR
to	_	_	O
tackle	_	_	O
a	_	_	O
certain	_	_	O
disease	_	_	O
.	_	_	O
Each	_	_	O
serving	_	_	O
of	_	_	O
fruit	_	_	B-VAR
contains	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
the	_	_	O
necessary	_	_	O
mineral	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
hydration	_	_	O
.	_	_	O
Each	_	_	O
serving	_	_	O
of	_	_	O
juice	_	_	B-VAR
contains	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
the	_	_	O
necessary	_	_	O
mineral	_	_	O
and	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
hydration	_	_	O
.	_	_	O
According	_	_	O
to	_	_	O
the	_	_	O
nutritionist	_	_	O
,	_	_	O
the	_	_	O
child	_	_	O
must	_	_	O
intake	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
60	_	_	B-LIMIT
units	_	_	O
of	_	_	O
the	_	_	O
necessary	_	_	O
mineral	_	_	O
every	_	_	O
week	_	_	O
and	_	_	O
40	_	_	B-LIMIT
units	_	_	O
of	_	_	O
hydration	_	_	O
for	_	_	O
their	_	_	O
body	_	_	O
to	_	_	O
better	_	_	O
absorb	_	_	O
the	_	_	O
mineral	_	_	O
into	_	_	O
their	_	_	O
body	_	_	O
.	_	_	O
Further	_	_	O
,	_	_	O
each	_	_	O
serving	_	_	O
of	_	_	O
fruit	_	_	B-VAR
contains	_	_	O
9	_	_	B-PARAM
units	_	_	O
of	_	_	O
sugar	_	_	B-OBJ_NAME
and	_	_	O
each	_	_	O
serving	_	_	O
of	_	_	O
juice	_	_	B-VAR
contains	_	_	O
14	_	_	B-PARAM
units	_	_	O
of	_	_	O
sugar	_	_	B-OBJ_NAME
.	_	_	O
Since	_	_	O
juice	_	_	B-VAR
is	_	_	O
more	_	_	O
convenient	_	_	O
,	_	_	O
the	_	_	O
child	_	_	O
wants	_	_	O
to	_	_	O
take	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-LIMIT
as	_	_	O
many	_	_	O
servings	_	_	O
of	_	_	O
juice	_	_	B-VAR
as	_	_	O
fruits	_	_	B-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
child	_	_	O
be	_	_	O
served	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
sugar	_	_	I-OBJ_NAME
intake	_	_	I-OBJ_NAME
?	_	_	O

An	_	_	O
MOA	_	_	O
checks	_	_	O
a	_	_	O
patient	_	_	O
’s	_	_	O
eye	_	_	O
pressure	_	_	O
one	_	_	O
-	_	_	O
by	_	_	O
-	_	_	O
one	_	_	O
either	_	_	O
by	_	_	O
using	_	_	O
a	_	_	O
tonometer	_	_	B-VAR
or	_	_	O
a	_	_	O
“	_	_	B-VAR
puff	_	_	I-VAR
of	_	_	I-VAR
air	_	_	I-VAR
”	_	_	I-VAR
test	_	_	I-VAR
.	_	_	O
The	_	_	O
tonometer	_	_	B-VAR
test	_	_	I-VAR
takes	_	_	O
0.05	_	_	B-PARAM
hours	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
reading	_	_	O
while	_	_	O
the	_	_	O
”	_	_	B-VAR
puff	_	_	I-VAR
of	_	_	I-VAR
air	_	_	I-VAR
”	_	_	I-VAR
test	_	_	I-VAR
takes	_	_	O
0.02	_	_	B-PARAM
hours	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
reading	_	_	O
.	_	_	O
Since	_	_	O
the	_	_	O
tonometer	_	_	B-VAR
is	_	_	O
more	_	_	O
standard	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
tonometer	_	_	B-VAR
tests	_	_	I-VAR
must	_	_	O
be	_	_	O
larger	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
“	_	_	B-VAR
puff	_	_	I-VAR
of	_	_	I-VAR
air	_	_	I-VAR
”	_	_	I-VAR
tests	_	_	I-VAR
.	_	_	O
Since	_	_	O
a	_	_	O
lot	_	_	O
of	_	_	O
these	_	_	O
patients	_	_	B-OBJ_NAME
are	_	_	O
low	_	_	O
risk	_	_	O
here	_	_	O
for	_	_	O
a	_	_	O
check	_	_	O
-	_	_	O
up	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
patients	_	_	B-OBJ_NAME
should	_	_	O
have	_	_	O
their	_	_	O
eye	_	_	O
pressure	_	_	O
checked	_	_	O
using	_	_	O
the	_	_	O
“	_	_	B-VAR
puff	_	_	I-VAR
of	_	_	I-VAR
air	_	_	I-VAR
”	_	_	I-VAR
test	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
office	_	_	O
is	_	_	O
open	_	_	B-CONST_DIR
for	_	_	I-CONST_DIR
8	_	_	B-LIMIT
hours	_	_	O
,	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
patients	_	_	I-OBJ_NAME
whose	_	_	O
temperature	_	_	O
can	_	_	O
be	_	_	O
taken	_	_	O
?	_	_	O

A	_	_	O
sample	_	_	O
can	_	_	O
be	_	_	O
analyzed	_	_	O
by	_	_	O
two	_	_	O
machines	_	_	O
for	_	_	O
their	_	_	O
chemical	_	_	O
make	_	_	O
-	_	_	O
up	_	_	O
,	_	_	O
Analyzer	_	_	B-VAR
3000	_	_	I-VAR
and	_	_	O
QuickAnalytics	_	_	B-VAR
.	_	_	I-VAR
Analyzer	_	_	B-VAR
3000	_	_	I-VAR
analyzes	_	_	O
20	_	_	B-PARAM
samples	_	_	O
of	_	_	O
water	_	_	O
and	_	_	O
30	_	_	B-PARAM
samples	_	_	O
of	_	_	O
dirt	_	_	O
per	_	_	O
hour	_	_	O
.	_	_	O
QuickAnalytics	_	_	B-VAR
examines	_	_	O
40	_	_	B-PARAM
samples	_	_	O
of	_	_	O
water	_	_	O
and	_	_	O
10	_	_	B-PARAM
samples	_	_	O
of	_	_	O
dirt	_	_	O
per	_	_	O
hour	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
Analyzer	_	_	B-VAR
3000	_	_	I-VAR
creates	_	_	O
3.5	_	_	B-PARAM
units	_	_	O
of	_	_	O
heat	_	_	B-OBJ_NAME
per	_	_	O
hour	_	_	O
while	_	_	O
QuickAnalytics	_	_	B-VAR
creates	_	_	O
4.5	_	_	B-PARAM
units	_	_	O
of	_	_	O
heat	_	_	B-OBJ_NAME
per	_	_	O
hour	_	_	O
.	_	_	O
If	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1000	_	_	B-LIMIT
samples	_	_	O
of	_	_	O
water	_	_	O
and	_	_	O
800	_	_	B-LIMIT
samples	_	_	O
of	_	_	O
dirt	_	_	O
must	_	_	O
be	_	_	O
analyzed	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
hours	_	_	O
should	_	_	O
each	_	_	O
machine	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
amount	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
heat	_	_	I-OBJ_NAME
produced	_	_	O
?	_	_	O

An	_	_	O
engineering	_	_	O
kids	_	_	O
kit	_	_	O
has	_	_	O
two	_	_	O
sets	_	_	O
,	_	_	O
a	_	_	O
mechanical	_	_	B-VAR
and	_	_	O
chemistry	_	_	B-VAR
kit	_	_	I-VAR
.	_	_	O
The	_	_	O
mechanical	_	_	B-VAR
kit	_	_	I-VAR
requires	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
plastic	_	_	O
,	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
materials	_	_	O
and	_	_	O
entertains	_	_	O
a	_	_	O
kid	_	_	O
for	_	_	O
4	_	_	B-PARAM
hours	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
chemistry	_	_	B-VAR
kit	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
plastic	_	_	O
,	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
materials	_	_	O
and	_	_	O
entertains	_	_	O
a	_	_	O
kid	_	_	O
for	_	_	O
2	_	_	B-PARAM
hours	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
chemistry	_	_	B-VAR
kit	_	_	I-VAR
however	_	_	O
produces	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
waste	_	_	O
while	_	_	O
the	_	_	O
mechanical	_	_	B-VAR
kit	_	_	I-VAR
produces	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
waste	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
plastic	_	_	O
and	_	_	O
450	_	_	B-LIMIT
units	_	_	O
of	_	_	O
materials	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
company	_	_	O
has	_	_	O
committed	_	_	O
to	_	_	O
producing	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
300	_	_	B-LIMIT
units	_	_	O
of	_	_	O
waste	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
kit	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	O
of	_	_	O
hours	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
entertainment	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
pharmaceutical	_	_	O
manufacturing	_	_	O
plant	_	_	O
has	_	_	B-CONST_DIR
1000	_	_	B-LIMIT
mg	_	_	O
of	_	_	O
cornstarch	_	_	O
to	_	_	O
rush	_	_	O
orders	_	_	O
of	_	_	O
diabetic	_	_	B-VAR
pills	_	_	I-VAR
and	_	_	O
latex	_	_	B-VAR
gloves	_	_	I-VAR
.	_	_	O
Each	_	_	O
diabetic	_	_	B-VAR
pill	_	_	I-VAR
requires	_	_	O
4	_	_	B-PARAM
mg	_	_	O
of	_	_	O
cornstarch	_	_	O
and	_	_	O
0.2	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
to	_	_	O
manufacture	_	_	O
.	_	_	O
Each	_	_	O
individual	_	_	O
latex	_	_	B-VAR
glove	_	_	I-VAR
requires	_	_	O
7	_	_	B-PARAM
mg	_	_	O
of	_	_	O
cornstarch	_	_	O
and	_	_	O
0.15	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
to	_	_	O
manufacture	_	_	O
.	_	_	O
The	_	_	O
pharmaceutical	_	_	O
manufacturing	_	_	O
plant	_	_	O
needs	_	_	O
to	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
diabetic	_	_	B-VAR
pills	_	_	I-VAR
.	_	_	O
Since	_	_	O
latex	_	_	B-VAR
gloves	_	_	I-VAR
are	_	_	O
important	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
60	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
produced	_	_	O
items	_	_	O
must	_	_	O
be	_	_	O
latex	_	_	B-VAR
gloves	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
pharmaceutical	_	_	O
manufacturing	_	_	O
plant	_	_	O
make	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
minutes	_	_	I-OBJ_NAME
needed	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
chemical	_	_	O
company	_	_	O
makes	_	_	O
an	_	_	O
acidic	_	_	O
liquid	_	_	O
and	_	_	O
a	_	_	O
basic	_	_	O
liquid	_	_	O
using	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
techniques	_	_	O
,	_	_	O
reaction	_	_	B-VAR
X	_	_	I-VAR
and	_	_	O
reaction	_	_	B-VAR
Y.	_	_	I-VAR
Reaction	_	_	B-VAR
X	_	_	I-VAR
can	_	_	O
make	_	_	O
35	_	_	B-PARAM
au	_	_	O
of	_	_	O
the	_	_	O
acidic	_	_	O
liquid	_	_	O
and	_	_	O
75	_	_	B-PARAM
au	_	_	O
of	_	_	O
the	_	_	O
basic	_	_	O
liquid	_	_	O
per	_	_	O
minute	_	_	B-OBJ_NAME
.	_	_	O
Reaction	_	_	B-VAR
Y	_	_	I-VAR
can	_	_	O
make	_	_	O
42	_	_	B-PARAM
au	_	_	O
of	_	_	O
the	_	_	O
acidic	_	_	O
liquid	_	_	O
and	_	_	O
35	_	_	B-PARAM
au	_	_	O
of	_	_	O
the	_	_	O
basic	_	_	O
liquid	_	_	O
per	_	_	O
minute	_	_	B-OBJ_NAME
.	_	_	O
Furthermore	_	_	O
,	_	_	O
reaction	_	_	B-VAR
X	_	_	I-VAR
requires	_	_	O
18	_	_	B-PARAM
units	_	_	O
of	_	_	O
heat	_	_	O
every	_	_	O
minute	_	_	B-OBJ_NAME
while	_	_	O
reaction	_	_	B-VAR
Y	_	_	I-VAR
requires	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
heat	_	_	O
every	_	_	O
minute	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
chemical	_	_	O
company	_	_	O
has	_	_	O
the	_	_	O
capacity	_	_	O
to	_	_	O
generate	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
1400	_	_	B-LIMIT
units	_	_	O
of	_	_	O
heat	_	_	O
every	_	_	O
minute	_	_	B-OBJ_NAME
.	_	_	O
If	_	_	O
the	_	_	O
chemical	_	_	O
company	_	_	O
needs	_	_	O
to	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
900	_	_	B-LIMIT
au	_	_	O
of	_	_	O
the	_	_	O
acidic	_	_	O
liquid	_	_	O
and	_	_	O
1200	_	_	B-LIMIT
au	_	_	O
of	_	_	O
the	_	_	O
basic	_	_	O
liquid	_	_	O
per	_	_	O
minute	_	_	B-OBJ_NAME
,	_	_	O
how	_	_	O
many	_	_	O
minutes	_	_	B-OBJ_NAME
should	_	_	O
each	_	_	O
reaction	_	_	O
be	_	_	O
run	_	_	O
for	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
time	_	_	I-OBJ_NAME
needed	_	_	O
?	_	_	O

A	_	_	O
government	_	_	O
sanitization	_	_	O
plant	_	_	O
processes	_	_	O
liquid	_	_	B-VAR
waste	_	_	I-VAR
and	_	_	O
solid	_	_	B-VAR
waste	_	_	I-VAR
in	_	_	O
batches	_	_	O
.	_	_	O
Liquid	_	_	B-VAR
waste	_	_	I-VAR
requires	_	_	O
30	_	_	B-PARAM
units	_	_	O
of	_	_	O
disinfectant	_	_	O
and	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
bacteria	_	_	O
.	_	_	O
Solid	_	_	B-VAR
waste	_	_	I-VAR
requires	_	_	O
25	_	_	B-PARAM
units	_	_	O
of	_	_	O
disinfectant	_	_	O
and	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
bacteria	_	_	O
.	_	_	O
The	_	_	O
sanitization	_	_	O
plant	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
1500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
disinfectant	_	_	O
and	_	_	O
1000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
bacteria	_	_	O
.	_	_	O
The	_	_	O
batches	_	_	O
of	_	_	O
liquid	_	_	B-VAR
waste	_	_	I-VAR
processed	_	_	O
must	_	_	B-CONST_DIR
be	_	_	I-CONST_DIR
twice	_	_	B-PARAM
the	_	_	O
number	_	_	O
of	_	_	O
solid	_	_	B-VAR
waste	_	_	I-VAR
processed	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
10	_	_	B-LIMIT
batches	_	_	O
of	_	_	O
solid	_	_	B-VAR
waste	_	_	I-VAR
can	_	_	O
be	_	_	O
processed	_	_	O
due	_	_	O
to	_	_	O
storage	_	_	O
limitations	_	_	O
.	_	_	O
If	_	_	O
each	_	_	O
liquid	_	_	B-VAR
waste	_	_	I-VAR
batch	_	_	O
is	_	_	O
the	_	_	O
result	_	_	O
of	_	_	O
10	_	_	B-PARAM
people	_	_	B-OBJ_NAME
and	_	_	O
each	_	_	O
solid	_	_	B-VAR
waste	_	_	I-VAR
batch	_	_	O
is	_	_	O
the	_	_	O
result	_	_	O
of	_	_	O
3	_	_	B-PARAM
people	_	_	B-OBJ_NAME
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
plant	_	_	O
process	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
people	_	_	I-OBJ_NAME
served	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
doctor	_	_	O
can	_	_	O
prescribe	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
medication	_	_	O
for	_	_	O
high	_	_	O
glucose	_	_	O
levels	_	_	O
,	_	_	O
a	_	_	O
diabetic	_	_	B-VAR
pill	_	_	I-VAR
and	_	_	O
a	_	_	O
diabetic	_	_	B-VAR
shot	_	_	I-VAR
.	_	_	O
Per	_	_	O
dose	_	_	O
,	_	_	O
diabetic	_	_	B-VAR
pill	_	_	I-VAR
delivers	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
glucose	_	_	O
reducing	_	_	O
medicine	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
blood	_	_	B-OBJ_NAME
pressure	_	_	I-OBJ_NAME
reducing	_	_	I-OBJ_NAME
medicine	_	_	I-OBJ_NAME
.	_	_	O
Per	_	_	O
dose	_	_	O
,	_	_	O
a	_	_	O
diabetic	_	_	B-VAR
shot	_	_	I-VAR
delivers	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
glucose	_	_	O
reducing	_	_	O
medicine	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
blood	_	_	B-OBJ_NAME
pressure	_	_	I-OBJ_NAME
reducing	_	_	I-OBJ_NAME
medicine	_	_	I-OBJ_NAME
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
diabetic	_	_	B-VAR
pills	_	_	I-VAR
provide	_	_	O
0.4	_	_	B-PARAM
units	_	_	O
of	_	_	O
stress	_	_	O
and	_	_	O
the	_	_	O
diabetic	_	_	B-VAR
shot	_	_	I-VAR
provides	_	_	O
0.9	_	_	B-PARAM
units	_	_	O
of	_	_	O
stress	_	_	O
.	_	_	O
At	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
20	_	_	B-LIMIT
units	_	_	O
of	_	_	O
stress	_	_	O
can	_	_	O
be	_	_	O
applied	_	_	O
over	_	_	O
a	_	_	O
week	_	_	O
and	_	_	O
the	_	_	O
doctor	_	_	O
must	_	_	O
deliver	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
units	_	_	O
of	_	_	O
glucose	_	_	O
reducing	_	_	O
medicine	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
doses	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
delivered	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
blood	_	_	I-OBJ_NAME
pressure	_	_	I-OBJ_NAME
reducing	_	_	I-OBJ_NAME
medicine	_	_	I-OBJ_NAME
delivaered	_	_	O
to	_	_	O
the	_	_	O
patient	_	_	O
?	_	_	O

A	_	_	O
lotion	_	_	O
company	_	_	O
has	_	_	B-CONST_DIR
1000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
emulsifiers	_	_	O
that	_	_	O
are	_	_	O
used	_	_	O
to	_	_	O
make	_	_	O
strong	_	_	B-VAR
topical	_	_	I-VAR
anesthetics	_	_	I-VAR
and	_	_	O
weak	_	_	B-VAR
topical	_	_	I-VAR
anesthetics	_	_	I-VAR
.	_	_	O
Each	_	_	O
container	_	_	O
of	_	_	O
strong	_	_	B-VAR
topical	_	_	I-VAR
anesthetics	_	_	I-VAR
takes	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
emulsifiers	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
salicylates	_	_	B-OBJ_NAME
.	_	_	O
A	_	_	O
container	_	_	O
of	_	_	O
weak	_	_	B-VAR
topical	_	_	I-VAR
anesthetics	_	_	I-VAR
requires	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
emulsifiers	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
salicylates	_	_	B-OBJ_NAME
.	_	_	O
Since	_	_	O
many	_	_	O
customers	_	_	O
are	_	_	O
purchasing	_	_	O
for	_	_	O
daily	_	_	O
applications	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
60	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
containers	_	_	O
made	_	_	O
must	_	_	O
be	_	_	O
weak	_	_	B-VAR
topical	_	_	I-VAR
anesthetics	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
300	_	_	B-LIMIT
containers	_	_	O
of	_	_	O
the	_	_	O
strong	_	_	B-VAR
topical	_	_	I-VAR
anesthetics	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
container	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
salicylates	_	_	I-OBJ_NAME
required	_	_	O
?	_	_	O

A	_	_	O
competitive	_	_	O
swimmer	_	_	O
is	_	_	O
training	_	_	O
heavily	_	_	O
and	_	_	O
to	_	_	O
do	_	_	O
so	_	_	O
,	_	_	O
plans	_	_	O
to	_	_	O
eat	_	_	O
steaks	_	_	B-VAR
and	_	_	O
chicken	_	_	B-VAR
breasts	_	_	I-VAR
over	_	_	O
the	_	_	O
coming	_	_	O
week	_	_	O
.	_	_	O
Each	_	_	O
steak	_	_	B-VAR
contains	_	_	O
900	_	_	B-PARAM
calories	_	_	B-OBJ_NAME
and	_	_	O
40	_	_	B-PARAM
g	_	_	O
of	_	_	O
protein	_	_	O
.	_	_	O
Each	_	_	O
chicken	_	_	B-VAR
breast	_	_	I-VAR
contains	_	_	O
700	_	_	B-PARAM
calories	_	_	B-OBJ_NAME
and	_	_	O
20	_	_	B-PARAM
g	_	_	O
of	_	_	O
protein	_	_	O
.	_	_	O
He	_	_	O
prefers	_	_	O
to	_	_	O
eat	_	_	O
chicken	_	_	B-VAR
breasts	_	_	I-VAR
and	_	_	O
decides	_	_	O
to	_	_	O
eat	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
2	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
many	_	_	O
chicken	_	_	B-VAR
breasts	_	_	I-VAR
as	_	_	O
steaks	_	_	B-VAR
over	_	_	O
the	_	_	O
coming	_	_	O
week	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
he	_	_	O
must	_	_	O
also	_	_	O
eat	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
steaks	_	_	B-VAR
over	_	_	O
the	_	_	O
week	_	_	O
.	_	_	O
If	_	_	O
he	_	_	O
must	_	_	O
consume	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1200	_	_	B-LIMIT
g	_	_	O
of	_	_	O
protein	_	_	O
over	_	_	O
this	_	_	O
coming	_	_	O
week	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
steaks	_	_	B-VAR
and	_	_	O
chicken	_	_	B-VAR
breasts	_	_	I-VAR
should	_	_	O
he	_	_	O
eat	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
calories	_	_	I-OBJ_NAME
he	_	_	O
is	_	_	O
eating	_	_	O
?	_	_	O

A	_	_	O
nurse	_	_	O
suggests	_	_	O
that	_	_	O
his	_	_	O
patient	_	_	O
drink	_	_	O
more	_	_	O
protein	_	_	B-VAR
shakes	_	_	I-VAR
and	_	_	O
milk	_	_	B-VAR
to	_	_	O
meet	_	_	O
their	_	_	O
calcium	_	_	O
and	_	_	O
protein	_	_	O
requirements	_	_	O
.	_	_	O
One	_	_	O
glass	_	_	O
of	_	_	O
protein	_	_	B-VAR
shake	_	_	I-VAR
contains	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
calcium	_	_	O
,	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
and	_	_	O
3	_	_	B-PARAM
grams	_	_	O
of	_	_	O
sugar	_	_	B-OBJ_NAME
.	_	_	O
One	_	_	O
glass	_	_	O
of	_	_	O
milk	_	_	B-VAR
contains	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
calcium	_	_	O
,	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
and	_	_	O
5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
sugar	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
patient	_	_	O
must	_	_	O
get	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
90	_	_	B-LIMIT
units	_	_	O
of	_	_	O
calcium	_	_	O
and	_	_	O
85	_	_	B-LIMIT
units	_	_	O
of	_	_	O
protein	_	_	O
.	_	_	O
Since	_	_	O
the	_	_	O
patent	_	_	O
prefers	_	_	O
milk	_	_	B-VAR
,	_	_	O
they	_	_	O
must	_	_	O
drink	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
many	_	_	O
glasses	_	_	O
of	_	_	O
milk	_	_	B-VAR
as	_	_	O
glasses	_	_	O
of	_	_	O
protein	_	_	B-VAR
shakes	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
glasses	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
drink	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
their	_	_	O
sugar	_	_	B-OBJ_NAME
intake	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
fitness	_	_	O
trainer	_	_	O
meal	_	_	O
-	_	_	O
preps	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
meals	_	_	O
,	_	_	O
a	_	_	O
salmon	_	_	B-VAR
lunch	_	_	I-VAR
and	_	_	O
a	_	_	O
bison	_	_	B-VAR
burger	_	_	I-VAR
.	_	_	O
The	_	_	O
salmon	_	_	B-VAR
lunch	_	_	I-VAR
contains	_	_	O
15	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
20	_	_	B-PARAM
grams	_	_	O
of	_	_	O
carbs	_	_	O
,	_	_	O
and	_	_	O
8	_	_	B-PARAM
grams	_	_	O
of	_	_	O
fat	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
bison	_	_	B-VAR
burger	_	_	I-VAR
contains	_	_	O
30	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
20	_	_	B-PARAM
grams	_	_	O
of	_	_	O
carbs	_	_	O
,	_	_	O
and	_	_	O
13	_	_	B-PARAM
grams	_	_	O
of	_	_	O
fat	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
fitness	_	_	O
trainer	_	_	O
wants	_	_	O
to	_	_	O
get	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
160	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
180	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
carbs	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
because	_	_	O
the	_	_	O
salmon	_	_	B-VAR
lunch	_	_	I-VAR
is	_	_	O
expensive	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
25	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
meals	_	_	O
should	_	_	O
be	_	_	O
salmon	_	_	B-VAR
lunch	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
meal	_	_	O
should	_	_	O
he	_	_	O
eat	_	_	O
if	_	_	O
he	_	_	O
wants	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
fat	_	_	B-OBJ_NAME
intake	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
physics	_	_	O
teacher	_	_	O
shows	_	_	O
her	_	_	O
students	_	_	O
two	_	_	O
experiments	_	_	O
,	_	_	O
a	_	_	O
force	_	_	B-VAR
experiment	_	_	I-VAR
and	_	_	O
a	_	_	O
hydraulics	_	_	B-VAR
experiment	_	_	I-VAR
.	_	_	O
In	_	_	O
the	_	_	O
force	_	_	B-VAR
experiment	_	_	I-VAR
,	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
the	_	_	O
solid	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
the	_	_	O
gas	_	_	O
mixes	_	_	O
and	_	_	O
reacts	_	_	O
to	_	_	O
create	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
excitement	_	_	B-OBJ_NAME
.	_	_	O
In	_	_	O
the	_	_	O
hydraulics	_	_	B-VAR
experiment	_	_	I-VAR
,	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
the	_	_	O
solid	_	_	O
and	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
the	_	_	O
gas	_	_	O
mixes	_	_	O
and	_	_	O
reacts	_	_	O
to	_	_	O
create	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
excitement	_	_	B-OBJ_NAME
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
the	_	_	O
hydraulics	_	_	B-VAR
experiment	_	_	I-VAR
produces	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
heat	_	_	O
while	_	_	O
the	_	_	O
force	_	_	B-VAR
experiment	_	_	I-VAR
produces	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
heat	_	_	O
.	_	_	O
The	_	_	O
lab	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
90	_	_	B-LIMIT
units	_	_	O
of	_	_	O
the	_	_	O
solid	_	_	O
and	_	_	O
85	_	_	B-LIMIT
units	_	_	O
of	_	_	O
the	_	_	O
gas	_	_	O
.	_	_	O
If	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
15	_	_	B-LIMIT
units	_	_	O
of	_	_	O
heat	_	_	O
can	_	_	O
be	_	_	O
produced	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
experiments	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
done	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
excitement	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
university	_	_	O
has	_	_	B-CONST_DIR
1200	_	_	B-LIMIT
units	_	_	O
of	_	_	O
antibiotics	_	_	O
to	_	_	O
make	_	_	O
two	_	_	O
creams	_	_	O
,	_	_	O
a	_	_	O
anti	_	_	B-VAR
-	_	_	I-VAR
inflammatory	_	_	I-VAR
cream	_	_	I-VAR
and	_	_	O
a	_	_	O
pain	_	_	B-VAR
-	_	_	I-VAR
killing	_	_	I-VAR
cream	_	_	I-VAR
.	_	_	O
A	_	_	O
container	_	_	O
of	_	_	O
anti	_	_	B-VAR
-	_	_	I-VAR
inflammatory	_	_	I-VAR
cream	_	_	I-VAR
requires	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
antibiotics	_	_	O
and	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	B-OBJ_NAME
.	_	_	O
A	_	_	O
container	_	_	O
of	_	_	O
pain	_	_	B-VAR
-	_	_	I-VAR
killing	_	_	I-VAR
cream	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
antibiotics	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
lab	_	_	O
has	_	_	O
to	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
anti	_	_	B-VAR
-	_	_	I-VAR
inflammatory	_	_	I-VAR
creams	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
since	_	_	O
pain	_	_	B-VAR
-	_	_	I-VAR
killing	_	_	I-VAR
creams	_	_	I-VAR
are	_	_	O
in	_	_	O
high	_	_	O
demand	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
55	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
total	_	_	O
number	_	_	O
of	_	_	O
creams	_	_	O
must	_	_	O
be	_	_	O
pain	_	_	B-VAR
-	_	_	I-VAR
killing	_	_	I-VAR
creams	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
water	_	_	I-OBJ_NAME
needed	_	_	O
?	_	_	O

A	_	_	O
fitness	_	_	O
trainer	_	_	O
is	_	_	O
scheduling	_	_	O
her	_	_	O
client	_	_	O
to	_	_	O
eat	_	_	O
more	_	_	O
fruits	_	_	B-VAR
and	_	_	O
vegetables	_	_	B-VAR
to	_	_	O
meet	_	_	O
their	_	_	O
vitamin	_	_	O
and	_	_	O
fiber	_	_	O
requirements	_	_	O
.	_	_	O
A	_	_	O
pack	_	_	B-VAR
of	_	_	I-VAR
fruits	_	_	I-VAR
contains	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
and	_	_	O
7.5	_	_	B-PARAM
units	_	_	O
of	_	_	O
fiber	_	_	O
.	_	_	O
A	_	_	O
pack	_	_	B-VAR
of	_	_	I-VAR
vegetables	_	_	I-VAR
contains	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
fiber	_	_	O
.	_	_	O
The	_	_	O
client	_	_	O
must	_	_	O
meet	_	_	O
their	_	_	O
weekly	_	_	O
minimum	_	_	B-CONST_DIR
requirements	_	_	O
of	_	_	O
100	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamin	_	_	O
and	_	_	O
120	_	_	B-LIMIT
units	_	_	O
of	_	_	O
fiber	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
because	_	_	O
fruits	_	_	B-VAR
contain	_	_	O
more	_	_	O
hydration	_	_	O
,	_	_	O
the	_	_	O
client	_	_	O
must	_	_	O
eat	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-PARAM
as	_	_	O
many	_	_	O
packs	_	_	B-VAR
of	_	_	I-VAR
fruits	_	_	I-VAR
as	_	_	O
packs	_	_	B-VAR
of	_	_	I-VAR
vegetables	_	_	I-VAR
.	_	_	O
If	_	_	O
a	_	_	O
pack	_	_	B-VAR
of	_	_	I-VAR
fruits	_	_	I-VAR
contains	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
sugar	_	_	B-OBJ_NAME
and	_	_	O
a	_	_	O
pack	_	_	B-VAR
of	_	_	I-VAR
vegetables	_	_	I-VAR
contains	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
sugar	_	_	B-OBJ_NAME
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
packs	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
client	_	_	O
consume	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
their	_	_	O
sugar	_	_	B-OBJ_NAME
intake	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
university	_	_	O
has	_	_	O
a	_	_	O
car	_	_	O
building	_	_	O
fundraiser	_	_	O
where	_	_	O
students	_	_	O
build	_	_	O
toy	_	_	B-VAR
cars	_	_	I-VAR
and	_	_	O
toy	_	_	B-VAR
trucks	_	_	I-VAR
using	_	_	O
wheels	_	_	O
and	_	_	O
wood	_	_	O
and	_	_	O
sell	_	_	O
to	_	_	O
benefit	_	_	O
a	_	_	O
nearby	_	_	O
shelter	_	_	O
.	_	_	O
A	_	_	O
toy	_	_	B-VAR
car	_	_	I-VAR
requires	_	_	O
4	_	_	B-PARAM
wheels	_	_	O
and	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
wood	_	_	O
while	_	_	O
a	_	_	O
toy	_	_	B-VAR
truck	_	_	I-VAR
requires	_	_	O
6	_	_	B-PARAM
wheels	_	_	O
and	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
wood	_	_	O
.	_	_	O
Each	_	_	O
team	_	_	O
has	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
40	_	_	B-LIMIT
wheels	_	_	O
and	_	_	O
75	_	_	B-LIMIT
units	_	_	O
of	_	_	O
wood	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
each	_	_	O
team	_	_	O
can	_	_	O
build	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
3	_	_	B-LIMIT
toy	_	_	B-VAR
cars	_	_	I-VAR
and	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
toy	_	_	B-VAR
trucks	_	_	I-VAR
must	_	_	B-CONST_DIR
be	_	_	I-CONST_DIR
larger	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
toy	_	_	B-VAR
cars	_	_	I-VAR
.	_	_	O
If	_	_	O
a	_	_	O
toy	_	_	B-VAR
car	_	_	I-VAR
can	_	_	O
fundraise	_	_	B-OBJ_NAME
$	_	_	O
30	_	_	B-PARAM
and	_	_	O
a	_	_	O
toy	_	_	B-VAR
truck	_	_	I-VAR
can	_	_	O
fundraise	_	_	B-OBJ_NAME
$	_	_	O
35	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
toy	_	_	O
should	_	_	O
a	_	_	O
team	_	_	O
build	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
amount	_	_	I-OBJ_NAME
fundraised	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
strawberry	_	_	O
farmer	_	_	O
delivers	_	_	O
his	_	_	O
strawberries	_	_	O
in	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
containers	_	_	O
,	_	_	O
a	_	_	O
box	_	_	B-VAR
and	_	_	O
a	_	_	O
bucket	_	_	B-VAR
.	_	_	O
A	_	_	O
box	_	_	B-VAR
contains	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
strawberries	_	_	B-OBJ_NAME
whereas	_	_	O
a	_	_	O
bucket	_	_	B-VAR
contains	_	_	O
9	_	_	B-PARAM
units	_	_	O
of	_	_	O
strawberries	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
farmer	_	_	O
has	_	_	O
access	_	_	B-CONST_DIR
to	_	_	O
500	_	_	B-LIMIT
boxes	_	_	B-VAR
and	_	_	O
300	_	_	B-LIMIT
buckets	_	_	B-VAR
.	_	_	O
Buckets	_	_	B-VAR
sell	_	_	O
for	_	_	O
more	_	_	O
profit	_	_	O
;	_	_	O
therefore	_	_	O
,	_	_	O
the	_	_	O
farmer	_	_	O
wants	_	_	O
to	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	I-PARAM
more	_	_	O
buckets	_	_	B-VAR
than	_	_	O
boxes	_	_	B-VAR
.	_	_	O
Additionally	_	_	O
,	_	_	O
he	_	_	O
can	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
650	_	_	B-LIMIT
containers	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
25	_	_	B-LIMIT
must	_	_	O
be	_	_	O
boxes	_	_	B-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
container	_	_	O
should	_	_	O
the	_	_	O
farmer	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
strawberries	_	_	I-OBJ_NAME
he	_	_	O
can	_	_	O
transport	_	_	O
?	_	_	O

A	_	_	O
food	_	_	O
distributer	_	_	O
can	_	_	O
either	_	_	O
move	_	_	O
their	_	_	O
product	_	_	O
using	_	_	O
trucks	_	_	B-VAR
or	_	_	O
boats	_	_	B-VAR
.	_	_	O
A	_	_	O
truck	_	_	B-VAR
can	_	_	O
take	_	_	O
30	_	_	B-PARAM
units	_	_	O
of	_	_	O
product	_	_	O
and	_	_	O
produces	_	_	O
80	_	_	B-PARAM
units	_	_	O
of	_	_	O
pollution	_	_	B-OBJ_NAME
per	_	_	O
trip	_	_	O
whereas	_	_	O
boats	_	_	B-VAR
take	_	_	O
50	_	_	B-PARAM
units	_	_	O
of	_	_	O
product	_	_	O
and	_	_	O
produces	_	_	O
60	_	_	B-PARAM
units	_	_	O
of	_	_	O
pollution	_	_	B-OBJ_NAME
per	_	_	O
trip	_	_	O
.	_	_	O
The	_	_	O
food	_	_	O
distributer	_	_	O
needs	_	_	B-CONST_DIR
to	_	_	I-CONST_DIR
move	_	_	I-CONST_DIR
1000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
product	_	_	O
and	_	_	O
must	_	_	O
have	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
40	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
trips	_	_	O
using	_	_	O
boats	_	_	B-VAR
due	_	_	O
to	_	_	O
limitations	_	_	O
of	_	_	O
sea	_	_	O
transportation	_	_	O
regulations	_	_	O
.	_	_	O
Additionally	_	_	O
,	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
trips	_	_	O
using	_	_	O
a	_	_	O
truck	_	_	B-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
form	_	_	O
of	_	_	O
transportation	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
pollution	_	_	I-OBJ_NAME
produced	_	_	O
?	_	_	O

A	_	_	O
landscaping	_	_	O
company	_	_	O
provides	_	_	O
services	_	_	O
from	_	_	O
an	_	_	O
expert	_	_	B-VAR
or	_	_	O
an	_	_	O
apprentice	_	_	B-VAR
.	_	_	O
An	_	_	O
expert	_	_	B-VAR
costs	_	_	O
the	_	_	O
company	_	_	O
500	_	_	B-PARAM
dollars	_	_	B-OBJ_NAME
for	_	_	O
each	_	_	O
shift	_	_	O
and	_	_	O
can	_	_	O
care	_	_	O
for	_	_	O
100	_	_	B-PARAM
square	_	_	O
meters	_	_	O
of	_	_	O
land	_	_	O
whereas	_	_	O
an	_	_	O
apprentice	_	_	B-VAR
costs	_	_	O
the	_	_	O
company	_	_	O
300	_	_	B-PARAM
dollars	_	_	B-OBJ_NAME
for	_	_	O
each	_	_	O
shift	_	_	O
and	_	_	O
can	_	_	O
care	_	_	O
for	_	_	O
80	_	_	B-PARAM
square	_	_	O
meters	_	_	O
of	_	_	O
land	_	_	O
.	_	_	O
Because	_	_	O
of	_	_	O
the	_	_	O
price	_	_	O
to	_	_	O
the	_	_	O
customer	_	_	O
,	_	_	O
the	_	_	O
company	_	_	O
expects	_	_	O
the	_	_	O
demand	_	_	O
of	_	_	O
the	_	_	O
public	_	_	O
to	_	_	O
want	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-PARAM
as	_	_	O
many	_	_	O
apprentices	_	_	B-VAR
than	_	_	O
experts	_	_	B-VAR
.	_	_	O
However	_	_	O
,	_	_	O
there	_	_	O
are	_	_	O
loyal	_	_	O
customers	_	_	O
that	_	_	O
prefer	_	_	O
the	_	_	O
experts	_	_	B-VAR
.	_	_	O
Therefore	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
shifts	_	_	O
must	_	_	O
be	_	_	O
expert	_	_	B-VAR
shifts	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
must	_	_	B-CONST_DIR
care	_	_	I-CONST_DIR
for	_	_	I-CONST_DIR
5000	_	_	B-LIMIT
square	_	_	O
meters	_	_	O
of	_	_	O
land	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
service	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
cost	_	_	I-OBJ_NAME
to	_	_	O
the	_	_	O
company	_	_	O
?	_	_	O

A	_	_	O
logging	_	_	O
company	_	_	O
ships	_	_	O
their	_	_	O
lumber	_	_	O
to	_	_	O
a	_	_	O
nearby	_	_	O
country	_	_	O
using	_	_	O
logging	_	_	B-VAR
trucks	_	_	I-VAR
and	_	_	O
by	_	_	O
lumber	_	_	B-VAR
carrier	_	_	I-VAR
vessels	_	_	I-VAR
.	_	_	O
Each	_	_	O
logging	_	_	B-VAR
truck	_	_	I-VAR
costs	_	_	B-OBJ_NAME
the	_	_	O
logging	_	_	O
company	_	_	O
$	_	_	O
250	_	_	B-PARAM
for	_	_	O
every	_	_	O
trip	_	_	O
and	_	_	O
moves	_	_	O
1000	_	_	B-PARAM
lbs	_	_	O
of	_	_	O
lumber	_	_	O
.	_	_	O
A	_	_	O
lumber	_	_	B-VAR
carrier	_	_	I-VAR
vessel	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
1000	_	_	B-PARAM
every	_	_	O
trip	_	_	O
and	_	_	O
moves	_	_	O
6000	_	_	B-PARAM
lbs	_	_	O
of	_	_	O
lumber	_	_	O
.	_	_	O
Due	_	_	O
to	_	_	O
limited	_	_	O
waters	_	_	O
and	_	_	O
difficulties	_	_	O
in	_	_	O
scheduling	_	_	O
the	_	_	O
trips	_	_	O
for	_	_	O
lumber	_	_	B-VAR
carrier	_	_	I-VAR
vessels	_	_	I-VAR
,	_	_	O
the	_	_	O
company	_	_	O
’s	_	_	O
management	_	_	O
asks	_	_	O
that	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
logging	_	_	B-VAR
trucks	_	_	I-VAR
must	_	_	B-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
lumber	_	_	B-VAR
carrier	_	_	I-VAR
vessels	_	_	I-VAR
.	_	_	O
The	_	_	O
logging	_	_	O
company	_	_	O
must	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
300000	_	_	B-LIMIT
lbs	_	_	O
of	_	_	O
lumber	_	_	O
to	_	_	O
the	_	_	O
nearby	_	_	O
country	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
transportation	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
schedule	_	_	O
to	_	_	O
move	_	_	O
their	_	_	O
lumber	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
cost	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
famous	_	_	O
chocolate	_	_	O
shop	_	_	O
is	_	_	O
expecting	_	_	O
a	_	_	O
lot	_	_	O
of	_	_	O
orders	_	_	O
because	_	_	O
of	_	_	O
an	_	_	O
upcoming	_	_	O
holiday	_	_	O
.	_	_	O
The	_	_	O
chocolate	_	_	O
shop	_	_	O
is	_	_	O
famous	_	_	O
for	_	_	O
selling	_	_	O
two	_	_	O
products	_	_	O
,	_	_	O
large	_	_	B-VAR
boxes	_	_	I-VAR
of	_	_	I-VAR
chocolates	_	_	I-VAR
,	_	_	O
or	_	_	O
small	_	_	B-VAR
boxes	_	_	I-VAR
of	_	_	I-VAR
chocolates	_	_	I-VAR
.	_	_	O
A	_	_	O
large	_	_	B-VAR
box	_	_	I-VAR
of	_	_	I-VAR
chocolate	_	_	I-VAR
has	_	_	O
24	_	_	B-PARAM
individual	_	_	B-OBJ_NAME
chocolates	_	_	I-OBJ_NAME
while	_	_	O
a	_	_	O
small	_	_	B-VAR
box	_	_	I-VAR
of	_	_	I-VAR
chocolate	_	_	I-VAR
has	_	_	O
12	_	_	B-PARAM
individual	_	_	B-OBJ_NAME
chocolates	_	_	I-OBJ_NAME
.	_	_	O
The	_	_	O
chocolate	_	_	O
shop	_	_	O
has	_	_	O
a	_	_	O
delivery	_	_	O
service	_	_	O
,	_	_	O
and	_	_	O
each	_	_	O
trip	_	_	O
,	_	_	O
the	_	_	O
shop	_	_	O
owner	_	_	O
can	_	_	O
prepare	_	_	O
ahead	_	_	O
of	_	_	O
time	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
110	_	_	B-LIMIT
large	_	_	B-VAR
boxes	_	_	I-VAR
of	_	_	I-VAR
chocolates	_	_	I-VAR
or	_	_	O
150	_	_	B-LIMIT
small	_	_	B-VAR
boxes	_	_	I-VAR
of	_	_	I-VAR
chocolates	_	_	I-VAR
.	_	_	O
Due	_	_	O
to	_	_	O
space	_	_	O
limitations	_	_	O
of	_	_	O
their	_	_	O
truck	_	_	O
,	_	_	O
the	_	_	O
truck	_	_	O
can	_	_	O
fit	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
90	_	_	B-LIMIT
total	_	_	O
boxes	_	_	O
of	_	_	O
chocolates	_	_	O
and	_	_	O
because	_	_	O
of	_	_	O
a	_	_	O
sale	_	_	O
,	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
large	_	_	B-VAR
boxes	_	_	I-VAR
of	_	_	I-VAR
chocolates	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
small	_	_	B-VAR
boxes	_	_	I-VAR
of	_	_	I-VAR
chocolates	_	_	I-VAR
are	_	_	O
less	_	_	O
expensive	_	_	O
and	_	_	O
the	_	_	O
shop	_	_	O
owner	_	_	O
expects	_	_	O
to	_	_	O
move	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
many	_	_	O
small	_	_	B-VAR
boxes	_	_	I-VAR
of	_	_	I-VAR
chocolates	_	_	I-VAR
than	_	_	O
large	_	_	B-VAR
boxes	_	_	I-VAR
of	_	_	I-VAR
chocolates	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
size	_	_	O
of	_	_	O
chocolate	_	_	O
box	_	_	O
should	_	_	O
the	_	_	O
shop	_	_	O
owner	_	_	O
put	_	_	O
in	_	_	O
their	_	_	O
truck	_	_	O
for	_	_	O
each	_	_	O
trip	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
individual	_	_	I-OBJ_NAME
chocolates	_	_	I-OBJ_NAME
transported	_	_	O
to	_	_	O
their	_	_	O
customers	_	_	O
?	_	_	O

An	_	_	O
internet	_	_	O
supplier	_	_	O
needs	_	_	O
to	_	_	O
deliver	_	_	O
routers	_	_	O
to	_	_	O
their	_	_	O
customers	_	_	O
when	_	_	O
they	_	_	O
first	_	_	O
sign	_	_	O
up	_	_	O
.	_	_	O
They	_	_	O
can	_	_	O
either	_	_	O
transport	_	_	O
using	_	_	O
their	_	_	O
internal	_	_	B-VAR
drivers	_	_	I-VAR
or	_	_	O
outsource	_	_	O
to	_	_	O
external	_	_	B-VAR
drivers	_	_	I-VAR
.	_	_	O
Internal	_	_	B-VAR
drivers	_	_	I-VAR
spend	_	_	O
more	_	_	O
time	_	_	O
to	_	_	O
help	_	_	O
the	_	_	O
customers	_	_	O
set	_	_	O
up	_	_	O
and	_	_	O
can	_	_	O
deliver	_	_	O
20	_	_	B-PARAM
routers	_	_	O
every	_	_	O
day	_	_	O
whereas	_	_	O
the	_	_	O
external	_	_	B-VAR
drivers	_	_	I-VAR
can	_	_	O
deliver	_	_	O
35	_	_	B-PARAM
routers	_	_	O
every	_	_	O
day	_	_	O
.	_	_	O
External	_	_	B-VAR
drivers	_	_	I-VAR
use	_	_	O
hybrid	_	_	O
cars	_	_	O
and	_	_	O
produce	_	_	O
5	_	_	B-PARAM
units	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
pollution	_	_	I-OBJ_NAME
while	_	_	O
the	_	_	O
internal	_	_	B-VAR
drivers	_	_	I-VAR
use	_	_	O
gasoline	_	_	O
cars	_	_	O
and	_	_	O
produce	_	_	O
12	_	_	B-PARAM
units	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
pollution	_	_	I-OBJ_NAME
.	_	_	O
The	_	_	O
internet	_	_	O
supplier	_	_	O
needs	_	_	O
to	_	_	O
deliver	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
500	_	_	B-LIMIT
routers	_	_	O
every	_	_	O
day	_	_	O
and	_	_	O
internal	_	_	B-VAR
drivers	_	_	I-VAR
must	_	_	O
make	_	_	O
up	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
all	_	_	O
drivers	_	_	O
due	_	_	O
to	_	_	O
their	_	_	O
customer	_	_	O
service	_	_	O
.	_	_	O
There	_	_	O
must	_	_	O
also	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
external	_	_	B-VAR
drivers	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
driver	_	_	O
should	_	_	O
the	_	_	O
internet	_	_	O
supplier	_	_	O
plan	_	_	O
to	_	_	O
contract	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
pollution	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
tourism	_	_	O
company	_	_	O
is	_	_	O
expecting	_	_	O
an	_	_	O
increase	_	_	O
in	_	_	O
tourists	_	_	O
after	_	_	O
a	_	_	O
pandemic	_	_	O
and	_	_	O
expects	_	_	B-CONST_DIR
10000	_	_	B-LIMIT
customers	_	_	O
in	_	_	O
the	_	_	O
coming	_	_	O
month	_	_	O
.	_	_	O
The	_	_	O
tourism	_	_	O
company	_	_	O
can	_	_	O
either	_	_	O
use	_	_	O
a	_	_	O
minivan	_	_	B-VAR
which	_	_	O
can	_	_	O
transport	_	_	O
6	_	_	B-PARAM
tourists	_	_	O
and	_	_	O
profits	_	_	B-OBJ_NAME
the	_	_	O
company	_	_	O
$	_	_	O
300	_	_	B-PARAM
each	_	_	O
time	_	_	O
.	_	_	O
They	_	_	O
can	_	_	O
also	_	_	O
use	_	_	O
a	_	_	O
tourism	_	_	B-VAR
bus	_	_	I-VAR
which	_	_	O
can	_	_	O
transport	_	_	O
30	_	_	B-PARAM
tourists	_	_	O
and	_	_	O
profits	_	_	B-OBJ_NAME
the	_	_	O
company	_	_	O
$	_	_	O
1800	_	_	B-PARAM
each	_	_	O
time	_	_	O
.	_	_	O
There	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
tourism	_	_	B-VAR
buses	_	_	I-VAR
in	_	_	O
the	_	_	O
coming	_	_	O
month	_	_	O
because	_	_	O
many	_	_	O
come	_	_	O
in	_	_	O
large	_	_	O
groups	_	_	O
.	_	_	O
Additionally	_	_	O
,	_	_	O
due	_	_	O
to	_	_	O
the	_	_	O
close	_	_	O
proximity	_	_	O
to	_	_	O
the	_	_	O
tour	_	_	O
guide	_	_	O
,	_	_	O
the	_	_	O
tourism	_	_	O
company	_	_	O
plans	_	_	O
to	_	_	O
have	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
45	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
trips	_	_	O
be	_	_	O
by	_	_	O
minivan	_	_	B-VAR
to	_	_	O
improve	_	_	O
customer	_	_	O
service	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
trips	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
vehicle	_	_	O
should	_	_	O
be	_	_	O
scheduled	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
profit	_	_	B-OBJ_NAME
for	_	_	O
the	_	_	O
company	_	_	O
?	_	_	O

A	_	_	O
skiing	_	_	O
resort	_	_	O
has	_	_	O
two	_	_	O
methods	_	_	O
of	_	_	O
getting	_	_	O
their	_	_	O
customers	_	_	O
up	_	_	O
to	_	_	O
their	_	_	O
resort	_	_	O
.	_	_	O
They	_	_	O
can	_	_	O
either	_	_	O
use	_	_	O
a	_	_	O
gondola	_	_	B-VAR
,	_	_	O
or	_	_	O
a	_	_	O
large	_	_	B-VAR
bus	_	_	I-VAR
.	_	_	O
On	_	_	O
average	_	_	O
,	_	_	O
a	_	_	O
gondola	_	_	B-VAR
can	_	_	O
transport	_	_	O
skiers	_	_	O
and	_	_	O
snowboarders	_	_	O
at	_	_	O
a	_	_	O
rate	_	_	O
of	_	_	O
20	_	_	B-PARAM
people	_	_	O
per	_	_	O
minute	_	_	O
whereas	_	_	O
a	_	_	O
large	_	_	B-VAR
bus	_	_	I-VAR
can	_	_	O
transport	_	_	O
at	_	_	O
a	_	_	O
rate	_	_	O
of	_	_	O
5	_	_	B-PARAM
people	_	_	O
per	_	_	O
minute	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
gondolas	_	_	B-VAR
cost	_	_	O
the	_	_	O
resort	_	_	O
a	_	_	O
lot	_	_	O
to	_	_	O
maintain	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
40	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
transportation	_	_	O
methods	_	_	O
implemented	_	_	O
can	_	_	O
be	_	_	O
gondolas	_	_	B-VAR
.	_	_	O
Since	_	_	O
large	_	_	B-VAR
buses	_	_	I-VAR
are	_	_	O
easier	_	_	O
to	_	_	O
implement	_	_	O
,	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
ten	_	_	B-LIMIT
times	_	_	I-LIMIT
more	_	_	O
large	_	_	B-VAR
buses	_	_	I-VAR
than	_	_	O
gondolas	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
manufacturer	_	_	O
wants	_	_	O
to	_	_	O
move	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
500	_	_	B-LIMIT
customers	_	_	O
every	_	_	O
minute	_	_	O
up	_	_	O
the	_	_	O
mountain	_	_	O
,	_	_	O
find	_	_	O
the	_	_	O
minimum	_	_	B-OBJ_DIR
transportation	_	_	B-OBJ_NAME
implementations	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
used	_	_	O
.	_	_	O

A	_	_	O
company	_	_	O
is	_	_	O
delivering	_	_	O
packages	_	_	O
using	_	_	O
two	_	_	O
methods	_	_	O
,	_	_	O
drones	_	_	B-VAR
and	_	_	O
couriers	_	_	B-VAR
.	_	_	O
A	_	_	O
drone	_	_	B-VAR
can	_	_	O
transport	_	_	O
4	_	_	B-PARAM
packages	_	_	B-OBJ_NAME
every	_	_	O
hour	_	_	O
while	_	_	O
a	_	_	O
courier	_	_	B-VAR
can	_	_	O
transport	_	_	O
25	_	_	B-PARAM
packages	_	_	B-OBJ_NAME
every	_	_	O
hour	_	_	O
.	_	_	O
Drones	_	_	B-VAR
cost	_	_	O
an	_	_	O
average	_	_	O
of	_	_	O
$	_	_	O
2	_	_	B-PARAM
per	_	_	O
hour	_	_	O
to	_	_	O
maintain	_	_	O
and	_	_	O
couriers	_	_	B-VAR
are	_	_	O
paid	_	_	O
$	_	_	O
20	_	_	B-PARAM
per	_	_	O
hour	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
needs	_	_	O
to	_	_	O
deliver	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
800	_	_	B-LIMIT
packages	_	_	O
and	_	_	O
they	_	_	O
can	_	_	O
spend	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
1300	_	_	B-LIMIT
per	_	_	O
hour	_	_	O
for	_	_	O
delivery	_	_	O
.	_	_	O
Since	_	_	O
drones	_	_	B-VAR
have	_	_	O
a	_	_	O
high	_	_	O
up	_	_	O
-	_	_	O
front	_	_	O
cost	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
drones	_	_	B-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
couriers	_	_	B-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
method	_	_	O
of	_	_	O
delivering	_	_	O
packages	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
deliveries	_	_	I-OBJ_NAME
using	_	_	O
drones	_	_	O
and	_	_	O
couriers	_	_	O
?	_	_	O

A	_	_	O
smoothie	_	_	O
company	_	_	O
offers	_	_	O
delivery	_	_	O
and	_	_	O
ships	_	_	O
in	_	_	O
specialty	_	_	O
delivery	_	_	O
and	_	_	O
medium	_	_	B-VAR
bags	_	_	I-VAR
.	_	_	O
A	_	_	O
specialty	_	_	B-VAR
delivery	_	_	I-VAR
bag	_	_	I-VAR
can	_	_	O
hold	_	_	O
12	_	_	B-PARAM
orders	_	_	B-OBJ_NAME
while	_	_	O
a	_	_	O
medium	_	_	B-VAR
bag	_	_	I-VAR
can	_	_	O
hold	_	_	O
7	_	_	B-PARAM
orders	_	_	B-OBJ_NAME
.	_	_	O
Most	_	_	O
delivery	_	_	O
drivers	_	_	O
prefer	_	_	O
medium	_	_	B-VAR
bags	_	_	I-VAR
,	_	_	O
so	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
many	_	_	O
medium	_	_	B-VAR
bags	_	_	I-VAR
must	_	_	O
be	_	_	O
used	_	_	O
as	_	_	O
specialty	_	_	B-VAR
delivery	_	_	I-VAR
bags	_	_	I-VAR
.	_	_	O
The	_	_	O
smoothie	_	_	O
company	_	_	O
has	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
45	_	_	B-LIMIT
medium	_	_	B-VAR
bags	_	_	I-VAR
and	_	_	O
60	_	_	B-LIMIT
specialty	_	_	B-VAR
delivery	_	_	I-VAR
bags	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
company	_	_	O
must	_	_	O
send	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
6	_	_	B-LIMIT
specialty	_	_	B-VAR
delivery	_	_	I-VAR
bags	_	_	I-VAR
and	_	_	O
can	_	_	O
send	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
50	_	_	B-LIMIT
bags	_	_	O
in	_	_	O
total	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
send	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
smoothies	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
delivered	_	_	O
?	_	_	O

A	_	_	O
florist	_	_	O
can	_	_	O
deliver	_	_	O
their	_	_	O
flowers	_	_	O
either	_	_	O
by	_	_	O
car	_	_	B-VAR
or	_	_	O
by	_	_	O
truck	_	_	B-VAR
.	_	_	O
A	_	_	O
car	_	_	B-VAR
can	_	_	O
deliver	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
flowers	_	_	O
and	_	_	O
uses	_	_	O
10	_	_	B-PARAM
units	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
gas	_	_	I-OBJ_NAME
.	_	_	O
A	_	_	O
truck	_	_	B-VAR
can	_	_	O
deliver	_	_	O
9	_	_	B-PARAM
units	_	_	O
of	_	_	O
flowers	_	_	O
and	_	_	O
uses	_	_	O
14	_	_	B-PARAM
units	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
gas	_	_	I-OBJ_NAME
.	_	_	O
The	_	_	O
florist	_	_	O
needs	_	_	O
to	_	_	O
deliver	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
130	_	_	B-LIMIT
units	_	_	O
of	_	_	O
flowers	_	_	O
.	_	_	O
Additionally	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
cars	_	_	B-VAR
used	_	_	O
must	_	_	B-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
trucks	_	_	B-VAR
used	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
gas	_	_	I-OBJ_NAME
used	_	_	O
?	_	_	O

A	_	_	O
garbage	_	_	O
collection	_	_	O
company	_	_	O
uses	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
vehicles	_	_	O
,	_	_	O
truck	_	_	B-VAR
A	_	_	I-VAR
and	_	_	O
truck	_	_	B-VAR
B.	_	_	I-VAR
Truck	_	_	B-VAR
A	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
workers	_	_	O
while	_	_	O
truck	_	_	B-VAR
B	_	_	I-VAR
requires	_	_	O
4	_	_	B-PARAM
workers	_	_	O
.	_	_	O
Truck	_	_	B-VAR
A	_	_	I-VAR
can	_	_	O
collect	_	_	O
40	_	_	B-PARAM
units	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
garbage	_	_	I-OBJ_NAME
and	_	_	O
truck	_	_	B-VAR
B	_	_	I-VAR
can	_	_	O
collect	_	_	O
50	_	_	B-PARAM
units	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
garbage	_	_	I-OBJ_NAME
.	_	_	O
The	_	_	O
garbage	_	_	O
collection	_	_	O
company	_	_	O
has	_	_	B-CONST_DIR
employed	_	_	O
150	_	_	B-LIMIT
workers	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
must	_	_	O
use	_	_	O
more	_	_	B-CONST_DIR
truck	_	_	B-VAR
A	_	_	I-VAR
models	_	_	O
than	_	_	O
truck	_	_	B-VAR
B	_	_	I-VAR
models	_	_	O
.	_	_	O
Additionally	_	_	O
,	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
truck	_	_	B-VAR
A	_	_	I-VAR
’s	_	_	O
and	_	_	O
8	_	_	B-LIMIT
truck	_	_	B-VAR
B	_	_	I-VAR
’s	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
vehicles	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
use	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
garbage	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
collected	_	_	O
?	_	_	O

In	_	_	O
the	_	_	O
North	_	_	O
,	_	_	O
a	_	_	O
delivery	_	_	O
service	_	_	O
can	_	_	O
deliver	_	_	O
using	_	_	O
either	_	_	O
sleds	_	_	B-VAR
or	_	_	O
snowmobile	_	_	B-VAR
.	_	_	O
Snowmobiles	_	_	B-VAR
can	_	_	O
deliver	_	_	O
150	_	_	B-PARAM
packages	_	_	O
while	_	_	O
sleds	_	_	B-VAR
can	_	_	O
deliver	_	_	O
125	_	_	B-PARAM
packages	_	_	O
.	_	_	O
Most	_	_	O
villages	_	_	O
do	_	_	O
not	_	_	O
want	_	_	O
snowmobiles	_	_	O
to	_	_	O
pollute	_	_	O
their	_	_	O
regions	_	_	O
.	_	_	O
Therefore	_	_	O
,	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
two	_	_	B-PARAM
times	_	_	I-PARAM
more	_	_	O
sleds	_	_	B-VAR
than	_	_	O
snowmobiles	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
delivery	_	_	O
service	_	_	O
wants	_	_	B-CONST_DIR
to	_	_	I-CONST_DIR
deliver	_	_	I-CONST_DIR
150000	_	_	B-LIMIT
packages	_	_	O
,	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
deliveries	_	_	I-OBJ_NAME
.	_	_	O

A	_	_	O
car	_	_	O
manufacturing	_	_	O
company	_	_	O
needs	_	_	O
to	_	_	O
distribute	_	_	O
their	_	_	O
cars	_	_	O
to	_	_	O
their	_	_	O
retail	_	_	O
stores	_	_	O
by	_	_	O
either	_	_	O
large	_	_	B-VAR
trailers	_	_	I-VAR
or	_	_	O
small	_	_	B-VAR
trailers	_	_	I-VAR
.	_	_	O
A	_	_	O
large	_	_	B-VAR
trailer	_	_	I-VAR
can	_	_	O
carry	_	_	O
6	_	_	B-PARAM
cars	_	_	O
while	_	_	O
a	_	_	O
small	_	_	B-VAR
trailer	_	_	I-VAR
can	_	_	O
carry	_	_	O
4	_	_	B-PARAM
cars	_	_	O
.	_	_	O
Since	_	_	O
large	_	_	B-VAR
trailers	_	_	I-VAR
are	_	_	O
harder	_	_	O
to	_	_	O
get	_	_	O
a	_	_	O
hold	_	_	O
of	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
small	_	_	B-VAR
trailers	_	_	I-VAR
used	_	_	O
has	_	_	O
to	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
large	_	_	B-VAR
trailers	_	_	I-VAR
used	_	_	O
.	_	_	O
If	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
80	_	_	B-LIMIT
cars	_	_	O
need	_	_	O
to	_	_	O
be	_	_	O
transported	_	_	O
,	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
trailers	_	_	I-OBJ_NAME
needed	_	_	O
.	_	_	O

A	_	_	O
construction	_	_	O
site	_	_	O
can	_	_	O
use	_	_	O
two	_	_	O
transfer	_	_	O
methods	_	_	O
to	_	_	O
move	_	_	O
equipment	_	_	O
using	_	_	O
cranes	_	_	B-VAR
or	_	_	O
elevators	_	_	B-VAR
.	_	_	O
Each	_	_	O
crane	_	_	B-VAR
can	_	_	O
transport	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
equipment	_	_	O
and	_	_	O
costs	_	_	O
$	_	_	O
2000	_	_	B-PARAM
per	_	_	O
hour	_	_	O
.	_	_	O
Each	_	_	O
elevator	_	_	B-VAR
can	_	_	O
transport	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
equipment	_	_	O
and	_	_	O
costs	_	_	O
$	_	_	O
500	_	_	B-PARAM
per	_	_	O
hour	_	_	O
.	_	_	O
The	_	_	O
construction	_	_	O
site	_	_	O
needs	_	_	O
to	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
90	_	_	B-LIMIT
units	_	_	O
of	_	_	O
equipment	_	_	O
and	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
$	_	_	O
30000	_	_	B-LIMIT
.	_	_	O
There	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	I-PARAM
more	_	_	O
elevators	_	_	B-VAR
than	_	_	O
cranes	_	_	B-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
transfer	_	_	O
method	_	_	O
should	_	_	O
be	_	_	O
done	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
transfer	_	_	I-OBJ_NAME
methods	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
toy	_	_	O
storage	_	_	O
company	_	_	O
needs	_	_	O
to	_	_	O
transport	_	_	O
toys	_	_	O
using	_	_	O
a	_	_	O
manual	_	_	B-VAR
pallet	_	_	I-VAR
jack	_	_	I-VAR
or	_	_	O
an	_	_	O
electric	_	_	B-VAR
pallet	_	_	I-VAR
jack	_	_	I-VAR
.	_	_	O
The	_	_	O
toy	_	_	O
storage	_	_	O
company	_	_	O
has	_	_	O
access	_	_	O
to	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
6	_	_	B-LIMIT
manual	_	_	B-VAR
pallet	_	_	I-VAR
jacks	_	_	I-VAR
and	_	_	O
15	_	_	B-LIMIT
electric	_	_	B-VAR
pallet	_	_	I-VAR
jacks	_	_	I-VAR
.	_	_	O
The	_	_	O
manual	_	_	B-VAR
pallet	_	_	I-VAR
jacks	_	_	I-VAR
can	_	_	O
transport	_	_	O
15	_	_	B-PARAM
boxes	_	_	B-OBJ_NAME
every	_	_	O
hour	_	_	O
while	_	_	O
electric	_	_	B-VAR
pallet	_	_	I-VAR
jacks	_	_	I-VAR
can	_	_	O
transport	_	_	O
25	_	_	B-PARAM
boxes	_	_	B-OBJ_NAME
every	_	_	O
hour	_	_	O
.	_	_	O
Since	_	_	O
electric	_	_	B-VAR
jacks	_	_	I-VAR
require	_	_	O
less	_	_	O
work	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
electric	_	_	B-VAR
pallet	_	_	I-VAR
jacks	_	_	I-VAR
must	_	_	B-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
manual	_	_	B-VAR
pallet	_	_	I-VAR
jacks	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
company	_	_	O
can	_	_	O
use	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
8	_	_	B-LIMIT
manual	_	_	B-VAR
pallet	_	_	I-VAR
jacks	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
electric	_	_	B-VAR
pallet	_	_	I-VAR
jacks	_	_	I-VAR
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
use	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
boxes	_	_	I-OBJ_NAME
they	_	_	O
can	_	_	O
transport	_	_	O
?	_	_	O

A	_	_	O
nearby	_	_	O
lake	_	_	O
is	_	_	O
frequently	_	_	O
artificially	_	_	O
seeded	_	_	O
with	_	_	O
trout	_	_	O
for	_	_	O
local	_	_	O
fishermen	_	_	O
.	_	_	O
The	_	_	O
trout	_	_	O
are	_	_	O
transported	_	_	O
using	_	_	O
either	_	_	O
large	_	_	B-VAR
trucks	_	_	I-VAR
or	_	_	O
by	_	_	O
boat	_	_	B-VAR
.	_	_	O
Transporting	_	_	O
using	_	_	O
large	_	_	B-VAR
trucks	_	_	I-VAR
can	_	_	O
take	_	_	O
2000	_	_	B-PARAM
trout	_	_	O
and	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
300	_	_	B-PARAM
per	_	_	O
trip	_	_	O
.	_	_	O
Transporting	_	_	O
with	_	_	O
boat	_	_	B-VAR
can	_	_	O
take	_	_	O
1200	_	_	B-PARAM
trout	_	_	O
and	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
100	_	_	B-PARAM
per	_	_	O
trip	_	_	O
.	_	_	O
Since	_	_	O
boats	_	_	O
take	_	_	O
extra	_	_	O
preparation	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
75	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
trips	_	_	O
should	_	_	O
be	_	_	O
by	_	_	O
large	_	_	B-VAR
trucks	_	_	I-VAR
.	_	_	O
Additionally	_	_	O
,	_	_	O
there	_	_	O
can	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
5	_	_	B-LIMIT
trips	_	_	O
by	_	_	O
boat	_	_	B-VAR
.	_	_	O
If	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
7000	_	_	B-LIMIT
trout	_	_	O
need	_	_	O
to	_	_	O
be	_	_	O
seeded	_	_	O
into	_	_	O
the	_	_	O
nearby	_	_	O
lake	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
trip	_	_	O
should	_	_	O
be	_	_	O
taken	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
cost	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
milk	_	_	O
company	_	_	O
is	_	_	O
delivering	_	_	O
milk	_	_	O
to	_	_	O
their	_	_	O
local	_	_	O
families	_	_	O
’	_	_	O
homes	_	_	O
directly	_	_	O
either	_	_	O
through	_	_	O
bikes	_	_	B-VAR
or	_	_	O
by	_	_	O
car	_	_	B-VAR
.	_	_	O
A	_	_	O
worker	_	_	O
on	_	_	O
a	_	_	O
bike	_	_	B-VAR
can	_	_	O
deliver	_	_	O
12	_	_	B-PARAM
orders	_	_	O
of	_	_	O
milk	_	_	O
and	_	_	O
takes	_	_	O
40	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
per	_	_	O
trip	_	_	O
.	_	_	O
A	_	_	O
worker	_	_	O
on	_	_	O
a	_	_	O
car	_	_	B-VAR
can	_	_	O
deliver	_	_	O
50	_	_	B-PARAM
orders	_	_	O
of	_	_	O
milk	_	_	O
and	_	_	O
takes	_	_	O
30	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
per	_	_	O
trip	_	_	O
.	_	_	O
The	_	_	O
milk	_	_	O
company	_	_	O
needs	_	_	O
to	_	_	O
deliver	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
850	_	_	B-LIMIT
orders	_	_	O
of	_	_	O
milk	_	_	O
.	_	_	O
Additionally	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
70	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
delivery	_	_	O
trips	_	_	O
must	_	_	O
be	_	_	O
by	_	_	O
bike	_	_	B-VAR
to	_	_	O
reduce	_	_	O
the	_	_	O
pollution	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
delivery	_	_	O
trips	_	_	O
must	_	_	O
be	_	_	O
scheduled	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	B-OBJ_NAME
minutes	_	_	I-OBJ_NAME
per	_	_	O
trip	_	_	O
?	_	_	O

Emergency	_	_	O
supplies	_	_	O
need	_	_	O
to	_	_	O
be	_	_	O
delivered	_	_	O
to	_	_	O
a	_	_	O
remote	_	_	O
area	_	_	O
and	_	_	O
can	_	_	O
either	_	_	O
go	_	_	O
by	_	_	O
airplane	_	_	B-VAR
or	_	_	O
helicopter	_	_	B-VAR
.	_	_	O
An	_	_	O
airplane	_	_	B-VAR
can	_	_	O
transport	_	_	O
35	_	_	B-PARAM
units	_	_	O
of	_	_	O
goods	_	_	O
and	_	_	O
takes	_	_	O
30	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
while	_	_	O
a	_	_	O
helicopter	_	_	B-VAR
can	_	_	O
transport	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
goods	_	_	O
and	_	_	O
takes	_	_	O
10	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
due	_	_	O
to	_	_	O
easier	_	_	O
take	_	_	O
-	_	_	O
off	_	_	O
and	_	_	O
landing	_	_	O
.	_	_	O
The	_	_	O
number	_	_	O
of	_	_	O
helicopters	_	_	B-VAR
must	_	_	B-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
airplanes	_	_	B-VAR
.	_	_	O
Additionally	_	_	O
,	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
airplanes	_	_	B-VAR
to	_	_	O
fully	_	_	O
utilize	_	_	O
the	_	_	O
landing	_	_	O
space	_	_	O
.	_	_	O
If	_	_	O
there	_	_	O
needs	_	_	O
to	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
goods	_	_	O
transported	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
transportation	_	_	O
should	_	_	O
be	_	_	O
utilized	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
minutes	_	_	I-OBJ_NAME
needed	_	_	O
?	_	_	O

A	_	_	O
house	_	_	O
painting	_	_	O
company	_	_	O
can	_	_	O
transport	_	_	O
their	_	_	O
paint	_	_	O
in	_	_	O
large	_	_	B-VAR
cans	_	_	I-VAR
or	_	_	O
small	_	_	B-VAR
cans	_	_	I-VAR
.	_	_	O
Large	_	_	B-VAR
cans	_	_	I-VAR
can	_	_	O
hold	_	_	O
6	_	_	B-PARAM
litres	_	_	O
of	_	_	O
paint	_	_	O
while	_	_	O
small	_	_	B-VAR
cans	_	_	I-VAR
can	_	_	O
hold	_	_	O
2	_	_	B-PARAM
litres	_	_	O
of	_	_	O
paint	_	_	O
.	_	_	O
Since	_	_	O
small	_	_	B-VAR
cans	_	_	I-VAR
can	_	_	O
be	_	_	O
used	_	_	O
up	_	_	O
quickly	_	_	O
and	_	_	O
thus	_	_	O
,	_	_	O
not	_	_	O
dry	_	_	O
up	_	_	O
as	_	_	O
easily	_	_	O
,	_	_	O
the	_	_	O
company	_	_	O
wants	_	_	O
to	_	_	O
have	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
cans	_	_	O
be	_	_	O
large	_	_	B-VAR
cans	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
there	_	_	O
has	_	_	O
to	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
large	_	_	B-VAR
cans	_	_	I-VAR
especially	_	_	O
for	_	_	O
the	_	_	O
basic	_	_	O
colours	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
company	_	_	O
needs	_	_	O
to	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
120	_	_	B-LIMIT
litres	_	_	O
of	_	_	O
paint	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
size	_	_	O
of	_	_	O
cans	_	_	O
should	_	_	O
be	_	_	O
transported	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
cans	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
researcher	_	_	O
is	_	_	O
transporting	_	_	O
their	_	_	O
arsenal	_	_	O
of	_	_	O
imaging	_	_	O
systems	_	_	O
using	_	_	O
two	_	_	O
different	_	_	O
methods	_	_	O
,	_	_	O
by	_	_	O
delivery	_	_	B-VAR
truck	_	_	I-VAR
and	_	_	O
by	_	_	O
van	_	_	B-VAR
.	_	_	O
Transporting	_	_	O
by	_	_	O
delivery	_	_	B-VAR
truck	_	_	I-VAR
takes	_	_	O
12	_	_	B-PARAM
hours	_	_	B-OBJ_NAME
and	_	_	O
costs	_	_	O
$	_	_	O
300	_	_	B-PARAM
per	_	_	O
trip	_	_	O
.	_	_	O
Transporting	_	_	O
by	_	_	O
van	_	_	B-VAR
takes	_	_	O
10	_	_	B-PARAM
hours	_	_	B-OBJ_NAME
and	_	_	O
costs	_	_	O
$	_	_	O
200	_	_	B-PARAM
per	_	_	O
trip	_	_	O
.	_	_	O
The	_	_	O
researcher	_	_	O
needs	_	_	B-CONST_DIR
to	_	_	I-CONST_DIR
transport	_	_	I-CONST_DIR
20	_	_	B-LIMIT
trips	_	_	O
worth	_	_	O
of	_	_	O
equipment	_	_	O
and	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
5500	_	_	B-LIMIT
.	_	_	O
Additionally	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
transports	_	_	O
by	_	_	O
the	_	_	O
delivery	_	_	B-VAR
truck	_	_	I-VAR
must	_	_	O
be	_	_	O
less	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
transports	_	_	O
by	_	_	O
van	_	_	B-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
transportation	_	_	O
method	_	_	O
should	_	_	O
they	_	_	O
use	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
hours	_	_	I-OBJ_NAME
spent	_	_	O
on	_	_	O
delivery	_	_	O
?	_	_	O

A	_	_	O
waste	_	_	O
treatment	_	_	O
company	_	_	O
must	_	_	O
remove	_	_	O
waste	_	_	O
using	_	_	O
a	_	_	O
large	_	_	B-VAR
container	_	_	I-VAR
or	_	_	O
a	_	_	O
medium	_	_	B-VAR
container	_	_	I-VAR
.	_	_	O
A	_	_	O
large	_	_	B-VAR
container	_	_	I-VAR
can	_	_	O
take	_	_	O
5	_	_	B-PARAM
tons	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
waste	_	_	I-OBJ_NAME
while	_	_	O
a	_	_	O
medium	_	_	B-VAR
container	_	_	I-VAR
can	_	_	O
take	_	_	O
3.5	_	_	B-PARAM
tons	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
waste	_	_	I-OBJ_NAME
.	_	_	O
The	_	_	O
treatment	_	_	O
plant	_	_	O
has	_	_	O
available	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
40	_	_	B-LIMIT
large	_	_	B-VAR
containers	_	_	I-VAR
and	_	_	O
35	_	_	B-LIMIT
medium	_	_	B-VAR
containers	_	_	I-VAR
.	_	_	O
Additionally	_	_	O
,	_	_	O
due	_	_	O
to	_	_	O
logistics	_	_	O
in	_	_	O
the	_	_	O
storage	_	_	O
warehouse	_	_	O
,	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
65	_	_	B-LIMIT
total	_	_	O
containers	_	_	O
and	_	_	O
they	_	_	O
must	_	_	O
use	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
6	_	_	B-LIMIT
medium	_	_	B-VAR
containers	_	_	I-VAR
.	_	_	O
Finally	_	_	O
,	_	_	O
there	_	_	O
must	_	_	B-CONST_DIR
be	_	_	I-CONST_DIR
twice	_	_	B-PARAM
as	_	_	O
many	_	_	O
medium	_	_	B-VAR
containers	_	_	I-VAR
than	_	_	O
large	_	_	B-VAR
containers	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
container	_	_	O
should	_	_	O
they	_	_	O
use	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
waste	_	_	I-OBJ_NAME
they	_	_	O
can	_	_	O
transport	_	_	O
?	_	_	O

A	_	_	O
clothing	_	_	O
manufacturing	_	_	O
company	_	_	O
needs	_	_	O
to	_	_	O
transport	_	_	O
their	_	_	O
product	_	_	O
by	_	_	O
cargo	_	_	B-VAR
ship	_	_	I-VAR
or	_	_	O
airplane	_	_	B-VAR
.	_	_	O
A	_	_	O
cargo	_	_	B-VAR
ship	_	_	I-VAR
can	_	_	O
transport	_	_	O
40	_	_	B-PARAM
units	_	_	O
per	_	_	O
trip	_	_	O
while	_	_	O
by	_	_	O
airplane	_	_	B-VAR
can	_	_	O
transport	_	_	O
60	_	_	B-PARAM
units	_	_	O
per	_	_	O
trip	_	_	O
.	_	_	O
A	_	_	O
cargo	_	_	B-VAR
ship	_	_	I-VAR
produces	_	_	O
20	_	_	B-PARAM
units	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
pollution	_	_	I-OBJ_NAME
and	_	_	O
an	_	_	O
airplane	_	_	B-VAR
produces	_	_	O
35	_	_	B-PARAM
units	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
pollution	_	_	I-OBJ_NAME
.	_	_	O
There	_	_	O
can	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
6	_	_	B-LIMIT
airplane	_	_	B-VAR
trips	_	_	I-VAR
made	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
25	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
all	_	_	O
trips	_	_	O
must	_	_	O
be	_	_	O
made	_	_	O
by	_	_	O
cargo	_	_	B-VAR
ship	_	_	I-VAR
.	_	_	O
The	_	_	O
company	_	_	O
needs	_	_	O
to	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
750	_	_	B-LIMIT
units	_	_	O
of	_	_	O
their	_	_	O
product	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
transportation	_	_	O
should	_	_	O
they	_	_	O
use	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
pollution	_	_	I-OBJ_NAME
produced	_	_	O
?	_	_	O

A	_	_	O
city	_	_	O
’s	_	_	O
dispatching	_	_	O
service	_	_	O
needs	_	_	O
to	_	_	O
send	_	_	O
out	_	_	O
firefighting	_	_	O
units	_	_	O
for	_	_	O
an	_	_	O
upcoming	_	_	O
extremely	_	_	O
dry	_	_	O
period	_	_	O
.	_	_	O
Firefighting	_	_	O
units	_	_	O
can	_	_	O
either	_	_	O
send	_	_	O
units	_	_	O
of	_	_	O
firefighters	_	_	B-VAR
or	_	_	O
volunteer	_	_	B-VAR
fire	_	_	I-VAR
patrols	_	_	I-VAR
.	_	_	O
Firemen	_	_	B-VAR
can	_	_	O
put	_	_	O
out	_	_	O
1000	_	_	B-LIMIT
sq	_	_	B-OBJ_NAME
ft	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
fire	_	_	I-OBJ_NAME
per	_	_	O
trip	_	_	O
and	_	_	O
takes	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
.	_	_	O
Volunteer	_	_	B-VAR
fire	_	_	I-VAR
patrols	_	_	I-VAR
can	_	_	O
put	_	_	O
out	_	_	O
800	_	_	B-LIMIT
sq	_	_	B-OBJ_NAME
ft	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
fire	_	_	I-OBJ_NAME
per	_	_	O
trip	_	_	O
and	_	_	O
takes	_	_	O
12	_	_	B-PARAM
minutes	_	_	O
.	_	_	O
There	_	_	O
is	_	_	O
a	_	_	O
dry	_	_	O
period	_	_	O
of	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
8000	_	_	B-LIMIT
minutes	_	_	I-LIMIT
that	_	_	O
has	_	_	O
to	_	_	O
be	_	_	O
covered	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
all	_	_	O
units	_	_	O
must	_	_	O
be	_	_	O
volunteer	_	_	B-VAR
fire	_	_	I-VAR
patrols	_	_	I-VAR
due	_	_	O
to	_	_	O
shortages	_	_	O
in	_	_	O
budget	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
there	_	_	O
can	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
units	_	_	O
dispatched	_	_	O
because	_	_	O
the	_	_	O
city	_	_	O
has	_	_	O
limited	_	_	O
fire	_	_	O
trucks	_	_	O
.	_	_	O
How	_	_	O
should	_	_	O
the	_	_	O
dispatcher	_	_	O
allocate	_	_	O
resources	_	_	O
to	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
firefighting	_	_	O
units	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
sq	_	_	I-OBJ_NAME
ft	_	_	I-OBJ_NAME
that	_	_	I-OBJ_NAME
can	_	_	I-OBJ_NAME
be	_	_	I-OBJ_NAME
put	_	_	I-OBJ_NAME
out	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
manufacturing	_	_	O
plant	_	_	O
has	_	_	O
the	_	_	O
option	_	_	O
to	_	_	O
offer	_	_	O
a	_	_	O
shuttle	_	_	B-VAR
bus	_	_	I-VAR
and	_	_	O
outsource	_	_	O
to	_	_	O
a	_	_	O
taxi	_	_	B-VAR
service	_	_	I-VAR
.	_	_	O
A	_	_	O
shuttle	_	_	B-VAR
bus	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
20	_	_	B-PARAM
and	_	_	O
carries	_	_	O
7	_	_	B-PARAM
workers	_	_	O
,	_	_	O
whereas	_	_	O
a	_	_	O
taxi	_	_	B-VAR
service	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
carries	_	_	O
5	_	_	B-PARAM
workers	_	_	O
.	_	_	O
The	_	_	O
manufacturing	_	_	O
plant	_	_	O
has	_	_	O
to	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
250	_	_	B-LIMIT
workers	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
5	_	_	B-LIMIT
shuttle	_	_	B-VAR
buses	_	_	I-VAR
can	_	_	O
be	_	_	O
used	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
transport	_	_	O
should	_	_	O
be	_	_	O
taken	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
cost	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
composting	_	_	O
company	_	_	O
can	_	_	O
store	_	_	O
compost	_	_	O
in	_	_	O
medium	_	_	B-VAR
containers	_	_	I-VAR
and	_	_	O
large	_	_	B-VAR
containers	_	_	I-VAR
.	_	_	O
A	_	_	O
medium	_	_	B-VAR
container	_	_	I-VAR
needs	_	_	O
to	_	_	O
be	_	_	O
checked	_	_	O
5	_	_	B-PARAM
times	_	_	B-OBJ_NAME
a	_	_	I-OBJ_NAME
week	_	_	I-OBJ_NAME
and	_	_	O
can	_	_	O
store	_	_	O
25	_	_	B-PARAM
units	_	_	O
of	_	_	O
compost	_	_	O
.	_	_	O
A	_	_	O
large	_	_	B-VAR
container	_	_	I-VAR
needs	_	_	O
to	_	_	O
be	_	_	O
checked	_	_	O
2	_	_	B-PARAM
times	_	_	B-OBJ_NAME
a	_	_	I-OBJ_NAME
week	_	_	I-OBJ_NAME
and	_	_	O
can	_	_	O
store	_	_	O
40	_	_	B-PARAM
units	_	_	O
of	_	_	O
compost	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
needs	_	_	O
to	_	_	O
store	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
compost	_	_	O
and	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-LIMIT
medium	_	_	B-VAR
containers	_	_	I-VAR
.	_	_	O
There	_	_	O
must	_	_	O
also	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
2	_	_	B-LIMIT
large	_	_	B-VAR
containers	_	_	I-VAR
and	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
large	_	_	B-VAR
containers	_	_	I-VAR
must	_	_	B-CONST_DIR
be	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
much	_	_	O
as	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
medium	_	_	B-VAR
containers	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
containers	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
times	_	_	I-OBJ_NAME
checking	_	_	I-OBJ_NAME
containers	_	_	I-OBJ_NAME
?	_	_	O

An	_	_	O
airport	_	_	O
can	_	_	O
transport	_	_	O
travelers	_	_	O
using	_	_	O
commercial	_	_	B-VAR
planes	_	_	I-VAR
and	_	_	O
private	_	_	B-VAR
planes	_	_	I-VAR
.	_	_	O
A	_	_	O
commercial	_	_	B-VAR
plane	_	_	I-VAR
can	_	_	O
carry	_	_	O
180	_	_	B-PARAM
travelers	_	_	O
while	_	_	O
a	_	_	O
private	_	_	B-VAR
plane	_	_	I-VAR
can	_	_	O
carry	_	_	O
30	_	_	B-PARAM
travelers	_	_	O
.	_	_	O
Because	_	_	O
the	_	_	O
destination	_	_	O
is	_	_	O
more	_	_	O
remote	_	_	O
,	_	_	O
there	_	_	O
are	_	_	O
few	_	_	O
airport	_	_	O
runways	_	_	O
.	_	_	O
Therefore	_	_	O
,	_	_	O
there	_	_	O
must	_	_	B-CONST_DIR
be	_	_	I-CONST_DIR
twice	_	_	B-PARAM
as	_	_	O
many	_	_	O
private	_	_	B-VAR
planes	_	_	I-VAR
as	_	_	O
commercial	_	_	B-VAR
planes	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
airport	_	_	O
needs	_	_	O
to	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3500	_	_	B-LIMIT
travelers	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
planes	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
planes	_	_	I-OBJ_NAME
used	_	_	O
.	_	_	O

A	_	_	O
gas	_	_	O
company	_	_	O
can	_	_	O
transport	_	_	O
gas	_	_	O
using	_	_	O
a	_	_	O
pipeline	_	_	B-VAR
or	_	_	O
by	_	_	O
train	_	_	B-VAR
.	_	_	O
A	_	_	O
pipeline	_	_	B-VAR
can	_	_	O
carry	_	_	O
8000	_	_	B-PARAM
units	_	_	O
of	_	_	O
gas	_	_	O
and	_	_	O
a	_	_	O
train	_	_	B-VAR
can	_	_	O
carry	_	_	O
2000	_	_	B-PARAM
units	_	_	O
of	_	_	O
gas	_	_	O
every	_	_	O
day	_	_	O
.	_	_	O
Due	_	_	O
to	_	_	O
recent	_	_	O
environmental	_	_	O
changes	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
trains	_	_	B-VAR
used	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-PARAM
as	_	_	O
many	_	_	O
as	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
pipelines	_	_	B-VAR
.	_	_	O
If	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1000000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
gas	_	_	O
needs	_	_	O
to	_	_	O
be	_	_	O
transported	_	_	O
every	_	_	O
day	_	_	O
,	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
pipelines	_	_	I-OBJ_NAME
and	_	_	I-OBJ_NAME
trains	_	_	I-OBJ_NAME
needed	_	_	I-OBJ_NAME
.	_	_	O
