-DOCSTART-	_	_	O

A	_	_	O
flooring	_	_	O
company	_	_	O
produces	_	_	O
engineered	_	_	O
hardwood	_	_	B-VAR
and	_	_	O
vinyl	_	_	B-VAR
planks	_	_	I-VAR
.	_	_	O
Their	_	_	O
sales	_	_	O
forecasts	_	_	O
show	_	_	O
an	_	_	O
expected	_	_	O
demand	_	_	O
of	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20,000	_	_	B-LIMIT
square	_	_	O
foot	_	_	O
of	_	_	O
hardwood	_	_	B-VAR
and	_	_	O
10,000	_	_	B-LIMIT
square	_	_	O
feet	_	_	O
of	_	_	O
vinyl	_	_	B-VAR
planks	_	_	I-VAR
each	_	_	O
week	_	_	O
.	_	_	O
To	_	_	O
satisfy	_	_	O
a	_	_	O
shipping	_	_	O
contract	_	_	O
,	_	_	O
a	_	_	O
total	_	_	O
of	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
60,000	_	_	B-LIMIT
square	_	_	O
feet	_	_	O
of	_	_	O
flooring	_	_	O
much	_	_	O
be	_	_	O
shipped	_	_	O
each	_	_	O
week	_	_	O
.	_	_	O
Due	_	_	O
to	_	_	O
a	_	_	O
labor	_	_	O
shortage	_	_	O
issue	_	_	O
,	_	_	O
no	_	_	B-CONST_DIR
more	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
50,000	_	_	B-LIMIT
square	_	_	O
feet	_	_	O
of	_	_	O
hardwood	_	_	B-VAR
and	_	_	O
30,000	_	_	B-LIMIT
square	_	_	O
feet	_	_	O
of	_	_	O
vinyl	_	_	B-VAR
can	_	_	O
be	_	_	O
produced	_	_	O
weekly	_	_	O
.	_	_	O
If	_	_	O
a	_	_	O
square	_	_	O
foot	_	_	O
of	_	_	O
hardwood	_	_	B-VAR
flooring	_	_	O
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
2.5	_	_	B-PARAM
and	_	_	O
a	_	_	O
square	_	_	O
foot	_	_	O
of	_	_	O
vinyl	_	_	B-VAR
planks	_	_	I-VAR
produces	_	_	O
a	_	_	O
$	_	_	O
3	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
flooring	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
weekly	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
company	_	_	O
's	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

John	_	_	O
has	_	_	B-CONST_DIR
a	_	_	O
300	_	_	B-LIMIT
acre	_	_	O
berry	_	_	O
farm	_	_	O
on	_	_	O
which	_	_	O
to	_	_	O
plant	_	_	O
blueberries	_	_	B-VAR
and	_	_	O
raspberries	_	_	B-VAR
.	_	_	I-VAR
John	_	_	O
has	_	_	O
$	_	_	O
10000	_	_	B-LIMIT
to	_	_	O
spend	_	_	O
on	_	_	O
watering	_	_	O
and	_	_	O
575	_	_	B-LIMIT
days	_	_	O
worth	_	_	O
of	_	_	O
labor	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
For	_	_	O
each	_	_	O
acre	_	_	O
of	_	_	O
blueberries	_	_	B-VAR
,	_	_	O
6	_	_	B-PARAM
days	_	_	O
worth	_	_	O
of	_	_	O
labor	_	_	O
and	_	_	O
$	_	_	O
22	_	_	B-PARAM
in	_	_	O
watering	_	_	O
costs	_	_	O
is	_	_	O
required	_	_	O
.	_	_	O
For	_	_	O
each	_	_	O
acre	_	_	O
of	_	_	O
raspberries	_	_	B-VAR
,	_	_	I-VAR
3	_	_	B-PARAM
days	_	_	O
worth	_	_	O
of	_	_	O
labor	_	_	O
and	_	_	O
$	_	_	O
25	_	_	B-PARAM
in	_	_	O
watering	_	_	O
costs	_	_	O
is	_	_	O
required	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
blueberries	_	_	B-VAR
is	_	_	O
$	_	_	O
56	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
raspberries	_	_	B-VAR
is	_	_	O
$	_	_	O
75	_	_	B-PARAM
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
problem	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
.	_	_	O

An	_	_	O
electronics	_	_	O
store	_	_	O
wants	_	_	O
to	_	_	O
optimize	_	_	O
how	_	_	O
many	_	_	O
phones	_	_	B-VAR
and	_	_	O
laptops	_	_	B-VAR
are	_	_	O
enough	_	_	O
to	_	_	O
keep	_	_	O
in	_	_	O
inventory	_	_	O
.	_	_	O
A	_	_	O
phone	_	_	B-VAR
will	_	_	O
earn	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
120	_	_	B-PARAM
in	_	_	O
profits	_	_	B-OBJ_NAME
,	_	_	O
and	_	_	O
a	_	_	O
laptop	_	_	B-VAR
will	_	_	O
earn	_	_	O
$	_	_	O
40	_	_	B-PARAM
.	_	_	O
A	_	_	O
phone	_	_	B-VAR
requires	_	_	O
1	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
of	_	_	O
floor	_	_	O
space	_	_	O
,	_	_	O
whereas	_	_	O
a	_	_	O
laptop	_	_	B-VAR
requires	_	_	O
4	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
.	_	_	O
In	_	_	O
total	_	_	O
,	_	_	O
400	_	_	B-LIMIT
sq	_	_	O
ft	_	_	O
of	_	_	O
floor	_	_	O
space	_	_	O
is	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
The	_	_	O
store	_	_	O
stocks	_	_	O
only	_	_	O
phones	_	_	B-VAR
and	_	_	O
laptops	_	_	B-VAR
.	_	_	O
Corporate	_	_	O
has	_	_	O
required	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
80	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
all	_	_	O
appliances	_	_	O
in	_	_	O
stock	_	_	O
be	_	_	O
laptops	_	_	B-VAR
.	_	_	O
Finally	_	_	O
,	_	_	O
a	_	_	O
phone	_	_	B-VAR
costs	_	_	O
$	_	_	O
400	_	_	B-PARAM
for	_	_	O
the	_	_	O
store	_	_	O
,	_	_	O
and	_	_	O
a	_	_	O
laptop	_	_	B-VAR
,	_	_	O
$	_	_	O
100	_	_	B-PARAM
.	_	_	O
The	_	_	O
store	_	_	O
wants	_	_	O
to	_	_	O
spend	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
6000	_	_	B-LIMIT
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
that	_	_	O
can	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
store	_	_	O
's	_	_	O
profit	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
food	_	_	O
truck	_	_	O
owner	_	_	O
can	_	_	O
spend	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
20000	_	_	B-LIMIT
on	_	_	O
mangos	_	_	B-VAR
and	_	_	O
guavas	_	_	B-VAR
.	_	_	O
A	_	_	O
mango	_	_	B-VAR
costs	_	_	O
the	_	_	O
food	_	_	O
truck	_	_	O
owner	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
a	_	_	O
guava	_	_	B-VAR
costs	_	_	O
him	_	_	O
$	_	_	O
3	_	_	B-PARAM
.	_	_	O
Spices	_	_	O
are	_	_	O
added	_	_	O
and	_	_	O
each	_	_	O
mango	_	_	B-VAR
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
3	_	_	B-PARAM
while	_	_	O
each	_	_	O
guava	_	_	B-VAR
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
4	_	_	B-PARAM
.	_	_	O
The	_	_	O
owner	_	_	O
estimates	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
mangos	_	_	B-VAR
but	_	_	O
at	_	_	B-CONST_DIR
the	_	_	I-CONST_DIR
most	_	_	I-CONST_DIR
150	_	_	B-LIMIT
are	_	_	O
sold	_	_	O
each	_	_	O
month	_	_	O
.	_	_	O
He	_	_	O
also	_	_	O
estimates	_	_	O
that	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
guavas	_	_	B-VAR
sold	_	_	O
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
a	_	_	O
third	_	_	B-PARAM
of	_	_	O
the	_	_	O
mangos	_	_	B-VAR
sold	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
mangos	_	_	B-VAR
and	_	_	O
guavas	_	_	B-VAR
should	_	_	O
be	_	_	O
sold	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

Jordan	_	_	O
is	_	_	O
a	_	_	O
chef	_	_	O
.	_	_	O
He	_	_	O
wants	_	_	O
to	_	_	O
design	_	_	O
a	_	_	O
diet	_	_	O
consisting	_	_	O
of	_	_	O
Kebabs	_	_	B-VAR
and	_	_	O
Rice	_	_	B-VAR
.	_	_	O
Assume	_	_	O
that	_	_	O
each	_	_	O
serving	_	_	O
of	_	_	O
Rice	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
3	_	_	B-PARAM
and	_	_	O
contains	_	_	O
300	_	_	B-PARAM
calories	_	_	O
and	_	_	O
4.5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
.	_	_	O
Assume	_	_	O
that	_	_	O
each	_	_	O
serving	_	_	O
of	_	_	O
Kebab	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
2	_	_	B-PARAM
and	_	_	O
contains	_	_	O
200	_	_	B-PARAM
calories	_	_	O
and	_	_	O
4	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
.	_	_	O
He	_	_	O
's	_	_	O
interested	_	_	O
in	_	_	O
spending	_	_	O
as	_	_	O
little	_	_	O
money	_	_	O
as	_	_	O
possible	_	_	O
but	_	_	O
he	_	_	O
wants	_	_	O
to	_	_	O
ensure	_	_	O
that	_	_	O
his	_	_	O
meals	_	_	O
have	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
2200	_	_	B-LIMIT
calories	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
protein	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
Formulate	_	_	O
a	_	_	O
linear	_	_	O
programming	_	_	O
problem	_	_	O
that	_	_	O
will	_	_	O
help	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
cost	_	_	B-OBJ_NAME
of	_	_	O
the	_	_	O
diet	_	_	O
.	_	_	O

A	_	_	O
teddy	_	_	O
bear	_	_	O
company	_	_	O
produces	_	_	O
three	_	_	O
different	_	_	O
colored	_	_	O
bears	_	_	O
:	_	_	O
black	_	_	O
,	_	_	O
white	_	_	O
,	_	_	O
and	_	_	O
brown	_	_	O
.	_	_	O
These	_	_	O
bears	_	_	O
are	_	_	O
made	_	_	O
in	_	_	O
two	_	_	O
different	_	_	O
factories	_	_	O
.	_	_	O
Running	_	_	O
factory	_	_	B-VAR
1	_	_	I-VAR
for	_	_	O
1	_	_	O
hour	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
300	_	_	B-PARAM
and	_	_	O
produces	_	_	O
5	_	_	B-PARAM
black	_	_	O
teddy	_	_	O
bears	_	_	O
,	_	_	O
6	_	_	B-PARAM
white	_	_	O
teddy	_	_	O
bears	_	_	O
,	_	_	O
and	_	_	O
3	_	_	B-PARAM
brown	_	_	O
ones	_	_	O
.	_	_	O
Running	_	_	O
factory	_	_	B-VAR
2	_	_	I-VAR
for	_	_	O
1	_	_	O
hour	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
600	_	_	B-PARAM
and	_	_	O
produces	_	_	O
10	_	_	B-PARAM
black	_	_	O
teddy	_	_	O
bears	_	_	O
and	_	_	O
10	_	_	B-PARAM
white	_	_	O
teddy	_	_	O
bears	_	_	O
.	_	_	O
(	_	_	O
but	_	_	O
no	_	_	O
brown	_	_	O
ones	_	_	O
)	_	_	O
.	_	_	O
To	_	_	O
meet	_	_	O
children	_	_	O
's	_	_	O
demand	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
black	_	_	O
teddy	_	_	O
bears	_	_	O
,	_	_	O
5	_	_	B-LIMIT
white	_	_	O
teddy	_	_	O
bears	_	_	O
,	_	_	O
and	_	_	O
15	_	_	B-LIMIT
brown	_	_	O
teddy	_	_	O
bears	_	_	O
must	_	_	O
be	_	_	O
made	_	_	O
daily	_	_	O
.	_	_	O
Given	_	_	O
this	_	_	O
information	_	_	O
,	_	_	O
develop	_	_	O
a	_	_	O
linear	_	_	O
programming	_	_	O
problem	_	_	O
assuming	_	_	O
the	_	_	O
teddy	_	_	O
bear	_	_	O
company	_	_	O
wants	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
cost	_	_	B-OBJ_NAME
of	_	_	O
production	_	_	O
.	_	_	O

A	_	_	O
grocery	_	_	O
store	_	_	O
wants	_	_	O
to	_	_	O
liquidate	_	_	O
its	_	_	O
stock	_	_	B-CONST_DIR
of	_	_	O
10	_	_	B-LIMIT
apples	_	_	O
,	_	_	O
20	_	_	B-LIMIT
bananas	_	_	O
,	_	_	O
and	_	_	O
80	_	_	B-LIMIT
grapes	_	_	O
.	_	_	O
Given	_	_	O
past	_	_	O
experience	_	_	O
,	_	_	O
the	_	_	O
store	_	_	O
knows	_	_	O
that	_	_	O
they	_	_	O
can	_	_	O
propose	_	_	O
a	_	_	O
banana	_	_	B-VAR
-	_	_	I-VAR
haters	_	_	I-VAR
package	_	_	I-VAR
with	_	_	O
6	_	_	B-PARAM
apples	_	_	O
and	_	_	O
30	_	_	B-PARAM
grapes	_	_	O
and	_	_	O
that	_	_	O
this	_	_	O
package	_	_	O
will	_	_	O
bring	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
six	_	_	B-PARAM
euros	_	_	O
.	_	_	O
Similarly	_	_	O
,	_	_	O
they	_	_	O
can	_	_	O
prepare	_	_	O
a	_	_	O
combo	_	_	B-VAR
package	_	_	I-VAR
with	_	_	O
5	_	_	B-PARAM
apples	_	_	O
,	_	_	O
6	_	_	B-PARAM
bananas	_	_	O
,	_	_	O
and	_	_	O
20	_	_	B-PARAM
grapes	_	_	O
,	_	_	O
yielding	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
seven	_	_	B-PARAM
euros	_	_	O
.	_	_	O
They	_	_	O
know	_	_	O
they	_	_	O
can	_	_	O
sell	_	_	O
any	_	_	O
quantity	_	_	O
of	_	_	O
these	_	_	O
two	_	_	O
packages	_	_	O
within	_	_	O
the	_	_	O
availability	_	_	O
of	_	_	O
its	_	_	O
stock	_	_	O
.	_	_	O
What	_	_	O
quantity	_	_	O
of	_	_	O
each	_	_	O
package	_	_	O
,	_	_	O
banana	_	_	B-VAR
-	_	_	I-VAR
haters	_	_	I-VAR
packages	_	_	I-VAR
and	_	_	O
combo	_	_	B-VAR
packages	_	_	I-VAR
,	_	_	O
should	_	_	O
the	_	_	O
store	_	_	O
prepare	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
net	_	_	B-OBJ_NAME
profit	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
candy	_	_	O
store	_	_	O
mixes	_	_	O
regular	_	_	O
candy	_	_	O
and	_	_	O
sour	_	_	O
candy	_	_	O
to	_	_	O
prepare	_	_	O
two	_	_	O
products	_	_	O
,	_	_	O
regular	_	_	B-VAR
mix	_	_	I-VAR
and	_	_	O
sour	_	_	B-VAR
surprise	_	_	I-VAR
mix	_	_	I-VAR
.	_	_	O
Each	_	_	O
kilogram	_	_	O
of	_	_	O
the	_	_	O
regular	_	_	B-VAR
mix	_	_	I-VAR
contains	_	_	O
0.8	_	_	B-PARAM
kg	_	_	O
of	_	_	O
regular	_	_	O
candy	_	_	O
and	_	_	O
0.2	_	_	B-PARAM
kg	_	_	O
of	_	_	O
sour	_	_	O
candy	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
kilogram	_	_	O
of	_	_	O
the	_	_	O
regular	_	_	B-VAR
mix	_	_	I-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
.	_	_	O
Each	_	_	O
kilogram	_	_	O
of	_	_	O
the	_	_	O
sour	_	_	B-VAR
surprise	_	_	I-VAR
mix	_	_	I-VAR
contains	_	_	O
0.1	_	_	B-PARAM
kg	_	_	O
of	_	_	O
regular	_	_	O
candy	_	_	O
and	_	_	O
0.9	_	_	B-PARAM
kg	_	_	O
of	_	_	O
sour	_	_	O
candy	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
kilogram	_	_	O
of	_	_	O
the	_	_	O
sour	_	_	B-VAR
surprise	_	_	I-VAR
mix	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
.	_	_	O
The	_	_	O
candy	_	_	O
store	_	_	O
has	_	_	O
80	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
regular	_	_	O
candy	_	_	O
and	_	_	O
60	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
sour	_	_	O
candy	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
How	_	_	O
many	_	_	O
kilograms	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
candy	_	_	O
mix	_	_	O
should	_	_	O
be	_	_	O
created	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profits	_	_	B-OBJ_NAME
?	_	_	O

Ayse	_	_	O
produces	_	_	O
a	_	_	O
plant	_	_	O
growth	_	_	O
compound	_	_	O
by	_	_	O
mixing	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
fertilizer	_	_	O
:	_	_	O
C	_	_	B-VAR
and	_	_	O
Y.	_	_	B-VAR
This	_	_	O
growth	_	_	O
compound	_	_	O
must	_	_	O
contain	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
units	_	_	O
of	_	_	O
nitrous	_	_	O
oxide	_	_	O
and	_	_	O
8	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamin	_	_	O
mix	_	_	O
.	_	_	O
Fertilizer	_	_	B-VAR
C	_	_	I-VAR
and	_	_	O
Y	_	_	B-VAR
cost	_	_	B-OBJ_NAME
$	_	_	O
2	_	_	B-PARAM
and	_	_	O
$	_	_	O
3	_	_	B-PARAM
per	_	_	O
kg	_	_	O
respectively	_	_	O
.	_	_	O
Fertilizer	_	_	B-VAR
C	_	_	I-VAR
contains	_	_	O
1.5	_	_	B-PARAM
units	_	_	O
of	_	_	O
nitrous	_	_	O
oxide	_	_	O
per	_	_	O
kg	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
mix	_	_	O
per	_	_	O
kg	_	_	O
.	_	_	O
Fertilizer	_	_	B-VAR
Y	_	_	I-VAR
contains	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
nitrous	_	_	O
oxide	_	_	O
per	_	_	O
kg	_	_	O
and	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
vitamin	_	_	O
mix	_	_	O
per	_	_	O
kg	_	_	O
.	_	_	O
Determine	_	_	O
the	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
of	_	_	O
Ayse	_	_	O
's	_	_	O
compound	_	_	O
.	_	_	O

A	_	_	O
bakery	_	_	O
bakes	_	_	O
bagels	_	_	B-VAR
and	_	_	O
croissants	_	_	B-VAR
.	_	_	O
A	_	_	O
batch	_	_	O
of	_	_	O
bagels	_	_	B-VAR
can	_	_	O
be	_	_	O
made	_	_	O
using	_	_	O
2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
oven	_	_	O
time	_	_	O
and	_	_	O
0.25	_	_	B-PARAM
hours	_	_	O
of	_	_	O
pastry	_	_	O
chef	_	_	O
time	_	_	O
.	_	_	O
A	_	_	O
batch	_	_	O
of	_	_	O
croissants	_	_	B-VAR
is	_	_	O
more	_	_	O
complicated	_	_	O
,	_	_	O
so	_	_	O
while	_	_	O
they	_	_	O
take	_	_	O
1	_	_	B-PARAM
hour	_	_	O
of	_	_	O
oven	_	_	O
time	_	_	O
,	_	_	O
they	_	_	O
take	_	_	O
2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
pastry	_	_	O
chef	_	_	O
time	_	_	O
.	_	_	O
In	_	_	O
a	_	_	O
day	_	_	O
,	_	_	O
the	_	_	O
bakery	_	_	O
has	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
70	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
the	_	_	O
oven	_	_	O
and	_	_	O
32	_	_	B-LIMIT
pastry	_	_	O
chef	_	_	O
hours	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
Using	_	_	O
all	_	_	O
the	_	_	O
available	_	_	O
capacity	_	_	O
,	_	_	O
what	_	_	O
is	_	_	O
the	_	_	O
maximum	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
the	_	_	O
bakery	_	_	O
can	_	_	O
generate	_	_	O
assuming	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
batch	_	_	O
is	_	_	O
$	_	_	O
20	_	_	B-PARAM
and	_	_	O
$	_	_	O
40	_	_	B-PARAM
respectively	_	_	O
for	_	_	O
a	_	_	O
batch	_	_	O
of	_	_	O
bagels	_	_	B-VAR
and	_	_	O
a	_	_	O
batch	_	_	O
of	_	_	O
croissants	_	_	B-VAR
.	_	_	O

A	_	_	O
farmer	_	_	O
wants	_	_	O
to	_	_	O
manufacture	_	_	O
a	_	_	O
special	_	_	O
plant	_	_	O
nutrition	_	_	O
using	_	_	O
fertilizers	_	_	O
A	_	_	B-VAR
and	_	_	O
B.	_	_	B-VAR
Each	_	_	O
kg	_	_	O
of	_	_	O
fertilizer	_	_	B-VAR
A	_	_	I-VAR
contains	_	_	O
13	_	_	B-PARAM
units	_	_	O
of	_	_	O
nitrogen	_	_	O
,	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
phosphoric	_	_	O
acid	_	_	O
,	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
A	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	B-OBJ_NAME
D.	_	_	I-OBJ_NAME
Each	_	_	O
kg	_	_	O
of	_	_	O
fertilizer	_	_	B-VAR
B	_	_	I-VAR
contains	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
nitrogen	_	_	O
,	_	_	O
14	_	_	B-PARAM
units	_	_	O
of	_	_	O
phosphoric	_	_	O
acid	_	_	O
,	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
A	_	_	O
and	_	_	O
9	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	B-OBJ_NAME
D.	_	_	I-OBJ_NAME
To	_	_	O
be	_	_	O
effective	_	_	O
,	_	_	O
the	_	_	O
plant	_	_	O
nutrition	_	_	O
requires	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
220	_	_	B-LIMIT
units	_	_	O
of	_	_	O
nitrogen	_	_	O
,	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
160	_	_	B-LIMIT
units	_	_	O
of	_	_	O
phosphoric	_	_	O
acid	_	_	O
,	_	_	O
and	_	_	O
no	_	_	B-CONST_DIR
more	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
350	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamin	_	_	O
A.	_	_	O
How	_	_	O
many	_	_	O
kg	_	_	O
of	_	_	O
each	_	_	O
fertilizer	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
vitamin	_	_	I-OBJ_NAME
D	_	_	I-OBJ_NAME
in	_	_	O
the	_	_	O
nutrition	_	_	O
?	_	_	O
What	_	_	O
is	_	_	O
the	_	_	O
minimum	_	_	O
amount	_	_	O
of	_	_	O
vitamin	_	_	O
D	_	_	O
?	_	_	O

A	_	_	O
bakery	_	_	O
uses	_	_	O
a	_	_	O
stand	_	_	O
-	_	_	O
mixer	_	_	O
and	_	_	O
a	_	_	O
slow	_	_	O
bake	_	_	O
oven	_	_	O
to	_	_	O
make	_	_	O
bread	_	_	B-VAR
and	_	_	O
cookies	_	_	B-VAR
.	_	_	O
Each	_	_	O
machine	_	_	O
can	_	_	O
run	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
3000	_	_	B-LIMIT
hours	_	_	O
per	_	_	O
year	_	_	O
.	_	_	O
To	_	_	O
bake	_	_	O
a	_	_	O
loaf	_	_	O
of	_	_	O
bread	_	_	B-VAR
takes	_	_	O
1	_	_	B-PARAM
hour	_	_	O
in	_	_	O
the	_	_	O
stand	_	_	O
mixer	_	_	O
and	_	_	O
3	_	_	B-PARAM
hours	_	_	O
in	_	_	O
the	_	_	O
oven	_	_	O
.	_	_	O
A	_	_	O
batch	_	_	O
of	_	_	O
cookies	_	_	B-VAR
requires	_	_	O
0.5	_	_	B-PARAM
hours	_	_	O
in	_	_	O
the	_	_	O
mixer	_	_	O
and	_	_	O
1	_	_	B-PARAM
hour	_	_	O
in	_	_	O
the	_	_	O
oven	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
loaf	_	_	O
of	_	_	O
bread	_	_	B-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
batch	_	_	O
of	_	_	O
cookies	_	_	B-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
.	_	_	O
How	_	_	O
should	_	_	O
the	_	_	O
bakery	_	_	O
operate	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
total	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
suspicious	_	_	O
factory	_	_	O
has	_	_	B-CONST_DIR
100	_	_	B-LIMIT
sq	_	_	O
.	_	_	O
feet	_	_	O
of	_	_	O
space	_	_	O
.	_	_	O
It	_	_	O
makes	_	_	O
bootleg	_	_	O
phones	_	_	B-VAR
and	_	_	O
laptops	_	_	B-VAR
.	_	_	O
Phones	_	_	B-VAR
require	_	_	O
2	_	_	B-PARAM
hours	_	_	O
of	_	_	O
labor	_	_	O
and	_	_	O
cost	_	_	O
$	_	_	O
12	_	_	B-PARAM
for	_	_	O
each	_	_	O
sq	_	_	O
.	_	_	O
foot	_	_	O
of	_	_	O
space	_	_	O
allocated	_	_	O
for	_	_	O
phone	_	_	B-VAR
production	_	_	O
(	_	_	O
cost	_	_	O
of	_	_	O
electricity	_	_	O
and	_	_	O
equipment	_	_	O
)	_	_	O
.	_	_	O
Laptops	_	_	B-VAR
require	_	_	O
3	_	_	B-PARAM
hours	_	_	O
of	_	_	O
labor	_	_	O
and	_	_	O
cost	_	_	O
$	_	_	O
15	_	_	B-PARAM
for	_	_	O
each	_	_	O
sq	_	_	O
.	_	_	O
foot	_	_	O
of	_	_	O
space	_	_	O
allocated	_	_	O
for	_	_	O
laptop	_	_	B-VAR
production	_	_	O
.	_	_	O
Phones	_	_	B-VAR
produce	_	_	O
a	_	_	O
net	_	_	B-OBJ_NAME
revenue	_	_	I-OBJ_NAME
of	_	_	O
$	_	_	O
50	_	_	B-PARAM
per	_	_	O
sq	_	_	O
.	_	_	O
foot	_	_	O
while	_	_	O
laptops	_	_	B-VAR
produce	_	_	O
a	_	_	O
net	_	_	B-OBJ_NAME
revenue	_	_	I-OBJ_NAME
of	_	_	O
$	_	_	O
70	_	_	B-PARAM
per	_	_	O
sq	_	_	O
.	_	_	O
foot	_	_	O
.	_	_	O
The	_	_	O
factory	_	_	O
wants	_	_	O
to	_	_	O
spend	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
5000	_	_	B-LIMIT
and	_	_	O
2000	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
labor	_	_	O
.	_	_	O
What	_	_	O
is	_	_	O
the	_	_	O
optimal	_	_	O
factory	_	_	O
layout	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
revenue	_	_	B-OBJ_NAME
?	_	_	O

You	_	_	O
are	_	_	O
designing	_	_	O
an	_	_	O
office	_	_	O
space	_	_	O
with	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
desks	_	_	O
:	_	_	O
long	_	_	B-VAR
desks	_	_	I-VAR
and	_	_	O
short	_	_	B-VAR
desks	_	_	I-VAR
.	_	_	O
You	_	_	O
can	_	_	O
spend	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
2000	_	_	B-LIMIT
.	_	_	O
Long	_	_	B-VAR
desks	_	_	I-VAR
cost	_	_	O
$	_	_	O
300	_	_	B-PARAM
,	_	_	O
take	_	_	O
up	_	_	O
10	_	_	B-PARAM
square	_	_	O
feet	_	_	O
of	_	_	O
space	_	_	O
,	_	_	O
and	_	_	O
seat	_	_	B-OBJ_NAME
6	_	_	B-PARAM
employees	_	_	O
.	_	_	O
Short	_	_	B-VAR
desks	_	_	I-VAR
cost	_	_	O
$	_	_	O
100	_	_	B-PARAM
,	_	_	O
take	_	_	O
up	_	_	O
4	_	_	B-PARAM
square	_	_	O
feet	_	_	O
of	_	_	O
space	_	_	O
,	_	_	O
and	_	_	O
seat	_	_	B-OBJ_NAME
2	_	_	B-PARAM
employees	_	_	O
.	_	_	O
The	_	_	O
office	_	_	O
can	_	_	O
have	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
200	_	_	B-LIMIT
square	_	_	O
feet	_	_	O
of	_	_	O
desks	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
desk	_	_	O
should	_	_	O
you	_	_	O
buy	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
seating	_	_	B-OBJ_NAME
availability	_	_	I-OBJ_NAME
?	_	_	O

Mrs.	_	_	O
Watson	_	_	O
wants	_	_	O
to	_	_	O
invest	_	_	O
in	_	_	O
the	_	_	O
real	_	_	O
-	_	_	O
estate	_	_	O
market	_	_	O
and	_	_	O
has	_	_	O
a	_	_	O
total	_	_	O
budget	_	_	O
of	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
760000	_	_	B-LIMIT
.	_	_	O
She	_	_	O
has	_	_	O
two	_	_	O
choices	_	_	O
which	_	_	O
include	_	_	O
condos	_	_	B-VAR
and	_	_	O
detached	_	_	B-VAR
houses	_	_	I-VAR
.	_	_	O
Each	_	_	O
dollar	_	_	O
invested	_	_	O
in	_	_	O
condos	_	_	B-VAR
yields	_	_	O
a	_	_	O
$	_	_	O
0.50	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
and	_	_	O
each	_	_	O
dollar	_	_	O
invested	_	_	O
in	_	_	O
detached	_	_	B-VAR
houses	_	_	I-VAR
yields	_	_	O
a	_	_	O
$	_	_	O
1	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
.	_	_	O
A	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
20	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
all	_	_	O
money	_	_	O
invested	_	_	O
must	_	_	O
be	_	_	O
in	_	_	O
condos	_	_	B-VAR
,	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
$	_	_	O
20000	_	_	B-LIMIT
must	_	_	O
be	_	_	O
in	_	_	O
detached	_	_	B-VAR
houses	_	_	I-VAR
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
that	_	_	O
can	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
total	_	_	O
profit	_	_	B-OBJ_NAME
earned	_	_	O
from	_	_	O
Mrs.	_	_	O
Watson	_	_	O
's	_	_	O
investment	_	_	O
.	_	_	O

A	_	_	O
souvenir	_	_	O
shop	_	_	O
makes	_	_	O
wooden	_	_	O
elephants	_	_	B-VAR
and	_	_	O
tigers	_	_	B-VAR
with	_	_	O
plastic	_	_	O
ornaments	_	_	O
.	_	_	O
Each	_	_	O
elephant	_	_	B-VAR
requires	_	_	O
50	_	_	B-PARAM
grams	_	_	O
of	_	_	O
wood	_	_	O
and	_	_	O
20	_	_	B-PARAM
grams	_	_	O
of	_	_	O
plastic	_	_	O
.	_	_	O
Each	_	_	O
tiger	_	_	B-VAR
requires	_	_	O
40	_	_	B-PARAM
grams	_	_	O
of	_	_	O
wood	_	_	O
and	_	_	O
30	_	_	B-PARAM
grams	_	_	O
of	_	_	O
plastic	_	_	O
.	_	_	O
In	_	_	O
a	_	_	O
week	_	_	O
,	_	_	O
5000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
wood	_	_	O
and	_	_	O
4000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
plastic	_	_	O
are	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
elephant	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
tiger	_	_	B-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
4	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
breakfast	_	_	O
joint	_	_	O
makes	_	_	O
two	_	_	O
different	_	_	O
sandwiches	_	_	O
:	_	_	O
a	_	_	O
regular	_	_	B-VAR
and	_	_	O
a	_	_	O
special	_	_	B-VAR
.	_	_	O
Both	_	_	O
need	_	_	O
eggs	_	_	O
and	_	_	O
bacon	_	_	O
.	_	_	O
Each	_	_	O
regular	_	_	B-VAR
sandwich	_	_	I-VAR
requires	_	_	O
2	_	_	B-PARAM
eggs	_	_	O
and	_	_	O
3	_	_	B-PARAM
slices	_	_	O
of	_	_	O
bacon	_	_	O
.	_	_	O
Each	_	_	O
special	_	_	B-VAR
sandwich	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
eggs	_	_	O
and	_	_	O
5	_	_	B-PARAM
slices	_	_	O
of	_	_	O
bacon	_	_	O
.	_	_	O
The	_	_	O
joint	_	_	O
has	_	_	B-CONST_DIR
a	_	_	O
total	_	_	O
of	_	_	O
40	_	_	B-LIMIT
eggs	_	_	O
and	_	_	O
70	_	_	B-LIMIT
slices	_	_	O
of	_	_	O
bacon	_	_	O
.	_	_	O
It	_	_	O
makes	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
3	_	_	B-PARAM
per	_	_	O
regular	_	_	B-VAR
sandwich	_	_	I-VAR
and	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
4	_	_	B-PARAM
per	_	_	O
special	_	_	B-VAR
sandwich	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
sandwich	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
company	_	_	O
is	_	_	O
deciding	_	_	O
where	_	_	O
to	_	_	O
promote	_	_	O
their	_	_	O
product	_	_	O
.	_	_	O
Some	_	_	O
options	_	_	O
include	_	_	O
z	_	_	B-VAR
-	_	_	I-VAR
tube	_	_	I-VAR
,	_	_	O
soorchle	_	_	B-VAR
engine	_	_	O
,	_	_	O
and	_	_	O
wassa	_	_	B-VAR
advertisements	_	_	O
.	_	_	O
The	_	_	O
cost	_	_	O
for	_	_	O
each	_	_	O
option	_	_	O
and	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
viewers	_	_	O
they	_	_	O
each	_	_	O
attract	_	_	O
is	_	_	O
given	_	_	O
.	_	_	O
On	_	_	O
z	_	_	B-VAR
-	_	_	I-VAR
tube	_	_	I-VAR
,	_	_	O
each	_	_	O
ad	_	_	O
costs	_	_	O
$	_	_	O
1000	_	_	B-PARAM
and	_	_	O
attracts	_	_	O
400,000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
On	_	_	O
soorchle	_	_	B-VAR
,	_	_	O
each	_	_	O
ad	_	_	O
costs	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
attracts	_	_	O
5,000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
On	_	_	O
wassa	_	_	B-VAR
,	_	_	O
each	_	_	O
ad	_	_	O
costs	_	_	O
$	_	_	O
100	_	_	B-PARAM
and	_	_	O
attracts	_	_	O
3,000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
Soorchle	_	_	B-VAR
limits	_	_	B-CONST_DIR
the	_	_	I-CONST_DIR
number	_	_	I-CONST_DIR
of	_	_	O
advertisements	_	_	O
from	_	_	O
a	_	_	O
single	_	_	O
company	_	_	O
to	_	_	O
fifteen	_	_	B-LIMIT
.	_	_	O
Moreover	_	_	O
,	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
balance	_	_	O
the	_	_	O
advertising	_	_	O
among	_	_	O
the	_	_	O
three	_	_	O
types	_	_	O
of	_	_	O
media	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
a	_	_	O
third	_	_	B-LIMIT
of	_	_	O
the	_	_	O
total	_	_	O
number	_	_	O
of	_	_	O
advertisements	_	_	O
should	_	_	O
occur	_	_	O
on	_	_	O
wassa	_	_	B-VAR
.	_	_	O
And	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
%	_	_	O
should	_	_	O
occur	_	_	O
on	_	_	O
z	_	_	B-VAR
-	_	_	I-VAR
tube	_	_	I-VAR
.	_	_	O
The	_	_	O
weekly	_	_	O
advertising	_	_	O
budget	_	_	B-CONST_DIR
is	_	_	O
$	_	_	O
10000	_	_	B-LIMIT
.	_	_	O
How	_	_	O
many	_	_	O
advertisements	_	_	O
should	_	_	O
be	_	_	O
run	_	_	O
in	_	_	O
each	_	_	O
of	_	_	O
the	_	_	O
three	_	_	O
types	_	_	O
of	_	_	O
media	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
audience	_	_	B-OBJ_NAME
?	_	_	O

My	_	_	O
grandma	_	_	O
is	_	_	O
required	_	_	O
to	_	_	O
take	_	_	O
two	_	_	O
medicines	_	_	O
Z1	_	_	O
and	_	_	O
D3	_	_	O
everyday	_	_	O
.	_	_	O
She	_	_	O
needs	_	_	O
to	_	_	O
take	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
Z1	_	_	O
and	_	_	O
10	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
D3	_	_	O
everyday	_	_	O
.	_	_	O
These	_	_	O
medicines	_	_	O
are	_	_	O
available	_	_	O
in	_	_	O
two	_	_	O
pills	_	_	O
named	_	_	O
Zodiac	_	_	B-VAR
and	_	_	O
Sunny	_	_	B-VAR
.	_	_	O
One	_	_	O
pill	_	_	O
of	_	_	O
Zodiac	_	_	B-VAR
contains	_	_	O
1.3	_	_	B-PARAM
grams	_	_	O
of	_	_	O
Z1	_	_	O
while	_	_	O
one	_	_	O
pill	_	_	O
of	_	_	O
Sunny	_	_	B-VAR
contains	_	_	O
1.2	_	_	B-PARAM
grams	_	_	O
of	_	_	O
Z1	_	_	O
.	_	_	O
On	_	_	O
the	_	_	O
other	_	_	O
hand	_	_	O
,	_	_	O
one	_	_	O
pill	_	_	O
of	_	_	O
Zodiac	_	_	B-VAR
contains	_	_	O
1.5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
D3	_	_	O
and	_	_	O
one	_	_	O
pill	_	_	O
of	_	_	O
Sunny	_	_	B-VAR
contains	_	_	O
5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
D3	_	_	O
.	_	_	O
The	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
pill	_	_	O
of	_	_	O
Zodiac	_	_	B-VAR
is	_	_	O
$	_	_	O
1	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
pill	_	_	O
of	_	_	O
Sunny	_	_	B-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
such	_	_	O
that	_	_	O
the	_	_	O
medicine	_	_	O
requirement	_	_	O
can	_	_	O
be	_	_	O
fulfilled	_	_	O
at	_	_	O
the	_	_	O
lowest	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
company	_	_	O
sells	_	_	O
custom	_	_	O
scooters	_	_	B-VAR
and	_	_	O
bikes	_	_	B-VAR
for	_	_	O
customers	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
scooter	_	_	B-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
bike	_	_	B-VAR
is	_	_	O
$	_	_	O
300	_	_	B-PARAM
.	_	_	O
Each	_	_	O
product	_	_	O
requires	_	_	O
time	_	_	O
with	_	_	O
the	_	_	O
design	_	_	O
team	_	_	O
and	_	_	O
engineering	_	_	O
team	_	_	O
.	_	_	O
Each	_	_	O
scooter	_	_	B-VAR
needs	_	_	O
2	_	_	B-PARAM
hours	_	_	O
with	_	_	O
the	_	_	O
design	_	_	O
team	_	_	O
and	_	_	O
3	_	_	B-PARAM
hours	_	_	O
with	_	_	O
the	_	_	O
engineering	_	_	O
team	_	_	O
.	_	_	O
Each	_	_	O
bike	_	_	B-VAR
needs	_	_	O
4	_	_	B-PARAM
hours	_	_	O
with	_	_	O
the	_	_	O
design	_	_	O
team	_	_	O
and	_	_	O
5	_	_	B-PARAM
hours	_	_	O
with	_	_	O
the	_	_	O
engineering	_	_	O
team	_	_	O
.	_	_	O
Per	_	_	O
month	_	_	O
,	_	_	O
there	_	_	O
are	_	_	O
5000	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
on	_	_	O
the	_	_	O
design	_	_	O
team	_	_	O
and	_	_	O
6000	_	_	B-LIMIT
hours	_	_	O
available	_	_	B-CONST_DIR
on	_	_	O
the	_	_	O
engineering	_	_	O
team	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
make	_	_	O
per	_	_	O
month	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

My	_	_	O
family	_	_	O
has	_	_	O
decided	_	_	O
to	_	_	O
invest	_	_	O
in	_	_	O
real	_	_	O
state	_	_	O
for	_	_	O
the	_	_	O
first	_	_	O
time	_	_	O
.	_	_	O
Currently	_	_	O
,	_	_	O
they	_	_	O
have	_	_	O
$	_	_	O
600,000	_	_	B-LIMIT
to	_	_	O
invest	_	_	B-CONST_DIR
,	_	_	O
some	_	_	O
in	_	_	O
apartments	_	_	B-VAR
and	_	_	O
the	_	_	O
rest	_	_	O
in	_	_	O
townhouses	_	_	B-VAR
.	_	_	O
The	_	_	O
money	_	_	O
invested	_	_	O
in	_	_	O
apartments	_	_	B-VAR
must	_	_	O
not	_	_	B-CONST_DIR
be	_	_	I-CONST_DIR
greater	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
$	_	_	O
200,000	_	_	B-LIMIT
.	_	_	O
They	_	_	O
have	_	_	O
decided	_	_	O
that	_	_	O
the	_	_	O
money	_	_	O
invested	_	_	O
in	_	_	O
apartments	_	_	B-VAR
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
a	_	_	O
half	_	_	B-PARAM
as	_	_	O
much	_	_	O
as	_	_	O
that	_	_	O
in	_	_	O
townhouses	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
apartments	_	_	B-VAR
earn	_	_	B-OBJ_NAME
10	_	_	B-PARAM
%	_	_	I-PARAM
,	_	_	O
and	_	_	O
the	_	_	O
townhouses	_	_	B-VAR
earn	_	_	B-OBJ_NAME
15	_	_	B-PARAM
%	_	_	I-PARAM
,	_	_	O
how	_	_	O
much	_	_	O
money	_	_	O
should	_	_	O
they	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
car	_	_	O
manufacturer	_	_	O
makes	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
car	_	_	O
oils	_	_	O
:	_	_	O
Oil	_	_	B-VAR
Max	_	_	I-VAR
and	_	_	O
Oil	_	_	B-VAR
Max	_	_	I-VAR
Pro	_	_	I-VAR
.	_	_	O
A	_	_	O
container	_	_	O
of	_	_	O
Oil	_	_	B-VAR
Max	_	_	I-VAR
contains	_	_	O
46	_	_	B-PARAM
grams	_	_	O
of	_	_	O
substance	_	_	O
A	_	_	O
,	_	_	O
43	_	_	B-PARAM
grams	_	_	O
of	_	_	O
substance	_	_	O
B	_	_	O
and	_	_	O
56	_	_	B-PARAM
grams	_	_	O
of	_	_	O
substance	_	_	O
C.	_	_	O
A	_	_	O
container	_	_	O
of	_	_	O
Oil	_	_	B-VAR
Max	_	_	I-VAR
Pro	_	_	I-VAR
contains	_	_	O
13	_	_	B-PARAM
grams	_	_	O
of	_	_	O
substance	_	_	O
A	_	_	O
,	_	_	O
4	_	_	B-PARAM
grams	_	_	O
of	_	_	O
substance	_	_	O
B	_	_	O
and	_	_	O
45	_	_	B-PARAM
grams	_	_	O
of	_	_	O
substance	_	_	O
C.	_	_	O
The	_	_	O
car	_	_	O
manufacturer	_	_	O
has	_	_	B-CONST_DIR
1345	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
substance	_	_	O
A	_	_	O
,	_	_	O
346	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
substance	_	_	O
B	_	_	O
,	_	_	O
1643	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
substance	_	_	O
C.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
container	_	_	O
of	_	_	O
Oil	_	_	B-VAR
Max	_	_	I-VAR
is	_	_	O
$	_	_	O
10	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
container	_	_	O
of	_	_	O
Oil	_	_	B-VAR
Max	_	_	I-VAR
Pro	_	_	I-VAR
is	_	_	O
$	_	_	O
15	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
containers	_	_	O
of	_	_	O
each	_	_	O
of	_	_	O
oil	_	_	O
should	_	_	O
the	_	_	O
car	_	_	O
manufacturer	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
farmer	_	_	O
wants	_	_	O
to	_	_	O
mix	_	_	O
his	_	_	O
animal	_	_	O
feeds	_	_	O
,	_	_	O
Feed	_	_	B-VAR
A	_	_	I-VAR
and	_	_	O
Feed	_	_	B-VAR
B	_	_	I-VAR
,	_	_	O
in	_	_	O
such	_	_	O
a	_	_	O
way	_	_	O
that	_	_	O
the	_	_	O
mixture	_	_	O
will	_	_	O
contain	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
30	_	_	B-LIMIT
units	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
50	_	_	B-LIMIT
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
Feed	_	_	B-VAR
A	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
100	_	_	B-PARAM
per	_	_	O
kilogram	_	_	O
and	_	_	O
contains	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
Feed	_	_	B-VAR
B	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
80	_	_	B-PARAM
per	_	_	O
kilogram	_	_	O
and	_	_	O
contains	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	O
.	_	_	O
Determine	_	_	O
the	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
of	_	_	O
the	_	_	O
mixture	_	_	O
.	_	_	O

A	_	_	O
glass	_	_	O
factory	_	_	O
makes	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
glass	_	_	O
panes	_	_	O
:	_	_	O
a	_	_	O
regular	_	_	B-VAR
glass	_	_	I-VAR
pane	_	_	I-VAR
and	_	_	O
a	_	_	O
tempered	_	_	B-VAR
glass	_	_	I-VAR
pane	_	_	I-VAR
.	_	_	O
Both	_	_	O
require	_	_	O
time	_	_	O
on	_	_	O
a	_	_	O
heating	_	_	O
and	_	_	O
cooling	_	_	O
machine	_	_	O
.	_	_	O
Both	_	_	O
machines	_	_	O
are	_	_	O
available	_	_	O
for	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
300	_	_	B-LIMIT
minutes	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
It	_	_	O
takes	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
in	_	_	O
the	_	_	O
heating	_	_	O
machine	_	_	O
and	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
in	_	_	O
the	_	_	O
cooling	_	_	O
machine	_	_	O
to	_	_	O
make	_	_	O
one	_	_	O
regular	_	_	B-VAR
glass	_	_	I-VAR
pane	_	_	I-VAR
.	_	_	O
It	_	_	O
takes	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
in	_	_	O
the	_	_	O
heating	_	_	O
machine	_	_	O
and	_	_	O
8	_	_	B-PARAM
minutes	_	_	O
in	_	_	O
the	_	_	O
cooling	_	_	O
machine	_	_	O
to	_	_	O
make	_	_	O
one	_	_	O
tempered	_	_	B-VAR
glass	_	_	I-VAR
pane	_	_	I-VAR
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
pane	_	_	O
of	_	_	O
regular	_	_	B-VAR
glass	_	_	I-VAR
is	_	_	O
$	_	_	O
8	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
pane	_	_	O
of	_	_	O
tempered	_	_	B-VAR
glass	_	_	I-VAR
is	_	_	O
$	_	_	O
10	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
panes	_	_	O
of	_	_	O
each	_	_	O
glass	_	_	O
type	_	_	O
should	_	_	O
the	_	_	O
factory	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O
What	_	_	O
is	_	_	O
the	_	_	O
maximum	_	_	O
profit	_	_	O
?	_	_	O

An	_	_	O
artisan	_	_	O
makes	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
terracotta	_	_	O
jars	_	_	O
:	_	_	O
a	_	_	O
thin	_	_	B-VAR
jar	_	_	I-VAR
and	_	_	O
a	_	_	O
stubby	_	_	B-VAR
jar	_	_	I-VAR
.	_	_	O
Each	_	_	O
thin	_	_	B-VAR
jar	_	_	I-VAR
requires	_	_	O
50	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
shaping	_	_	O
time	_	_	O
and	_	_	O
90	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
baking	_	_	O
time	_	_	O
.	_	_	O
Each	_	_	O
stubby	_	_	B-VAR
jar	_	_	I-VAR
requires	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
shaping	_	_	O
time	_	_	O
and	_	_	O
150	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
baking	_	_	O
time	_	_	O
.	_	_	O
Per	_	_	O
week	_	_	O
,	_	_	O
there	_	_	O
are	_	_	O
3000	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
shaping	_	_	O
and	_	_	O
4000	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
baking	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
thin	_	_	B-VAR
jar	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
stubby	_	_	B-VAR
jar	_	_	I-VAR
is	_	_	O
$	_	_	O
9	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
jars	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
the	_	_	O
artisan	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
nutritionist	_	_	O
is	_	_	O
making	_	_	O
a	_	_	O
special	_	_	O
vitamin	_	_	O
mix	_	_	O
using	_	_	O
two	_	_	O
drinks	_	_	O
:	_	_	O
A	_	_	B-VAR
and	_	_	O
B.	_	_	B-VAR
The	_	_	O
vitamin	_	_	O
mix	_	_	O
must	_	_	O
contain	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
150	_	_	B-LIMIT
units	_	_	O
of	_	_	O
Vitamin	_	_	O
A	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
300	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamin	_	_	O
D	_	_	O
,	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
400	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamin	_	_	O
E.	_	_	O
A	_	_	O
cup	_	_	O
of	_	_	O
drink	_	_	B-VAR
A	_	_	I-VAR
contains	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
Vitamin	_	_	O
A	_	_	O
,	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
Vitamin	_	_	O
D	_	_	O
,	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
Vitamin	_	_	O
E	_	_	O
,	_	_	O
and	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
Vitamin	_	_	B-OBJ_NAME
K.	_	_	I-OBJ_NAME
A	_	_	O
cup	_	_	O
of	_	_	O
drink	_	_	B-VAR
B	_	_	I-VAR
contains	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
Vitamin	_	_	O
A	_	_	O
,	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
Vitamin	_	_	O
D	_	_	O
,	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
Vitamin	_	_	O
E	_	_	O
,	_	_	O
and	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
Vitamin	_	_	B-OBJ_NAME
K.	_	_	I-OBJ_NAME
How	_	_	O
many	_	_	O
cups	_	_	O
of	_	_	O
each	_	_	O
drink	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
make	_	_	O
the	_	_	O
vitamin	_	_	O
mix	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
Vitamin	_	_	I-OBJ_NAME
K	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
berry	_	_	O
farmer	_	_	O
has	_	_	O
two	_	_	O
farms	_	_	O
,	_	_	O
an	_	_	O
old	_	_	B-VAR
and	_	_	O
new	_	_	B-VAR
farm	_	_	I-VAR
,	_	_	O
where	_	_	O
he	_	_	O
grows	_	_	O
raspberries	_	_	O
,	_	_	O
blueberries	_	_	O
,	_	_	O
and	_	_	O
strawberries	_	_	O
.	_	_	O
He	_	_	O
has	_	_	O
a	_	_	O
contract	_	_	O
to	_	_	O
provide	_	_	B-CONST_DIR
a	_	_	O
local	_	_	O
store	_	_	O
with	_	_	O
10	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
raspberries	_	_	O
,	_	_	O
9	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
blueberries	_	_	O
,	_	_	O
and	_	_	O
15	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
strawberries	_	_	O
.	_	_	O
At	_	_	O
his	_	_	O
old	_	_	B-VAR
farm	_	_	I-VAR
,	_	_	O
it	_	_	O
cost	_	_	B-OBJ_NAME
$	_	_	O
300	_	_	B-PARAM
to	_	_	O
operate	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
he	_	_	O
can	_	_	O
harvest	_	_	O
and	_	_	O
deliver	_	_	O
2	_	_	B-PARAM
kg	_	_	O
of	_	_	O
raspberries	_	_	O
,	_	_	O
2	_	_	B-PARAM
kg	_	_	O
of	_	_	O
blueberries	_	_	O
,	_	_	O
and	_	_	O
4	_	_	B-PARAM
kg	_	_	O
of	_	_	O
strawberries	_	_	O
in	_	_	O
a	_	_	O
day	_	_	O
.	_	_	O
At	_	_	O
his	_	_	O
new	_	_	B-VAR
farm	_	_	I-VAR
,	_	_	O
it	_	_	O
costs	_	_	B-OBJ_NAME
$	_	_	O
200	_	_	B-PARAM
to	_	_	O
operate	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
he	_	_	O
can	_	_	O
harvest	_	_	O
and	_	_	O
deliver	_	_	O
4	_	_	B-PARAM
kg	_	_	O
of	_	_	O
raspberries	_	_	O
,	_	_	O
1	_	_	B-PARAM
kg	_	_	O
of	_	_	O
blueberries	_	_	O
,	_	_	O
and	_	_	O
2	_	_	B-PARAM
kg	_	_	O
of	_	_	O
strawberries	_	_	O
in	_	_	O
a	_	_	O
day	_	_	O
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
meet	_	_	O
his	_	_	O
contract	_	_	O
while	_	_	O
minimizing	_	_	B-OBJ_DIR
his	_	_	O
cost	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
car	_	_	O
manufacturer	_	_	O
makes	_	_	O
two	_	_	O
versions	_	_	O
of	_	_	O
the	_	_	O
same	_	_	O
car	_	_	O
,	_	_	O
a	_	_	O
regular	_	_	B-VAR
model	_	_	I-VAR
and	_	_	O
a	_	_	O
premium	_	_	B-VAR
model	_	_	I-VAR
.	_	_	O
They	_	_	O
make	_	_	O
x1	_	_	O
regular	_	_	B-VAR
models	_	_	I-VAR
per	_	_	O
day	_	_	O
and	_	_	O
x2	_	_	O
premium	_	_	B-VAR
models	_	_	I-VAR
per	_	_	O
day	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
regular	_	_	B-VAR
model	_	_	I-VAR
is	_	_	O
$	_	_	O
5000	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
premium	_	_	B-VAR
model	_	_	I-VAR
is	_	_	O
$	_	_	O
8500	_	_	B-PARAM
(	_	_	O
x1	_	_	O
and	_	_	O
x2	_	_	O
are	_	_	O
unknown	_	_	O
values	_	_	O
both	_	_	O
greater	_	_	O
than	_	_	O
or	_	_	O
equal	_	_	O
to	_	_	O
0	_	_	O
)	_	_	O
.	_	_	O
The	_	_	O
daily	_	_	O
demand	_	_	O
for	_	_	O
these	_	_	O
cars	_	_	O
is	_	_	O
limited	_	_	O
to	_	_	O
and	_	_	O
most	_	_	B-CONST_DIR
8	_	_	B-LIMIT
regular	_	_	B-VAR
models	_	_	I-VAR
and	_	_	O
6	_	_	B-LIMIT
premium	_	_	B-VAR
models	_	_	I-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
the	_	_	O
manufacturer	_	_	O
can	_	_	O
make	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
12	_	_	B-LIMIT
cars	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
cars	_	_	O
of	_	_	O
each	_	_	O
model	_	_	O
should	_	_	O
the	_	_	O
manufacturer	_	_	O
make	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Mark	_	_	O
has	_	_	O
50	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
available	_	_	B-CONST_DIR
to	_	_	O
grow	_	_	O
potatoes	_	_	B-VAR
and	_	_	O
cucumbers	_	_	B-VAR
that	_	_	O
he	_	_	O
sells	_	_	O
at	_	_	O
a	_	_	O
farmers	_	_	O
'	_	_	O
market	_	_	O
.	_	_	O
He	_	_	O
must	_	_	O
grow	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
12	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
potatoes	_	_	B-VAR
and	_	_	O
15	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
cucumbers	_	_	B-VAR
to	_	_	O
meet	_	_	O
his	_	_	O
contract	_	_	O
.	_	_	O
Mark	_	_	O
prefers	_	_	O
to	_	_	O
grow	_	_	O
more	_	_	O
cucumbers	_	_	B-VAR
than	_	_	O
potatoes	_	_	B-VAR
,	_	_	O
but	_	_	O
he	_	_	O
only	_	_	O
has	_	_	O
enough	_	_	O
resources	_	_	O
to	_	_	O
grow	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
twice	_	_	B-PARAM
the	_	_	O
amount	_	_	O
of	_	_	O
cucumbers	_	_	B-VAR
as	_	_	O
potatoes	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
potatoes	_	_	B-VAR
is	_	_	O
$	_	_	O
500	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
cucumbers	_	_	B-VAR
is	_	_	O
$	_	_	O
650	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
grow	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O
What	_	_	O
is	_	_	O
that	_	_	O
profit	_	_	O
?	_	_	O

An	_	_	O
ice	_	_	O
cream	_	_	O
store	_	_	O
makes	_	_	O
chocolate	_	_	B-VAR
and	_	_	O
vanilla	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
by	_	_	O
the	_	_	O
gallon	_	_	O
.	_	_	O
In	_	_	O
a	_	_	O
week	_	_	O
,	_	_	O
they	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
gallons	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
but	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
10	_	_	B-LIMIT
gallons	_	_	O
of	_	_	O
chocolate	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
8	_	_	B-LIMIT
gallons	_	_	O
of	_	_	O
vanilla	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
.	_	_	O
It	_	_	O
takes	_	_	O
1	_	_	B-PARAM
hour	_	_	O
to	_	_	O
produce	_	_	O
a	_	_	O
gallon	_	_	O
of	_	_	O
chocolate	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
and	_	_	O
2	_	_	B-PARAM
hours	_	_	O
to	_	_	O
produce	_	_	O
a	_	_	O
gallon	_	_	O
of	_	_	O
vanilla	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
.	_	_	O
In	_	_	O
a	_	_	O
week	_	_	O
,	_	_	O
30	_	_	B-LIMIT
hours	_	_	O
are	_	_	O
available	_	_	B-CONST_DIR
to	_	_	O
make	_	_	O
ice	_	_	O
cream	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
6	_	_	B-LIMIT
workers	_	_	O
are	_	_	O
needed	_	_	O
with	_	_	O
1	_	_	B-PARAM
working	_	_	O
on	_	_	O
the	_	_	O
chocolate	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
and	_	_	O
2	_	_	B-PARAM
on	_	_	O
the	_	_	O
vanilla	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
at	_	_	O
any	_	_	O
time	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
gallon	_	_	O
of	_	_	O
chocolate	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
gallon	_	_	O
of	_	_	O
vanilla	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
is	_	_	O
$	_	_	O
300	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
gallons	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
cleaning	_	_	O
company	_	_	O
located	_	_	O
in	_	_	O
Edmonton	_	_	O
wants	_	_	O
to	_	_	O
get	_	_	O
the	_	_	O
best	_	_	O
exposure	_	_	O
possible	_	_	O
for	_	_	O
promoting	_	_	O
their	_	_	O
new	_	_	O
dishwashing	_	_	O
detergent	_	_	O
without	_	_	B-CONST_DIR
exceeding	_	_	I-CONST_DIR
their	_	_	O
$	_	_	O
250,000	_	_	B-LIMIT
advertising	_	_	O
budget	_	_	O
.	_	_	O
To	_	_	O
do	_	_	O
so	_	_	O
,	_	_	O
the	_	_	O
company	_	_	O
decides	_	_	O
to	_	_	O
spend	_	_	O
their	_	_	O
money	_	_	O
on	_	_	O
two	_	_	O
forms	_	_	O
of	_	_	O
advertising	_	_	O
:	_	_	O
(	_	_	O
1	_	_	O
)	_	_	O
radio	_	_	B-VAR
ads	_	_	I-VAR
and	_	_	O
(	_	_	O
2	_	_	O
)	_	_	O
social	_	_	B-VAR
media	_	_	I-VAR
ads	_	_	I-VAR
.	_	_	O
Each	_	_	O
radio	_	_	B-VAR
ad	_	_	I-VAR
costs	_	_	O
$	_	_	O
5,000	_	_	B-PARAM
;	_	_	O
each	_	_	O
social	_	_	B-VAR
media	_	_	I-VAR
ad	_	_	I-VAR
costs	_	_	O
$	_	_	O
9,150	_	_	B-PARAM
.	_	_	O
The	_	_	O
expected	_	_	O
exposure	_	_	B-OBJ_NAME
,	_	_	O
based	_	_	O
on	_	_	O
industry	_	_	O
ratings	_	_	O
,	_	_	O
is	_	_	O
60,500	_	_	B-PARAM
viewers	_	_	O
for	_	_	O
each	_	_	O
radio	_	_	B-VAR
ad	_	_	I-VAR
.	_	_	O
Additionally	_	_	O
,	_	_	O
the	_	_	O
expected	_	_	O
exposure	_	_	B-OBJ_NAME
for	_	_	O
each	_	_	O
social	_	_	B-VAR
media	_	_	I-VAR
ad	_	_	I-VAR
is	_	_	O
50,000	_	_	B-PARAM
viewers	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
decides	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
15	_	_	B-LIMIT
but	_	_	O
no	_	_	B-CONST_DIR
more	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
40	_	_	B-LIMIT
radio	_	_	B-VAR
ads	_	_	I-VAR
should	_	_	O
be	_	_	O
ordered	_	_	O
,	_	_	O
and	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
35	_	_	B-LIMIT
social	_	_	B-VAR
media	_	_	I-VAR
ads	_	_	I-VAR
should	_	_	O
be	_	_	O
contracted	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
ads	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
be	_	_	O
run	_	_	O
to	_	_	O
obtain	_	_	O
maximum	_	_	B-OBJ_DIR
exposure	_	_	B-OBJ_NAME
while	_	_	O
staying	_	_	O
within	_	_	O
the	_	_	O
budget	_	_	O
?	_	_	O

There	_	_	O
is	_	_	O
1000	_	_	B-LIMIT
mg	_	_	O
of	_	_	O
gold	_	_	O
available	_	_	B-CONST_DIR
that	_	_	O
is	_	_	O
needed	_	_	O
to	_	_	O
make	_	_	O
long	_	_	B-VAR
and	_	_	O
short	_	_	B-VAR
cables	_	_	I-VAR
.	_	_	O
Long	_	_	B-VAR
cables	_	_	I-VAR
require	_	_	O
10	_	_	B-PARAM
mg	_	_	O
of	_	_	O
gold	_	_	O
while	_	_	O
short	_	_	B-VAR
cables	_	_	I-VAR
require	_	_	O
7	_	_	B-PARAM
mg	_	_	O
of	_	_	O
gold	_	_	O
.	_	_	O
Because	_	_	O
of	_	_	O
their	_	_	O
compact	_	_	O
size	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-PARAM
times	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
short	_	_	B-VAR
cables	_	_	I-VAR
are	_	_	O
needed	_	_	O
than	_	_	O
the	_	_	O
long	_	_	B-VAR
cables	_	_	I-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
there	_	_	O
needs	_	_	O
to	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
long	_	_	B-VAR
cables	_	_	I-VAR
made	_	_	O
.	_	_	O
If	_	_	O
each	_	_	O
long	_	_	B-VAR
cable	_	_	I-VAR
sold	_	_	O
results	_	_	O
in	_	_	O
a	_	_	O
$	_	_	O
12	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
and	_	_	O
each	_	_	O
short	_	_	B-VAR
cable	_	_	I-VAR
sold	_	_	O
results	_	_	O
in	_	_	O
a	_	_	O
$	_	_	O
5	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
cable	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
chair	_	_	B-VAR
produced	_	_	O
by	_	_	O
Elm	_	_	O
Furniture	_	_	O
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
43	_	_	B-PARAM
,	_	_	O
while	_	_	O
every	_	_	O
dresser	_	_	B-VAR
yields	_	_	O
a	_	_	O
$	_	_	O
52	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
.	_	_	O
Each	_	_	O
week	_	_	O
,	_	_	O
17	_	_	B-LIMIT
gallons	_	_	O
of	_	_	O
stain	_	_	O
and	_	_	O
11	_	_	B-LIMIT
lengths	_	_	O
of	_	_	O
oak	_	_	O
wood	_	_	O
are	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
Each	_	_	O
chair	_	_	B-VAR
requires	_	_	O
1.4	_	_	B-PARAM
gallons	_	_	O
of	_	_	O
stain	_	_	O
and	_	_	O
2	_	_	B-PARAM
lengths	_	_	O
of	_	_	O
oak	_	_	O
wood	_	_	O
,	_	_	O
while	_	_	O
each	_	_	O
dresser	_	_	B-VAR
requires	_	_	O
1.1	_	_	B-PARAM
gallons	_	_	O
of	_	_	O
stain	_	_	O
and	_	_	O
3	_	_	B-PARAM
lengths	_	_	O
of	_	_	O
oak	_	_	O
wood	_	_	O
.	_	_	O
Determine	_	_	O
the	_	_	O
maximum	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
electronics	_	_	O
store	_	_	O
sells	_	_	O
premium	_	_	B-VAR
desktops	_	_	I-VAR
with	_	_	O
more	_	_	O
power	_	_	O
as	_	_	O
well	_	_	O
as	_	_	O
regular	_	_	B-VAR
desktops	_	_	I-VAR
for	_	_	O
everyday	_	_	O
use	_	_	O
.	_	_	O
Each	_	_	O
premium	_	_	B-VAR
desktop	_	_	I-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
2000	_	_	B-PARAM
to	_	_	O
make	_	_	O
and	_	_	O
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
500	_	_	B-PARAM
.	_	_	O
Each	_	_	O
regular	_	_	B-VAR
desktop	_	_	I-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
1000	_	_	B-PARAM
to	_	_	O
make	_	_	O
and	_	_	O
yields	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
300	_	_	B-PARAM
.	_	_	O
The	_	_	O
store	_	_	O
sells	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
200	_	_	B-LIMIT
desktops	_	_	O
each	_	_	O
month	_	_	O
and	_	_	O
wants	_	_	O
to	_	_	O
spend	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
300000	_	_	B-LIMIT
on	_	_	O
making	_	_	O
the	_	_	O
desktops	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
and	_	_	O
sold	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
store	_	_	O
employs	_	_	O
senior	_	_	B-VAR
citizens	_	_	I-VAR
who	_	_	O
earn	_	_	B-OBJ_NAME
$	_	_	O
500	_	_	B-PARAM
per	_	_	O
week	_	_	O
and	_	_	O
young	_	_	B-VAR
adults	_	_	I-VAR
who	_	_	O
earn	_	_	B-OBJ_NAME
$	_	_	O
750	_	_	B-PARAM
per	_	_	O
week	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
must	_	_	O
keep	_	_	O
the	_	_	O
weekly	_	_	O
wage	_	_	O
bill	_	_	O
below	_	_	B-CONST_DIR
$	_	_	O
30000	_	_	B-LIMIT
.	_	_	O
On	_	_	O
any	_	_	O
day	_	_	O
,	_	_	O
the	_	_	O
store	_	_	O
requires	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
workers	_	_	O
,	_	_	O
of	_	_	O
whom	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
must	_	_	O
be	_	_	O
young	_	_	B-VAR
adults	_	_	I-VAR
.	_	_	O
To	_	_	O
ensure	_	_	O
the	_	_	O
store	_	_	O
runs	_	_	O
smoothly	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
young	_	_	B-VAR
adults	_	_	I-VAR
should	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
a	_	_	O
third	_	_	B-PARAM
the	_	_	O
number	_	_	O
of	_	_	O
senior	_	_	B-VAR
citizens	_	_	I-VAR
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	B-OBJ_NAME
wage	_	_	I-OBJ_NAME
bill	_	_	I-OBJ_NAME
.	_	_	O

A	_	_	O
farmer	_	_	O
has	_	_	B-CONST_DIR
500	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
to	_	_	O
grow	_	_	O
turnips	_	_	B-VAR
and	_	_	O
pumpkins	_	_	B-VAR
.	_	_	O
Turnips	_	_	B-VAR
require	_	_	O
50	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
watering	_	_	O
and	_	_	O
$	_	_	O
80	_	_	B-PARAM
worth	_	_	O
of	_	_	O
pesticide	_	_	O
per	_	_	O
acre	_	_	O
.	_	_	O
Pumpkins	_	_	B-VAR
require	_	_	O
90	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
watering	_	_	O
and	_	_	O
$	_	_	O
50	_	_	B-PARAM
worth	_	_	O
of	_	_	O
pesticide	_	_	O
per	_	_	O
acre	_	_	O
.	_	_	O
The	_	_	O
farmer	_	_	O
has	_	_	O
40000	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
watering	_	_	O
and	_	_	O
$	_	_	O
34000	_	_	B-LIMIT
available	_	_	B-CONST_DIR
to	_	_	O
spend	_	_	O
on	_	_	O
pesticide	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
revenue	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
turnips	_	_	B-VAR
is	_	_	O
$	_	_	O
300	_	_	B-PARAM
and	_	_	O
the	_	_	O
revenue	_	_	B-OBJ_NAME
per	_	_	O
acre	_	_	O
of	_	_	O
pumpkins	_	_	B-VAR
is	_	_	O
$	_	_	O
450	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
grow	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
revenue	_	_	B-OBJ_NAME
.	_	_	O

Sleep	_	_	O
inducing	_	_	O
medicine	_	_	O
and	_	_	O
anti	_	_	O
-	_	_	O
inflammatory	_	_	O
medicine	_	_	O
is	_	_	O
found	_	_	O
in	_	_	O
two	_	_	O
pills	_	_	O
,	_	_	O
pill	_	_	B-VAR
A	_	_	I-VAR
and	_	_	O
pill	_	_	B-VAR
B.	_	_	I-VAR
One	_	_	O
pill	_	_	B-VAR
A	_	_	I-VAR
contains	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
sleep	_	_	O
inducing	_	_	O
medicine	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
anti	_	_	O
-	_	_	O
inflammatory	_	_	O
medicine	_	_	O
.	_	_	O
One	_	_	O
pill	_	_	B-VAR
B	_	_	I-VAR
contains	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
sleep	_	_	O
-	_	_	O
inducing	_	_	O
medicine	_	_	O
and	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
anti	_	_	O
-	_	_	O
inflammatory	_	_	O
medicine	_	_	O
.	_	_	O
The	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
pill	_	_	O
for	_	_	O
pill	_	_	B-VAR
A	_	_	I-VAR
is	_	_	O
$	_	_	O
4	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
pill	_	_	O
for	_	_	O
pill	_	_	B-VAR
B	_	_	I-VAR
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
.	_	_	O
A	_	_	O
patient	_	_	O
must	_	_	O
consume	_	_	O
these	_	_	O
two	_	_	O
pills	_	_	O
to	_	_	O
get	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
40	_	_	B-LIMIT
units	_	_	O
of	_	_	O
sleep	_	_	O
-	_	_	O
inducing	_	_	O
medicine	_	_	O
and	_	_	O
50	_	_	B-LIMIT
units	_	_	O
of	_	_	O
anti	_	_	O
-	_	_	O
inflammatory	_	_	O
medicine	_	_	O
.	_	_	O
Formulate	_	_	O
a	_	_	O
LP	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
cost	_	_	B-OBJ_NAME
for	_	_	O
the	_	_	O
patient	_	_	O
.	_	_	O

An	_	_	O
art	_	_	O
store	_	_	O
makes	_	_	O
large	_	_	B-VAR
and	_	_	O
small	_	_	B-VAR
art	_	_	I-VAR
pieces	_	_	I-VAR
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
100	_	_	B-LIMIT
units	_	_	O
of	_	_	O
paint	_	_	O
,	_	_	O
50	_	_	B-LIMIT
units	_	_	O
of	_	_	O
glitter	_	_	O
,	_	_	O
and	_	_	O
70	_	_	B-LIMIT
units	_	_	O
of	_	_	O
glue	_	_	O
.	_	_	O
To	_	_	O
make	_	_	O
a	_	_	O
large	_	_	B-VAR
art	_	_	I-VAR
piece	_	_	I-VAR
requires	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
paint	_	_	O
,	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
glitter	_	_	O
,	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
glue	_	_	O
.	_	_	O
To	_	_	O
make	_	_	O
a	_	_	O
small	_	_	B-VAR
art	_	_	I-VAR
piece	_	_	I-VAR
requires	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
paint	_	_	O
,	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
glitter	_	_	O
,	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
glue	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
units	_	_	O
of	_	_	O
each	_	_	O
large	_	_	B-VAR
and	_	_	O
small	_	_	B-VAR
art	_	_	I-VAR
pieces	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
large	_	_	B-VAR
art	_	_	I-VAR
piece	_	_	I-VAR
is	_	_	O
$	_	_	O
30	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
small	_	_	B-VAR
art	_	_	I-VAR
piece	_	_	I-VAR
is	_	_	O
$	_	_	O
15	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
man	_	_	O
only	_	_	O
eats	_	_	O
vegetable	_	_	B-VAR
and	_	_	O
fruits	_	_	B-VAR
.	_	_	O
A	_	_	O
serving	_	_	O
of	_	_	O
vegetables	_	_	B-VAR
contains	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamins	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
minerals	_	_	O
.	_	_	O
A	_	_	O
serving	_	_	O
of	_	_	O
fruit	_	_	B-VAR
contains	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamins	_	_	O
and	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
minerals	_	_	O
.	_	_	O
He	_	_	O
wants	_	_	O
to	_	_	O
eat	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamins	_	_	O
and	_	_	O
30	_	_	B-LIMIT
units	_	_	O
of	_	_	O
minerals	_	_	O
.	_	_	O
If	_	_	O
vegetables	_	_	B-VAR
cost	_	_	B-OBJ_NAME
$	_	_	O
3	_	_	B-PARAM
per	_	_	O
serving	_	_	O
and	_	_	O
fruits	_	_	B-VAR
cost	_	_	B-OBJ_NAME
$	_	_	O
5	_	_	B-PARAM
per	_	_	O
serving	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
servings	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
eat	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
cost	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
hobbyist	_	_	O
makes	_	_	O
model	_	_	B-VAR
trains	_	_	I-VAR
and	_	_	O
planes	_	_	B-VAR
using	_	_	O
wood	_	_	O
and	_	_	O
paint	_	_	O
.	_	_	O
A	_	_	O
model	_	_	B-VAR
train	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
wood	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
paint	_	_	O
.	_	_	O
A	_	_	O
model	_	_	B-VAR
plane	_	_	I-VAR
requires	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
wood	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
paint	_	_	O
.	_	_	O
The	_	_	O
hobbyist	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
120	_	_	B-LIMIT
units	_	_	O
of	_	_	O
wood	_	_	O
and	_	_	O
90	_	_	B-LIMIT
units	_	_	O
of	_	_	O
paint	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
model	_	_	B-VAR
train	_	_	I-VAR
is	_	_	O
$	_	_	O
8	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
model	_	_	B-VAR
plane	_	_	I-VAR
is	_	_	O
$	_	_	O
10	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

Mr.	_	_	O
Roberts	_	_	O
want	_	_	O
to	_	_	O
invest	_	_	O
in	_	_	O
the	_	_	O
telecom	_	_	B-VAR
and	_	_	O
healthcare	_	_	B-VAR
industries	_	_	O
.	_	_	O
He	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
100000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
.	_	_	O
He	_	_	O
has	_	_	O
decided	_	_	O
that	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
telecom	_	_	B-VAR
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	O
as	_	_	O
much	_	_	O
as	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
healthcare	_	_	B-VAR
.	_	_	O
But	_	_	O
the	_	_	O
money	_	_	O
invested	_	_	O
in	_	_	O
telecom	_	_	B-VAR
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
70000	_	_	B-LIMIT
.	_	_	O
If	_	_	O
investments	_	_	O
in	_	_	O
telecom	_	_	B-VAR
earn	_	_	B-OBJ_NAME
3	_	_	B-PARAM
%	_	_	I-PARAM
and	_	_	O
investments	_	_	O
in	_	_	O
healthcare	_	_	B-VAR
earn	_	_	B-OBJ_NAME
1	_	_	B-PARAM
%	_	_	I-PARAM
,	_	_	O
how	_	_	O
much	_	_	O
should	_	_	O
Mr.	_	_	O
Roberts	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
fishery	_	_	O
wants	_	_	O
to	_	_	O
transport	_	_	O
their	_	_	O
catch	_	_	O
.	_	_	O
They	_	_	O
can	_	_	O
either	_	_	O
use	_	_	O
local	_	_	O
sled	_	_	B-VAR
dogs	_	_	I-VAR
or	_	_	O
trucks	_	_	B-VAR
.	_	_	O
Local	_	_	O
sled	_	_	B-VAR
dogs	_	_	I-VAR
can	_	_	O
take	_	_	O
100	_	_	B-PARAM
fish	_	_	B-OBJ_NAME
per	_	_	O
trip	_	_	O
while	_	_	O
trucks	_	_	B-VAR
can	_	_	O
take	_	_	O
300	_	_	B-PARAM
fish	_	_	B-OBJ_NAME
per	_	_	O
trip	_	_	O
.	_	_	O
The	_	_	O
cost	_	_	O
per	_	_	O
trip	_	_	O
for	_	_	O
sled	_	_	B-VAR
dogs	_	_	I-VAR
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
while	_	_	O
the	_	_	O
cost	_	_	O
per	_	_	O
trip	_	_	O
for	_	_	O
a	_	_	O
truck	_	_	B-VAR
is	_	_	O
$	_	_	O
100	_	_	B-PARAM
.	_	_	O
The	_	_	O
budget	_	_	B-CONST_DIR
is	_	_	O
at	_	_	O
most	_	_	O
$	_	_	O
1000	_	_	B-LIMIT
and	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
sled	_	_	B-VAR
dog	_	_	I-VAR
trips	_	_	O
must	_	_	O
be	_	_	O
less	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
truck	_	_	B-VAR
trips	_	_	O
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
fish	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
transported	_	_	O
.	_	_	O

An	_	_	O
accounting	_	_	O
firm	_	_	O
has	_	_	O
senior	_	_	B-VAR
accountants	_	_	I-VAR
earning	_	_	B-OBJ_NAME
$	_	_	O
3000	_	_	B-PARAM
per	_	_	O
week	_	_	O
and	_	_	O
junior	_	_	B-VAR
accountants	_	_	I-VAR
earning	_	_	B-OBJ_NAME
$	_	_	O
1000	_	_	B-PARAM
per	_	_	O
week	_	_	O
.	_	_	O
The	_	_	O
contracts	_	_	O
with	_	_	O
companies	_	_	O
to	_	_	O
provide	_	_	O
accounting	_	_	O
services	_	_	O
require	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
accountants	_	_	O
,	_	_	O
of	_	_	O
whom	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
must	_	_	O
be	_	_	O
senior	_	_	B-VAR
accountants	_	_	I-VAR
.	_	_	O
To	_	_	O
make	_	_	O
sure	_	_	O
there	_	_	O
is	_	_	O
enough	_	_	O
experience	_	_	O
on	_	_	O
the	_	_	O
accounting	_	_	O
team	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
senior	_	_	B-VAR
accountants	_	_	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
junior	_	_	B-VAR
accountants	_	_	I-VAR
.	_	_	O
The	_	_	O
firm	_	_	O
wants	_	_	O
to	_	_	O
keep	_	_	O
the	_	_	O
weekly	_	_	O
wage	_	_	O
bill	_	_	O
below	_	_	B-CONST_DIR
$	_	_	O
150000	_	_	B-LIMIT
.	_	_	O
Formulate	_	_	O
an	_	_	O
LP	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
wage	_	_	B-OBJ_NAME
bill	_	_	I-OBJ_NAME
.	_	_	O

A	_	_	O
lighting	_	_	O
company	_	_	O
makes	_	_	O
desk	_	_	B-VAR
-	_	_	I-VAR
lamps	_	_	I-VAR
and	_	_	O
night	_	_	B-VAR
-	_	_	I-VAR
lamps	_	_	I-VAR
.	_	_	O
There	_	_	O
is	_	_	O
an	_	_	O
expected	_	_	O
demand	_	_	O
of	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
desk	_	_	B-VAR
-	_	_	I-VAR
lamps	_	_	I-VAR
and	_	_	O
50	_	_	B-LIMIT
night	_	_	B-VAR
-	_	_	I-VAR
lamps	_	_	I-VAR
each	_	_	O
day	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
due	_	_	O
to	_	_	O
the	_	_	O
size	_	_	O
of	_	_	O
their	_	_	O
factory	_	_	O
,	_	_	O
they	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
150	_	_	B-LIMIT
desk	_	_	B-VAR
-	_	_	I-VAR
lamps	_	_	I-VAR
and	_	_	O
180	_	_	B-LIMIT
night	_	_	B-VAR
-	_	_	I-VAR
lamps	_	_	I-VAR
per	_	_	O
day	_	_	O
.	_	_	O
To	_	_	O
satisfy	_	_	O
a	_	_	O
contract	_	_	O
,	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
100	_	_	B-LIMIT
lamps	_	_	O
must	_	_	O
be	_	_	O
made	_	_	O
each	_	_	O
day	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
desk	_	_	B-VAR
-	_	_	I-VAR
lamp	_	_	I-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
night	_	_	B-VAR
-	_	_	I-VAR
lamp	_	_	I-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
8	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
lamps	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
audio	_	_	O
company	_	_	O
make	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
headphones	_	_	O
:	_	_	O
wired	_	_	B-VAR
headphones	_	_	I-VAR
and	_	_	O
wireless	_	_	B-VAR
headphones	_	_	I-VAR
.	_	_	O
Two	_	_	O
different	_	_	O
teams	_	_	O
make	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
headphones	_	_	O
.	_	_	O
The	_	_	O
wired	_	_	O
team	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
wired	_	_	B-VAR
headphones	_	_	I-VAR
per	_	_	O
day	_	_	O
and	_	_	O
the	_	_	O
wireless	_	_	O
team	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
170	_	_	B-LIMIT
wireless	_	_	B-VAR
headphones	_	_	I-VAR
per	_	_	O
day	_	_	O
.	_	_	O
Both	_	_	O
teams	_	_	O
require	_	_	O
use	_	_	O
of	_	_	O
a	_	_	O
shared	_	_	O
audio	_	_	O
testing	_	_	O
machine	_	_	O
,	_	_	O
and	_	_	O
this	_	_	O
machine	_	_	O
can	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
150	_	_	B-LIMIT
headphones	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
wired	_	_	B-VAR
headphone	_	_	I-VAR
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
wireless	_	_	B-VAR
headphone	_	_	I-VAR
$	_	_	O
20	_	_	B-PARAM
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
headphone	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Each	_	_	O
month	_	_	O
a	_	_	O
store	_	_	O
owner	_	_	O
can	_	_	O
spend	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
500	_	_	B-LIMIT
on	_	_	O
carrots	_	_	B-VAR
and	_	_	O
cucumbers	_	_	B-VAR
.	_	_	O
A	_	_	O
carrot	_	_	B-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
owner	_	_	O
$	_	_	O
0.30	_	_	B-PARAM
and	_	_	O
a	_	_	O
cucumber	_	_	B-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
owner	_	_	O
$	_	_	O
0.50	_	_	B-PARAM
.	_	_	O
Each	_	_	O
carrot	_	_	B-VAR
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
0.75	_	_	B-PARAM
and	_	_	O
each	_	_	O
cucumber	_	_	B-VAR
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
0.80	_	_	B-PARAM
.	_	_	O
The	_	_	O
owner	_	_	O
estimates	_	_	O
that	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
cucumbers	_	_	B-VAR
sold	_	_	O
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
a	_	_	O
third	_	_	B-PARAM
of	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
carrots	_	_	B-VAR
sold	_	_	O
.	_	_	O
He	_	_	O
also	_	_	O
estimates	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
300	_	_	B-LIMIT
carrots	_	_	B-VAR
but	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
500	_	_	B-LIMIT
carrots	_	_	B-VAR
are	_	_	O
sold	_	_	O
each	_	_	O
month	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
,	_	_	O
carrots	_	_	B-VAR
and	_	_	O
cucumbers	_	_	B-VAR
,	_	_	O
should	_	_	O
be	_	_	O
sold	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

Ben	_	_	O
is	_	_	O
growing	_	_	O
apples	_	_	B-VAR
and	_	_	O
pears	_	_	B-VAR
on	_	_	O
his	_	_	O
orchard	_	_	O
.	_	_	O
He	_	_	O
has	_	_	O
50	_	_	B-LIMIT
acres	_	_	O
available	_	_	B-CONST_DIR
on	_	_	O
which	_	_	O
he	_	_	O
must	_	_	O
grow	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
5	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
apples	_	_	B-VAR
and	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
10	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
pears	_	_	B-VAR
to	_	_	O
meet	_	_	O
demands	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
apple	_	_	B-VAR
is	_	_	O
$	_	_	O
2	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
pear	_	_	B-VAR
is	_	_	O
$	_	_	O
4	_	_	B-PARAM
.	_	_	O
He	_	_	O
prefers	_	_	O
to	_	_	O
grow	_	_	O
more	_	_	O
pears	_	_	B-VAR
than	_	_	O
apples	_	_	B-VAR
but	_	_	O
limitations	_	_	O
in	_	_	O
his	_	_	O
workforce	_	_	O
allow	_	_	O
him	_	_	O
to	_	_	O
grow	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
twice	_	_	B-PARAM
the	_	_	O
amount	_	_	O
of	_	_	O
pears	_	_	B-VAR
as	_	_	O
apples	_	_	B-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
fruit	_	_	O
should	_	_	O
Ben	_	_	O
grow	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O
What	_	_	O
is	_	_	O
that	_	_	O
profit	_	_	O
?	_	_	O

An	_	_	O
office	_	_	O
supply	_	_	O
company	_	_	O
makes	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
printers	_	_	O
:	_	_	O
color	_	_	B-VAR
printers	_	_	I-VAR
and	_	_	O
black	_	_	B-VAR
and	_	_	I-VAR
white	_	_	I-VAR
printers	_	_	I-VAR
.	_	_	O
Different	_	_	O
sections	_	_	O
of	_	_	O
the	_	_	O
factory	_	_	O
with	_	_	O
different	_	_	O
teams	_	_	O
produce	_	_	O
each	_	_	O
printer	_	_	O
.	_	_	O
The	_	_	O
color	_	_	O
printer	_	_	O
team	_	_	O
can	_	_	O
produce	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
20	_	_	B-LIMIT
color	_	_	B-VAR
printers	_	_	I-VAR
per	_	_	O
day	_	_	O
while	_	_	O
the	_	_	O
black	_	_	O
and	_	_	O
white	_	_	O
printer	_	_	O
team	_	_	O
can	_	_	O
produce	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
black	_	_	B-VAR
and	_	_	I-VAR
white	_	_	I-VAR
printers	_	_	I-VAR
per	_	_	O
day	_	_	O
.	_	_	O
Both	_	_	O
teams	_	_	O
require	_	_	O
use	_	_	O
of	_	_	O
the	_	_	O
same	_	_	O
paper	_	_	O
tray	_	_	O
installing	_	_	O
machine	_	_	O
and	_	_	O
this	_	_	O
machine	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
35	_	_	B-LIMIT
printers	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
each	_	_	O
day	_	_	O
.	_	_	O
Color	_	_	B-VAR
printers	_	_	I-VAR
generate	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
200	_	_	B-PARAM
per	_	_	O
printer	_	_	O
while	_	_	O
black	_	_	B-VAR
and	_	_	I-VAR
white	_	_	I-VAR
printers	_	_	I-VAR
generate	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
70	_	_	B-PARAM
per	_	_	O
printer	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
printer	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
company	_	_	O
's	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

Jacob	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
3000	_	_	B-LIMIT
to	_	_	O
invest	_	_	O
.	_	_	O
He	_	_	O
has	_	_	O
decided	_	_	O
to	_	_	O
invest	_	_	O
in	_	_	O
his	_	_	O
favorite	_	_	O
clothing	_	_	B-VAR
company	_	_	I-VAR
and	_	_	O
his	_	_	O
favorite	_	_	O
tech	_	_	B-VAR
company	_	_	I-VAR
.	_	_	O
He	_	_	O
has	_	_	O
decided	_	_	O
that	_	_	O
the	_	_	O
money	_	_	O
invested	_	_	O
in	_	_	O
his	_	_	O
favorite	_	_	O
clothing	_	_	B-VAR
company	_	_	I-VAR
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
four	_	_	B-PARAM
times	_	_	O
as	_	_	O
much	_	_	O
as	_	_	O
the	_	_	O
amount	_	_	O
invested	_	_	O
in	_	_	O
his	_	_	O
favorite	_	_	O
tech	_	_	B-VAR
company	_	_	I-VAR
.	_	_	O
He	_	_	O
has	_	_	O
also	_	_	O
limited	_	_	O
himself	_	_	O
to	_	_	O
invest	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
500	_	_	B-LIMIT
in	_	_	O
his	_	_	O
favorite	_	_	O
tech	_	_	B-VAR
company	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
money	_	_	O
invested	_	_	O
in	_	_	O
his	_	_	O
favorite	_	_	O
clothing	_	_	B-VAR
company	_	_	I-VAR
earns	_	_	B-OBJ_NAME
7	_	_	B-PARAM
%	_	_	I-PARAM
and	_	_	O
the	_	_	O
money	_	_	O
invested	_	_	O
in	_	_	O
his	_	_	O
favorite	_	_	O
tech	_	_	B-VAR
company	_	_	I-VAR
earns	_	_	B-OBJ_NAME
10	_	_	B-PARAM
%	_	_	I-PARAM
,	_	_	O
how	_	_	O
much	_	_	O
should	_	_	O
he	_	_	O
invest	_	_	O
in	_	_	O
each	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
farmer	_	_	O
has	_	_	O
140	_	_	B-LIMIT
hectares	_	_	O
available	_	_	B-CONST_DIR
to	_	_	O
grow	_	_	O
tomatoes	_	_	B-VAR
and	_	_	O
potatoes	_	_	B-VAR
.	_	_	O
She	_	_	O
prefers	_	_	O
to	_	_	O
plant	_	_	O
more	_	_	O
tomatoes	_	_	B-VAR
than	_	_	O
potatoes	_	_	B-VAR
,	_	_	O
but	_	_	O
the	_	_	O
soil	_	_	O
and	_	_	O
weather	_	_	O
conditions	_	_	O
allow	_	_	O
her	_	_	O
to	_	_	O
grow	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
twice	_	_	B-PARAM
the	_	_	O
amount	_	_	O
of	_	_	O
tomatoes	_	_	B-VAR
to	_	_	O
that	_	_	O
of	_	_	O
potatoes	_	_	B-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
she	_	_	O
must	_	_	O
grow	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
hectares	_	_	O
of	_	_	O
tomatoes	_	_	B-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
hectares	_	_	O
of	_	_	O
potatoes	_	_	B-VAR
to	_	_	O
meet	_	_	O
community	_	_	O
demands	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
hectare	_	_	O
of	_	_	O
tomatoes	_	_	B-VAR
is	_	_	O
$	_	_	O
350	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
hectare	_	_	O
of	_	_	O
potatoes	_	_	B-VAR
is	_	_	O
$	_	_	O
600	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
hectares	_	_	O
of	_	_	O
each	_	_	O
crop	_	_	O
should	_	_	O
she	_	_	O
plant	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O
What	_	_	O
is	_	_	O
this	_	_	O
profit	_	_	O
?	_	_	O

A	_	_	O
chocolate	_	_	O
company	_	_	O
can	_	_	O
transport	_	_	O
their	_	_	O
boxes	_	_	O
of	_	_	O
chocolate	_	_	O
either	_	_	O
using	_	_	O
their	_	_	O
own	_	_	O
vans	_	_	B-VAR
or	_	_	O
by	_	_	O
renting	_	_	O
trucks	_	_	B-VAR
.	_	_	O
Their	_	_	O
vans	_	_	B-VAR
can	_	_	O
transport	_	_	O
50	_	_	B-PARAM
boxes	_	_	O
per	_	_	O
trip	_	_	O
while	_	_	O
a	_	_	O
truck	_	_	B-VAR
can	_	_	O
transport	_	_	O
80	_	_	B-PARAM
boxes	_	_	O
per	_	_	O
trip	_	_	O
.	_	_	O
Since	_	_	O
they	_	_	O
own	_	_	O
their	_	_	O
vans	_	_	B-VAR
,	_	_	O
the	_	_	O
cost	_	_	O
per	_	_	O
van	_	_	B-VAR
trip	_	_	O
is	_	_	O
$	_	_	O
30	_	_	B-PARAM
while	_	_	O
the	_	_	O
cost	_	_	O
per	_	_	O
truck	_	_	B-VAR
trip	_	_	O
is	_	_	O
$	_	_	O
50	_	_	B-PARAM
.	_	_	O
The	_	_	O
company	_	_	O
needs	_	_	O
to	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1500	_	_	B-LIMIT
boxes	_	_	O
of	_	_	O
chocolate	_	_	O
and	_	_	O
they	_	_	O
have	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
1000	_	_	B-LIMIT
.	_	_	O
Since	_	_	O
the	_	_	O
vans	_	_	B-VAR
also	_	_	O
provide	_	_	O
advertising	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
trips	_	_	O
by	_	_	O
van	_	_	B-VAR
must	_	_	B-CONST_DIR
be	_	_	I-CONST_DIR
larger	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
trips	_	_	O
by	_	_	O
trucks	_	_	B-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
trip	_	_	O
by	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
done	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
trips	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
bee	_	_	O
farmer	_	_	O
transports	_	_	O
his	_	_	O
honey	_	_	O
in	_	_	O
small	_	_	B-VAR
and	_	_	O
large	_	_	B-VAR
bottles	_	_	O
.	_	_	O
A	_	_	O
small	_	_	B-VAR
bottle	_	_	I-VAR
can	_	_	O
take	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
honey	_	_	B-OBJ_NAME
while	_	_	O
a	_	_	O
large	_	_	B-VAR
bottle	_	_	I-VAR
can	_	_	O
take	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
honey	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
farmer	_	_	O
has	_	_	O
available	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
300	_	_	B-LIMIT
small	_	_	B-VAR
bottles	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
large	_	_	B-VAR
bottles	_	_	I-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
since	_	_	O
small	_	_	B-VAR
bottles	_	_	I-VAR
are	_	_	O
easier	_	_	O
to	_	_	O
sell	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-PARAM
as	_	_	O
many	_	_	O
small	_	_	B-VAR
bottles	_	_	I-VAR
must	_	_	O
be	_	_	O
used	_	_	O
than	_	_	O
large	_	_	B-VAR
bottles	_	_	I-VAR
.	_	_	O
Finally	_	_	O
,	_	_	O
he	_	_	O
can	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
200	_	_	B-LIMIT
bottles	_	_	O
total	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
must	_	_	O
be	_	_	O
large	_	_	B-VAR
bottles	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
bottle	_	_	O
should	_	_	O
be	_	_	O
use	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
honey	_	_	I-OBJ_NAME
he	_	_	O
can	_	_	O
transport	_	_	O
?	_	_	O

An	_	_	O
international	_	_	O
goods	_	_	O
exporter	_	_	O
uses	_	_	O
ships	_	_	B-VAR
and	_	_	O
planes	_	_	B-VAR
to	_	_	O
transport	_	_	O
goods	_	_	O
.	_	_	O
A	_	_	O
ship	_	_	B-VAR
can	_	_	O
take	_	_	O
40	_	_	B-PARAM
containers	_	_	O
worth	_	_	O
of	_	_	O
goods	_	_	O
and	_	_	O
uses	_	_	O
500	_	_	B-PARAM
liters	_	_	O
of	_	_	O
fuel	_	_	B-OBJ_NAME
per	_	_	O
trip	_	_	O
.	_	_	O
A	_	_	O
plane	_	_	B-VAR
can	_	_	O
take	_	_	O
20	_	_	B-PARAM
containers	_	_	O
worth	_	_	O
of	_	_	O
goods	_	_	O
and	_	_	O
uses	_	_	O
300	_	_	B-PARAM
liters	_	_	O
of	_	_	O
fuel	_	_	B-OBJ_NAME
per	_	_	O
trip	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
needs	_	_	O
to	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
500	_	_	B-LIMIT
containers	_	_	O
worth	_	_	O
of	_	_	O
goods	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
there	_	_	O
can	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
10	_	_	B-LIMIT
plane	_	_	B-VAR
trips	_	_	O
made	_	_	O
and	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
50	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
trips	_	_	O
made	_	_	O
must	_	_	O
be	_	_	O
by	_	_	O
ship	_	_	B-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
trip	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
amount	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
fuel	_	_	I-OBJ_NAME
consumed	_	_	O
?	_	_	O

There	_	_	O
has	_	_	O
been	_	_	O
an	_	_	O
oil	_	_	O
spill	_	_	O
in	_	_	O
the	_	_	O
ocean	_	_	O
and	_	_	O
ducks	_	_	O
need	_	_	O
to	_	_	O
be	_	_	O
taken	_	_	O
to	_	_	O
shore	_	_	O
to	_	_	O
be	_	_	O
cleaned	_	_	O
either	_	_	O
by	_	_	O
boat	_	_	B-VAR
or	_	_	O
by	_	_	O
canoe	_	_	B-VAR
.	_	_	O
A	_	_	O
boat	_	_	B-VAR
can	_	_	O
take	_	_	O
10	_	_	B-PARAM
ducks	_	_	O
per	_	_	O
trip	_	_	O
while	_	_	O
a	_	_	O
canoe	_	_	B-VAR
can	_	_	O
take	_	_	O
8	_	_	B-PARAM
ducks	_	_	O
per	_	_	O
trip	_	_	O
.	_	_	O
Since	_	_	O
the	_	_	O
boats	_	_	B-VAR
are	_	_	O
motor	_	_	O
powered	_	_	O
,	_	_	O
they	_	_	O
take	_	_	O
20	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
per	_	_	O
trip	_	_	O
while	_	_	O
the	_	_	O
canoes	_	_	B-VAR
take	_	_	O
40	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
per	_	_	O
trip	_	_	O
.	_	_	O
In	_	_	O
order	_	_	O
to	_	_	O
avoid	_	_	O
further	_	_	O
environmental	_	_	O
damage	_	_	O
,	_	_	O
there	_	_	O
can	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
12	_	_	B-LIMIT
boat	_	_	B-VAR
trips	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
60	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
trips	_	_	O
should	_	_	O
be	_	_	O
by	_	_	O
canoe	_	_	B-VAR
.	_	_	O
If	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
300	_	_	B-LIMIT
ducks	_	_	O
need	_	_	O
to	_	_	O
be	_	_	O
taken	_	_	O
to	_	_	O
shore	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
transportation	_	_	O
method	_	_	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
time	_	_	I-OBJ_NAME
needed	_	_	O
to	_	_	O
transport	_	_	O
the	_	_	O
ducks	_	_	O
?	_	_	O

A	_	_	O
soda	_	_	O
company	_	_	O
sends	_	_	O
bottles	_	_	O
of	_	_	O
their	_	_	O
soda	_	_	O
to	_	_	O
stores	_	_	O
around	_	_	O
the	_	_	O
city	_	_	O
in	_	_	O
old	_	_	B-VAR
and	_	_	O
new	_	_	B-VAR
vans	_	_	I-VAR
.	_	_	O
An	_	_	O
old	_	_	B-VAR
van	_	_	I-VAR
can	_	_	O
take	_	_	O
100	_	_	B-PARAM
soda	_	_	O
bottles	_	_	O
while	_	_	O
a	_	_	O
new	_	_	B-VAR
van	_	_	I-VAR
can	_	_	O
take	_	_	O
80	_	_	B-PARAM
soda	_	_	O
bottles	_	_	O
.	_	_	O
An	_	_	O
old	_	_	B-VAR
van	_	_	I-VAR
produces	_	_	O
50	_	_	B-PARAM
units	_	_	O
of	_	_	O
pollution	_	_	B-OBJ_NAME
while	_	_	O
a	_	_	O
new	_	_	B-VAR
van	_	_	I-VAR
only	_	_	O
produces	_	_	O
30	_	_	B-PARAM
units	_	_	O
of	_	_	O
pollution	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
company	_	_	O
needs	_	_	O
to	_	_	O
send	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5000	_	_	B-LIMIT
bottles	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
new	_	_	B-VAR
vans	_	_	I-VAR
can	_	_	O
be	_	_	O
used	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
van	_	_	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
lawn	_	_	O
mowing	_	_	O
service	_	_	O
provides	_	_	O
neighborhood	_	_	O
services	_	_	O
using	_	_	O
small	_	_	B-VAR
teams	_	_	I-VAR
and	_	_	O
large	_	_	B-VAR
teams	_	_	I-VAR
.	_	_	O
A	_	_	O
small	_	_	B-VAR
team	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
employees	_	_	O
and	_	_	O
can	_	_	O
mow	_	_	O
50	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
of	_	_	O
lawn	_	_	B-OBJ_NAME
.	_	_	O
A	_	_	O
large	_	_	B-VAR
team	_	_	I-VAR
requires	_	_	O
5	_	_	B-PARAM
employees	_	_	O
and	_	_	O
can	_	_	O
mow	_	_	O
80	_	_	B-PARAM
sq	_	_	O
ft	_	_	O
of	_	_	O
lawn	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
150	_	_	B-LIMIT
employees	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
Because	_	_	O
most	_	_	O
people	_	_	O
have	_	_	O
smaller	_	_	O
lawns	_	_	O
in	_	_	O
the	_	_	O
city	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
small	_	_	B-VAR
teams	_	_	I-VAR
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	O
as	_	_	O
much	_	_	O
as	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
large	_	_	B-VAR
teams	_	_	I-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
to	_	_	O
make	_	_	O
sure	_	_	O
the	_	_	O
company	_	_	O
can	_	_	O
meet	_	_	O
all	_	_	O
demands	_	_	O
,	_	_	O
there	_	_	O
has	_	_	O
to	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
6	_	_	B-LIMIT
large	_	_	B-VAR
teams	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
small	_	_	B-VAR
teams	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
team	_	_	O
type	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
lawn	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
mowed	_	_	O
?	_	_	O

An	_	_	O
aquarium	_	_	O
does	_	_	O
shows	_	_	O
using	_	_	O
otters	_	_	B-VAR
and	_	_	O
dolphins	_	_	B-VAR
.	_	_	O
An	_	_	O
otter	_	_	B-VAR
will	_	_	O
do	_	_	O
3	_	_	B-PARAM
tricks	_	_	B-OBJ_NAME
at	_	_	O
a	_	_	O
time	_	_	O
and	_	_	O
requires	_	_	O
3	_	_	B-PARAM
treats	_	_	O
to	_	_	O
do	_	_	O
so	_	_	O
.	_	_	O
A	_	_	O
dolphin	_	_	B-VAR
will	_	_	O
do	_	_	O
1	_	_	B-PARAM
trick	_	_	B-OBJ_NAME
at	_	_	O
a	_	_	O
time	_	_	O
and	_	_	O
requires	_	_	O
5	_	_	B-PARAM
treats	_	_	O
to	_	_	O
do	_	_	O
so	_	_	O
.	_	_	O
Since	_	_	O
dolphins	_	_	B-VAR
are	_	_	O
more	_	_	O
popular	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
dolphins	_	_	B-VAR
must	_	_	O
be	_	_	O
used	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
performers	_	_	O
can	_	_	O
be	_	_	O
otters	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
aquarium	_	_	O
only	_	_	O
has	_	_	O
200	_	_	B-LIMIT
treats	_	_	O
available	_	_	B-CONST_DIR
,	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
tricks	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
preformed	_	_	O
.	_	_	O

A	_	_	O
shoe	_	_	O
company	_	_	O
supplies	_	_	O
shoes	_	_	O
to	_	_	O
stores	_	_	O
via	_	_	O
vans	_	_	B-VAR
and	_	_	O
trucks	_	_	B-VAR
.	_	_	O
A	_	_	O
van	_	_	B-VAR
can	_	_	O
transport	_	_	O
50	_	_	B-PARAM
pairs	_	_	O
of	_	_	O
shoes	_	_	O
while	_	_	O
a	_	_	O
truck	_	_	B-VAR
can	_	_	O
transport	_	_	O
100	_	_	B-PARAM
pairs	_	_	O
of	_	_	O
shoes	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
must	_	_	O
supply	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
2000	_	_	B-LIMIT
pairs	_	_	O
of	_	_	O
shoes	_	_	O
around	_	_	O
the	_	_	O
city	_	_	O
.	_	_	O
Since	_	_	O
most	_	_	O
stores	_	_	O
are	_	_	O
small	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
trucks	_	_	B-VAR
used	_	_	O
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
vans	_	_	B-VAR
used	_	_	O
.	_	_	O
Find	_	_	O
the	_	_	O
minimum	_	_	B-OBJ_DIR
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
vans	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
used	_	_	O
?	_	_	O

An	_	_	O
oil	_	_	O
and	_	_	O
gas	_	_	O
company	_	_	O
is	_	_	O
sending	_	_	O
their	_	_	O
oil	_	_	O
to	_	_	O
the	_	_	O
port	_	_	O
using	_	_	O
containers	_	_	B-VAR
and	_	_	O
trucks	_	_	B-VAR
.	_	_	O
A	_	_	O
container	_	_	B-VAR
can	_	_	O
hold	_	_	O
30	_	_	B-PARAM
units	_	_	O
of	_	_	O
oil	_	_	O
while	_	_	O
a	_	_	O
truck	_	_	B-VAR
can	_	_	O
hold	_	_	O
40	_	_	B-PARAM
units	_	_	O
of	_	_	O
oil	_	_	O
.	_	_	O
Due	_	_	O
to	_	_	O
government	_	_	O
restrictions	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
trucks	_	_	B-VAR
used	_	_	O
has	_	_	O
to	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
half	_	_	B-PARAM
the	_	_	O
number	_	_	O
of	_	_	O
containers	_	_	B-VAR
used	_	_	O
.	_	_	O
If	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
2000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
oil	_	_	O
need	_	_	O
to	_	_	O
be	_	_	O
sent	_	_	O
to	_	_	O
the	_	_	O
port	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
15	_	_	B-LIMIT
containers	_	_	B-VAR
need	_	_	O
to	_	_	O
be	_	_	O
used	_	_	O
,	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
containers	_	_	I-OBJ_NAME
and	_	_	I-OBJ_NAME
trucks	_	_	I-OBJ_NAME
needed	_	_	O
.	_	_	O

A	_	_	O
school	_	_	O
is	_	_	O
organizing	_	_	O
a	_	_	O
field	_	_	O
trip	_	_	O
to	_	_	O
a	_	_	O
science	_	_	O
center	_	_	O
and	_	_	O
wants	_	_	O
to	_	_	O
hire	_	_	O
small	_	_	B-VAR
buses	_	_	I-VAR
and	_	_	O
large	_	_	B-VAR
buses	_	_	I-VAR
.	_	_	O
A	_	_	O
small	_	_	B-VAR
bus	_	_	I-VAR
can	_	_	O
carry	_	_	O
20	_	_	B-PARAM
students	_	_	O
while	_	_	O
a	_	_	O
large	_	_	B-VAR
bus	_	_	I-VAR
can	_	_	O
carry	_	_	O
50	_	_	B-PARAM
students	_	_	O
.	_	_	O
The	_	_	O
school	_	_	O
needs	_	_	O
to	_	_	O
provide	_	_	O
transportation	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
500	_	_	B-LIMIT
students	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
since	_	_	O
the	_	_	O
parking	_	_	O
lot	_	_	O
is	_	_	O
rather	_	_	O
small	_	_	O
,	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
20	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
buses	_	_	O
can	_	_	O
be	_	_	O
large	_	_	B-VAR
buses	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
bus	_	_	O
should	_	_	O
be	_	_	O
hired	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
buses	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
meat	_	_	O
shop	_	_	O
ships	_	_	O
their	_	_	O
burger	_	_	O
patties	_	_	O
using	_	_	O
refrigerated	_	_	O
trucks	_	_	B-VAR
and	_	_	O
vans	_	_	B-VAR
.	_	_	O
Each	_	_	O
truck	_	_	B-VAR
can	_	_	O
take	_	_	O
1000	_	_	B-PARAM
patties	_	_	O
at	_	_	O
a	_	_	O
cost	_	_	O
of	_	_	O
$	_	_	O
300	_	_	B-PARAM
per	_	_	O
trip	_	_	O
.	_	_	O
Each	_	_	O
van	_	_	B-VAR
can	_	_	O
take	_	_	O
500	_	_	B-PARAM
patties	_	_	O
at	_	_	O
a	_	_	O
cost	_	_	O
of	_	_	O
$	_	_	O
100	_	_	B-PARAM
per	_	_	O
trip	_	_	O
.	_	_	O
Because	_	_	O
the	_	_	O
trucks	_	_	B-VAR
have	_	_	O
difficulty	_	_	O
moving	_	_	O
around	_	_	O
in	_	_	O
the	_	_	O
city	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
trucks	_	_	B-VAR
must	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
vans	_	_	B-VAR
.	_	_	O
The	_	_	O
meat	_	_	O
shop	_	_	O
has	_	_	O
to	_	_	O
ship	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50000	_	_	B-LIMIT
patties	_	_	O
and	_	_	O
they	_	_	O
have	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
12500	_	_	B-LIMIT
.	_	_	O
How	_	_	O
should	_	_	O
they	_	_	O
plan	_	_	O
their	_	_	O
shipment	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
trips	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
florist	_	_	O
transports	_	_	O
his	_	_	O
flowers	_	_	O
to	_	_	O
stores	_	_	O
in	_	_	O
small	_	_	B-VAR
bouquets	_	_	I-VAR
and	_	_	O
large	_	_	B-VAR
bouquets	_	_	I-VAR
.	_	_	O
A	_	_	O
small	_	_	B-VAR
bouquet	_	_	I-VAR
has	_	_	O
5	_	_	B-PARAM
flowers	_	_	B-OBJ_NAME
while	_	_	O
a	_	_	O
large	_	_	B-VAR
bouquet	_	_	I-VAR
has	_	_	O
10	_	_	B-PARAM
flowers	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
florist	_	_	O
can	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
80	_	_	B-LIMIT
small	_	_	B-VAR
bouquets	_	_	I-VAR
and	_	_	O
50	_	_	B-LIMIT
large	_	_	B-VAR
bouquets	_	_	I-VAR
.	_	_	O
In	_	_	O
total	_	_	O
,	_	_	O
he	_	_	O
can	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
70	_	_	B-LIMIT
bouquets	_	_	O
and	_	_	O
he	_	_	O
must	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
large	_	_	B-VAR
bouquets	_	_	I-VAR
.	_	_	O
Since	_	_	O
small	_	_	B-VAR
bouquets	_	_	I-VAR
are	_	_	O
more	_	_	O
popular	_	_	O
,	_	_	O
he	_	_	O
must	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-PARAM
as	_	_	O
many	_	_	O
small	_	_	B-VAR
bouquets	_	_	I-VAR
as	_	_	O
large	_	_	B-VAR
bouquets	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
bouquet	_	_	O
should	_	_	O
he	_	_	O
transport	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
flowers	_	_	I-OBJ_NAME
that	_	_	O
reach	_	_	O
the	_	_	O
stores	_	_	O
?	_	_	O

A	_	_	O
toy	_	_	O
store	_	_	O
decides	_	_	O
to	_	_	O
deliver	_	_	O
gifts	_	_	O
using	_	_	O
two	_	_	O
shipping	_	_	O
companies	_	_	O
,	_	_	O
a	_	_	O
new	_	_	B-VAR
one	_	_	I-VAR
and	_	_	O
an	_	_	O
old	_	_	B-VAR
one	_	_	I-VAR
.	_	_	O
The	_	_	O
new	_	_	B-VAR
company	_	_	I-VAR
can	_	_	O
deliver	_	_	O
50	_	_	B-PARAM
gifts	_	_	O
per	_	_	O
trip	_	_	O
while	_	_	O
the	_	_	O
old	_	_	B-VAR
company	_	_	I-VAR
can	_	_	O
deliver	_	_	O
70	_	_	B-PARAM
gifts	_	_	O
per	_	_	O
trip	_	_	O
.	_	_	O
The	_	_	O
new	_	_	B-VAR
company	_	_	I-VAR
uses	_	_	O
30	_	_	B-PARAM
liters	_	_	O
of	_	_	O
diesel	_	_	B-OBJ_NAME
per	_	_	O
trip	_	_	O
while	_	_	O
the	_	_	O
old	_	_	B-VAR
company	_	_	I-VAR
uses	_	_	O
40	_	_	B-PARAM
liters	_	_	O
of	_	_	O
diesel	_	_	B-OBJ_NAME
per	_	_	O
trip	_	_	O
.	_	_	O
The	_	_	O
toy	_	_	O
store	_	_	O
needs	_	_	O
to	_	_	O
deliver	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1000	_	_	B-LIMIT
gifts	_	_	O
.	_	_	O
There	_	_	O
can	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
15	_	_	B-LIMIT
trips	_	_	O
made	_	_	O
by	_	_	O
the	_	_	O
new	_	_	B-VAR
company	_	_	I-VAR
.	_	_	O
In	_	_	O
order	_	_	O
to	_	_	O
make	_	_	O
sure	_	_	O
that	_	_	O
the	_	_	O
old	_	_	B-VAR
company	_	_	I-VAR
does	_	_	O
not	_	_	O
go	_	_	O
out	_	_	O
of	_	_	O
business	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
40	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
all	_	_	O
trips	_	_	O
must	_	_	O
be	_	_	O
made	_	_	O
by	_	_	O
the	_	_	O
old	_	_	B-VAR
company	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
trips	_	_	O
should	_	_	O
each	_	_	O
company	_	_	O
make	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
amount	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
diesel	_	_	I-OBJ_NAME
used	_	_	O
?	_	_	O

A	_	_	O
zoo	_	_	O
needs	_	_	O
to	_	_	O
transport	_	_	O
their	_	_	O
monkeys	_	_	O
to	_	_	O
the	_	_	O
vet	_	_	O
either	_	_	O
by	_	_	O
bus	_	_	B-VAR
or	_	_	O
by	_	_	O
car	_	_	B-VAR
.	_	_	O
A	_	_	O
bus	_	_	B-VAR
can	_	_	O
transport	_	_	O
20	_	_	B-PARAM
monkeys	_	_	O
per	_	_	O
trip	_	_	O
and	_	_	O
takes	_	_	O
30	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
.	_	_	O
A	_	_	O
car	_	_	B-VAR
can	_	_	O
transport	_	_	O
6	_	_	B-PARAM
monkeys	_	_	O
per	_	_	O
trip	_	_	O
and	_	_	O
takes	_	_	O
15	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
.	_	_	O
There	_	_	O
can	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
10	_	_	B-LIMIT
bus	_	_	B-VAR
trips	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
since	_	_	O
the	_	_	O
monkeys	_	_	O
get	_	_	O
aggressive	_	_	O
when	_	_	O
there	_	_	O
are	_	_	O
too	_	_	O
many	_	_	O
in	_	_	O
one	_	_	O
place	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
60	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
trips	_	_	O
should	_	_	O
be	_	_	O
by	_	_	O
car	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
zoo	_	_	O
needs	_	_	B-CONST_DIR
to	_	_	O
transport	_	_	O
300	_	_	B-LIMIT
monkeys	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
trips	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
done	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
time	_	_	I-OBJ_NAME
required	_	_	O
to	_	_	O
transport	_	_	O
the	_	_	O
monkeys	_	_	O
?	_	_	O

A	_	_	O
farmer	_	_	O
decides	_	_	O
to	_	_	O
move	_	_	O
his	_	_	O
cows	_	_	O
to	_	_	O
a	_	_	O
nearby	_	_	O
farm	_	_	O
using	_	_	O
helicopters	_	_	B-VAR
and	_	_	O
trucks	_	_	B-VAR
.	_	_	O
A	_	_	O
helicopter	_	_	B-VAR
can	_	_	O
take	_	_	O
3	_	_	B-PARAM
cows	_	_	O
per	_	_	O
trip	_	_	O
and	_	_	O
creates	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
pollution	_	_	B-OBJ_NAME
.	_	_	O
A	_	_	O
truck	_	_	B-VAR
can	_	_	O
take	_	_	O
7	_	_	B-PARAM
cows	_	_	O
per	_	_	O
trip	_	_	O
and	_	_	O
creates	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
pollution	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
farmer	_	_	O
needs	_	_	B-CONST_DIR
to	_	_	I-CONST_DIR
transport	_	_	I-CONST_DIR
80	_	_	B-LIMIT
cows	_	_	O
and	_	_	O
he	_	_	O
only	_	_	O
has	_	_	O
enough	_	_	O
money	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
8	_	_	B-LIMIT
truck	_	_	B-VAR
trips	_	_	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	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
pollution	_	_	I-OBJ_NAME
produced	_	_	O
?	_	_	O

A	_	_	O
sand	_	_	O
company	_	_	O
delivers	_	_	O
sand	_	_	O
for	_	_	O
playgrounds	_	_	O
in	_	_	O
small	_	_	B-VAR
and	_	_	O
large	_	_	B-VAR
containers	_	_	O
.	_	_	O
A	_	_	O
small	_	_	B-VAR
container	_	_	I-VAR
requires	_	_	O
1	_	_	B-PARAM
person	_	_	O
to	_	_	O
unload	_	_	O
and	_	_	O
can	_	_	O
hold	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
sand	_	_	B-OBJ_NAME
.	_	_	O
A	_	_	O
large	_	_	B-VAR
container	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
people	_	_	O
to	_	_	O
unload	_	_	O
and	_	_	O
can	_	_	O
hold	_	_	O
50	_	_	B-PARAM
units	_	_	O
of	_	_	O
sand	_	_	B-OBJ_NAME
.	_	_	O
Since	_	_	O
most	_	_	O
playgrounds	_	_	O
are	_	_	O
small	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
small	_	_	B-VAR
containers	_	_	I-VAR
used	_	_	O
must	_	_	B-CONST_DIR
be	_	_	I-CONST_DIR
thrice	_	_	B-PARAM
the	_	_	O
number	_	_	O
of	_	_	O
large	_	_	B-VAR
containers	_	_	I-VAR
used	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
small	_	_	B-VAR
containers	_	_	I-VAR
and	_	_	O
3	_	_	B-LIMIT
large	_	_	B-VAR
containers	_	_	I-VAR
used	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
company	_	_	O
has	_	_	O
100	_	_	B-LIMIT
people	_	_	O
available	_	_	B-CONST_DIR
,	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
sand	_	_	I-OBJ_NAME
that	_	_	O
they	_	_	O
can	_	_	O
deliver	_	_	O
.	_	_	O

A	_	_	O
meal	_	_	O
service	_	_	O
company	_	_	O
delivers	_	_	O
meals	_	_	O
to	_	_	O
customers	_	_	O
either	_	_	O
on	_	_	O
electric	_	_	B-VAR
bikes	_	_	I-VAR
or	_	_	O
scooters	_	_	B-VAR
.	_	_	O
A	_	_	O
bike	_	_	B-VAR
can	_	_	O
hold	_	_	O
8	_	_	B-PARAM
meals	_	_	B-OBJ_NAME
and	_	_	O
requires	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
charge	_	_	O
.	_	_	O
A	_	_	O
scooter	_	_	B-VAR
can	_	_	O
hold	_	_	O
5	_	_	B-PARAM
meals	_	_	B-OBJ_NAME
and	_	_	O
requires	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
charge	_	_	O
.	_	_	O
Since	_	_	O
the	_	_	O
city	_	_	O
is	_	_	O
more	_	_	O
friendly	_	_	O
towards	_	_	O
scooters	_	_	B-VAR
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
electric	_	_	O
vehicles	_	_	O
can	_	_	O
be	_	_	O
bikes	_	_	B-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
scooters	_	_	B-VAR
must	_	_	O
be	_	_	O
used	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
company	_	_	O
only	_	_	O
has	_	_	O
200	_	_	B-LIMIT
units	_	_	O
of	_	_	O
charge	_	_	O
available	_	_	B-CONST_DIR
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
vehicle	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
meals	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
delivered	_	_	O
?	_	_	O

A	_	_	O
car	_	_	O
manufacturer	_	_	O
ships	_	_	O
their	_	_	O
cars	_	_	O
on	_	_	O
large	_	_	B-VAR
and	_	_	O
small	_	_	B-VAR
planes	_	_	O
.	_	_	O
A	_	_	O
large	_	_	B-VAR
plane	_	_	I-VAR
can	_	_	O
carry	_	_	O
30	_	_	B-PARAM
cars	_	_	O
while	_	_	O
a	_	_	O
small	_	_	B-VAR
plane	_	_	I-VAR
can	_	_	O
carry	_	_	O
10	_	_	B-PARAM
cars	_	_	O
.	_	_	O
Since	_	_	O
large	_	_	B-VAR
planes	_	_	I-VAR
cause	_	_	O
more	_	_	O
pollution	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
large	_	_	B-VAR
planes	_	_	I-VAR
must	_	_	O
be	_	_	O
less	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
small	_	_	B-VAR
planes	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
manufacturer	_	_	O
wants	_	_	O
to	_	_	O
deliver	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
300	_	_	B-LIMIT
cars	_	_	O
,	_	_	O
find	_	_	O
the	_	_	O
minimum	_	_	B-OBJ_DIR
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
planes	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
used	_	_	O
.	_	_	O

A	_	_	O
mine	_	_	O
sends	_	_	O
ore	_	_	O
to	_	_	O
the	_	_	O
surface	_	_	O
in	_	_	O
small	_	_	B-VAR
and	_	_	O
large	_	_	B-VAR
wagons	_	_	O
.	_	_	O
A	_	_	O
small	_	_	B-VAR
wagon	_	_	I-VAR
hold	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
ore	_	_	O
while	_	_	O
a	_	_	O
large	_	_	B-VAR
wagon	_	_	I-VAR
holds	_	_	O
50	_	_	B-PARAM
units	_	_	O
of	_	_	O
ore	_	_	O
.	_	_	O
To	_	_	O
avoid	_	_	O
taking	_	_	O
up	_	_	O
too	_	_	O
much	_	_	O
space	_	_	O
on	_	_	O
the	_	_	O
ramps	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
small	_	_	B-VAR
wagons	_	_	I-VAR
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-PARAM
as	_	_	O
much	_	_	O
as	_	_	O
the	_	_	O
number	_	_	O
or	_	_	O
large	_	_	B-VAR
wagons	_	_	I-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
large	_	_	B-VAR
wagons	_	_	I-VAR
must	_	_	O
be	_	_	O
used	_	_	O
.	_	_	O
If	_	_	O
2000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
ore	_	_	O
need	_	_	B-CONST_DIR
to	_	_	I-CONST_DIR
taken	_	_	I-CONST_DIR
to	_	_	O
the	_	_	O
surface	_	_	O
,	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
wagons	_	_	I-OBJ_NAME
needed	_	_	O
.	_	_	O

A	_	_	O
theme	_	_	O
park	_	_	O
transports	_	_	O
its	_	_	O
visitors	_	_	O
around	_	_	O
the	_	_	O
park	_	_	O
either	_	_	O
by	_	_	O
scooter	_	_	B-VAR
or	_	_	O
rickshaw	_	_	B-VAR
.	_	_	O
A	_	_	O
scooter	_	_	B-VAR
can	_	_	O
carry	_	_	O
2	_	_	B-PARAM
people	_	_	O
while	_	_	O
a	_	_	O
rickshaw	_	_	B-VAR
can	_	_	O
carry	_	_	O
3	_	_	B-PARAM
people	_	_	O
.	_	_	O
To	_	_	O
avoid	_	_	O
excessive	_	_	O
pollution	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
40	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
vehicles	_	_	O
used	_	_	O
can	_	_	O
be	_	_	O
rickshaws	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
park	_	_	O
needs	_	_	O
to	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
300	_	_	B-LIMIT
visitors	_	_	O
,	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
scooters	_	_	I-OBJ_NAME
used	_	_	O
.	_	_	O

A	_	_	O
company	_	_	O
in	_	_	O
the	_	_	O
middle	_	_	O
east	_	_	O
delivers	_	_	O
their	_	_	O
packages	_	_	O
to	_	_	O
customers	_	_	O
on	_	_	O
camels	_	_	B-VAR
and	_	_	O
horses	_	_	B-VAR
.	_	_	O
A	_	_	O
camel	_	_	B-VAR
can	_	_	O
carry	_	_	O
50	_	_	B-PARAM
packages	_	_	O
while	_	_	O
a	_	_	O
horse	_	_	B-VAR
can	_	_	O
carry	_	_	O
60	_	_	B-PARAM
packages	_	_	O
.	_	_	O
A	_	_	O
camel	_	_	B-VAR
requires	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
food	_	_	O
while	_	_	O
a	_	_	O
horse	_	_	B-VAR
requires	_	_	O
30	_	_	B-PARAM
units	_	_	O
of	_	_	O
food	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
needs	_	_	O
to	_	_	O
deliver	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1000	_	_	B-LIMIT
packages	_	_	O
and	_	_	O
they	_	_	O
have	_	_	O
450	_	_	B-LIMIT
units	_	_	O
of	_	_	O
food	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
Since	_	_	O
horses	_	_	B-VAR
are	_	_	O
not	_	_	O
as	_	_	O
suited	_	_	O
for	_	_	O
the	_	_	O
hot	_	_	O
climate	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
horses	_	_	B-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
camels	_	_	B-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
animal	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
animals	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
snack	_	_	O
exporter	_	_	O
sends	_	_	O
snacks	_	_	O
to	_	_	O
his	_	_	O
customer	_	_	O
in	_	_	O
small	_	_	B-VAR
and	_	_	O
large	_	_	B-VAR
suitcases	_	_	O
.	_	_	O
A	_	_	O
small	_	_	B-VAR
suitcase	_	_	I-VAR
can	_	_	O
hold	_	_	O
50	_	_	B-PARAM
snacks	_	_	B-OBJ_NAME
while	_	_	O
a	_	_	O
large	_	_	B-VAR
suitcase	_	_	I-VAR
can	_	_	O
hold	_	_	O
80	_	_	B-PARAM
snacks	_	_	B-OBJ_NAME
.	_	_	O
Most	_	_	O
customer	_	_	O
prefer	_	_	O
small	_	_	B-VAR
suitcases	_	_	I-VAR
,	_	_	O
and	_	_	O
so	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-PARAM
as	_	_	O
many	_	_	O
small	_	_	B-VAR
suitcases	_	_	I-VAR
must	_	_	O
be	_	_	O
used	_	_	O
as	_	_	O
large	_	_	B-VAR
suitcases	_	_	I-VAR
.	_	_	O
The	_	_	O
exporter	_	_	O
has	_	_	O
available	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
70	_	_	B-LIMIT
small	_	_	B-VAR
suitcases	_	_	I-VAR
and	_	_	O
50	_	_	B-LIMIT
large	_	_	B-VAR
suitcases	_	_	I-VAR
.	_	_	O
If	_	_	O
he	_	_	O
must	_	_	O
send	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
15	_	_	B-LIMIT
large	_	_	B-VAR
suitcases	_	_	I-VAR
and	_	_	O
can	_	_	O
send	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
70	_	_	B-LIMIT
suitcases	_	_	O
in	_	_	O
total	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
send	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
snacks	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
delivered	_	_	O
?	_	_	O

A	_	_	O
mail	_	_	O
delivery	_	_	O
service	_	_	O
in	_	_	O
an	_	_	O
island	_	_	O
village	_	_	O
delivers	_	_	O
mail	_	_	O
by	_	_	O
regular	_	_	B-VAR
and	_	_	O
speed	_	_	B-VAR
boats	_	_	I-VAR
.	_	_	O
A	_	_	O
regular	_	_	B-VAR
boat	_	_	I-VAR
can	_	_	O
carry	_	_	O
20	_	_	B-PARAM
pieces	_	_	O
of	_	_	O
mail	_	_	O
per	_	_	O
trip	_	_	O
and	_	_	O
uses	_	_	O
10	_	_	B-PARAM
liters	_	_	O
of	_	_	O
gas	_	_	B-OBJ_NAME
.	_	_	O
A	_	_	O
speed	_	_	B-VAR
boat	_	_	I-VAR
can	_	_	O
carry	_	_	O
30	_	_	B-PARAM
pieces	_	_	O
of	_	_	O
mail	_	_	O
per	_	_	O
trip	_	_	O
and	_	_	O
uses	_	_	O
20	_	_	B-PARAM
liters	_	_	O
of	_	_	O
gas	_	_	B-OBJ_NAME
.	_	_	O
There	_	_	O
can	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
20	_	_	B-LIMIT
regular	_	_	B-VAR
boat	_	_	I-VAR
trips	_	_	O
.	_	_	O
Since	_	_	O
customers	_	_	O
want	_	_	O
their	_	_	O
mail	_	_	O
as	_	_	O
fast	_	_	O
as	_	_	O
possible	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
trips	_	_	O
must	_	_	O
be	_	_	O
made	_	_	O
by	_	_	O
speed	_	_	B-VAR
boats	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
service	_	_	O
needs	_	_	B-CONST_DIR
to	_	_	I-CONST_DIR
deliver	_	_	I-CONST_DIR
1000	_	_	B-LIMIT
pieces	_	_	O
of	_	_	O
mail	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
trips	_	_	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
gas	_	_	I-OBJ_NAME
consumed	_	_	O
?	_	_	O

A	_	_	O
chicken	_	_	O
farmer	_	_	O
has	_	_	O
sold	_	_	O
his	_	_	O
chicken	_	_	O
and	_	_	O
they	_	_	O
need	_	_	O
to	_	_	O
be	_	_	O
transported	_	_	O
either	_	_	O
by	_	_	O
bus	_	_	B-VAR
or	_	_	O
by	_	_	O
car	_	_	B-VAR
.	_	_	O
A	_	_	O
bus	_	_	B-VAR
can	_	_	O
take	_	_	O
100	_	_	B-PARAM
chicken	_	_	O
and	_	_	O
takes	_	_	O
2	_	_	B-PARAM
hours	_	_	B-OBJ_NAME
per	_	_	O
trip	_	_	O
.	_	_	O
A	_	_	O
car	_	_	B-VAR
can	_	_	O
take	_	_	O
40	_	_	B-PARAM
chicken	_	_	O
and	_	_	O
takes	_	_	O
1.5	_	_	B-PARAM
hours	_	_	B-OBJ_NAME
per	_	_	O
trip	_	_	O
.	_	_	O
There	_	_	O
can	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
10	_	_	B-LIMIT
bus	_	_	B-VAR
trips	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
60	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
trips	_	_	O
must	_	_	O
be	_	_	O
by	_	_	O
car	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
farmer	_	_	O
needs	_	_	B-CONST_DIR
to	_	_	I-CONST_DIR
transport	_	_	I-CONST_DIR
1200	_	_	B-LIMIT
chicken	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
trips	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
done	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
time	_	_	I-OBJ_NAME
needed	_	_	O
to	_	_	O
transport	_	_	O
the	_	_	O
chicken	_	_	O
?	_	_	O

Children	_	_	O
can	_	_	O
go	_	_	O
to	_	_	O
school	_	_	O
either	_	_	O
by	_	_	O
van	_	_	B-VAR
or	_	_	O
by	_	_	O
minibus	_	_	B-VAR
.	_	_	O
A	_	_	O
van	_	_	B-VAR
can	_	_	O
take	_	_	O
6	_	_	B-PARAM
kids	_	_	O
and	_	_	O
produces	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
pollution	_	_	B-OBJ_NAME
.	_	_	O
A	_	_	O
minibus	_	_	B-VAR
can	_	_	O
take	_	_	O
10	_	_	B-PARAM
kids	_	_	O
and	_	_	O
produced	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
pollution	_	_	B-OBJ_NAME
.	_	_	O
There	_	_	O
are	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
150	_	_	B-LIMIT
kids	_	_	O
than	_	_	O
need	_	_	O
to	_	_	O
go	_	_	O
to	_	_	O
school	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
10	_	_	B-LIMIT
minibuses	_	_	B-VAR
can	_	_	O
be	_	_	O
used	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
vans	_	_	B-VAR
used	_	_	O
must	_	_	B-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
minibuses	_	_	B-VAR
.	_	_	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
pollution	_	_	I-OBJ_NAME
produced	_	_	O
?	_	_	O

A	_	_	O
recycling	_	_	O
company	_	_	O
collects	_	_	O
recycling	_	_	O
from	_	_	O
neighborhoods	_	_	O
using	_	_	O
small	_	_	B-VAR
and	_	_	O
large	_	_	B-VAR
bins	_	_	I-VAR
.	_	_	O
A	_	_	O
small	_	_	B-VAR
bin	_	_	I-VAR
requires	_	_	O
2	_	_	B-PARAM
workers	_	_	O
while	_	_	O
a	_	_	O
large	_	_	B-VAR
bin	_	_	I-VAR
requires	_	_	O
5	_	_	B-PARAM
workers	_	_	O
.	_	_	O
A	_	_	O
small	_	_	B-VAR
bin	_	_	I-VAR
can	_	_	O
hold	_	_	O
25	_	_	B-PARAM
units	_	_	O
of	_	_	O
recycling	_	_	B-OBJ_NAME
material	_	_	I-OBJ_NAME
and	_	_	O
a	_	_	O
large	_	_	B-VAR
bin	_	_	I-VAR
can	_	_	O
hold	_	_	O
60	_	_	B-PARAM
units	_	_	O
of	_	_	O
recycling	_	_	B-OBJ_NAME
material	_	_	I-OBJ_NAME
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
100	_	_	B-LIMIT
workers	_	_	O
.	_	_	O
Because	_	_	O
most	_	_	O
people	_	_	O
do	_	_	O
n't	_	_	O
recycle	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
small	_	_	B-VAR
bins	_	_	I-VAR
must	_	_	B-CONST_DIR
be	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
large	_	_	B-VAR
bins	_	_	I-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
small	_	_	B-VAR
bins	_	_	I-VAR
and	_	_	O
4	_	_	B-LIMIT
large	_	_	B-VAR
bins	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
bin	_	_	O
type	_	_	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
recycling	_	_	I-OBJ_NAME
material	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
collected	_	_	O
?	_	_	O

A	_	_	O
toy	_	_	O
store	_	_	O
hires	_	_	O
seasonal	_	_	B-VAR
and	_	_	O
full	_	_	B-VAR
-	_	_	I-VAR
time	_	_	I-VAR
volunteers	_	_	O
to	_	_	O
deliver	_	_	O
gifts	_	_	O
and	_	_	O
gives	_	_	O
them	_	_	O
points	_	_	O
for	_	_	O
service	_	_	O
.	_	_	O
A	_	_	O
seasonal	_	_	B-VAR
volunteer	_	_	I-VAR
can	_	_	O
deliver	_	_	O
5	_	_	B-PARAM
gifts	_	_	B-OBJ_NAME
and	_	_	O
gets	_	_	O
2	_	_	B-PARAM
points	_	_	O
.	_	_	O
A	_	_	O
full	_	_	B-VAR
-	_	_	I-VAR
time	_	_	I-VAR
volunteer	_	_	I-VAR
can	_	_	O
deliver	_	_	O
8	_	_	B-PARAM
gifts	_	_	B-OBJ_NAME
and	_	_	O
gets	_	_	O
5	_	_	B-PARAM
points	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
can	_	_	O
only	_	_	B-CONST_DIR
give	_	_	O
out	_	_	O
200	_	_	B-LIMIT
points	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
30	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
volunteers	_	_	O
can	_	_	O
be	_	_	O
seasonal	_	_	B-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
must	_	_	O
be	_	_	O
full	_	_	B-VAR
-	_	_	I-VAR
time	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
volunteer	_	_	O
is	_	_	O
needed	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
gifts	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
delivered	_	_	O
?	_	_	O

A	_	_	O
jam	_	_	O
company	_	_	O
sends	_	_	O
its	_	_	O
product	_	_	O
out	_	_	O
in	_	_	O
small	_	_	B-VAR
and	_	_	O
large	_	_	B-VAR
jars	_	_	O
.	_	_	O
A	_	_	O
small	_	_	B-VAR
jar	_	_	I-VAR
can	_	_	O
hold	_	_	O
50	_	_	B-PARAM
ml	_	_	O
of	_	_	O
jam	_	_	O
while	_	_	O
a	_	_	O
large	_	_	B-VAR
jar	_	_	I-VAR
can	_	_	O
hold	_	_	O
200	_	_	B-PARAM
ml	_	_	O
of	_	_	O
jam	_	_	O
.	_	_	O
Most	_	_	O
store	_	_	O
prefer	_	_	O
the	_	_	O
smaller	_	_	O
size	_	_	O
and	_	_	O
so	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
large	_	_	B-VAR
jars	_	_	I-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
small	_	_	B-VAR
jars	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
company	_	_	O
wants	_	_	O
to	_	_	O
ship	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100000	_	_	B-LIMIT
ml	_	_	O
of	_	_	O
jam	_	_	O
,	_	_	O
find	_	_	O
the	_	_	O
minimum	_	_	B-OBJ_DIR
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
jars	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
used	_	_	O
.	_	_	O

A	_	_	O
corn	_	_	O
farmer	_	_	O
sends	_	_	O
his	_	_	O
corn	_	_	O
to	_	_	O
the	_	_	O
city	_	_	O
by	_	_	O
either	_	_	O
tractor	_	_	B-VAR
or	_	_	O
car	_	_	B-VAR
.	_	_	O
A	_	_	O
tractor	_	_	B-VAR
can	_	_	O
carry	_	_	O
40	_	_	B-PARAM
kg	_	_	O
of	_	_	O
corn	_	_	O
while	_	_	O
a	_	_	O
car	_	_	B-VAR
can	_	_	O
carry	_	_	O
20	_	_	B-PARAM
kg	_	_	O
of	_	_	O
corn	_	_	O
.	_	_	O
Since	_	_	O
tractors	_	_	O
are	_	_	O
very	_	_	O
slow	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
cars	_	_	B-VAR
used	_	_	O
has	_	_	O
to	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-PARAM
the	_	_	O
number	_	_	O
of	_	_	O
tractors	_	_	B-VAR
used	_	_	O
.	_	_	O
If	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
500	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
corn	_	_	O
need	_	_	O
to	_	_	O
be	_	_	O
sent	_	_	O
to	_	_	O
the	_	_	O
city	_	_	O
,	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
tractors	_	_	I-OBJ_NAME
and	_	_	I-OBJ_NAME
cars	_	_	I-OBJ_NAME
needed	_	_	O
.	_	_	O

A	_	_	O
village	_	_	O
hosts	_	_	O
a	_	_	O
banquet	_	_	O
and	_	_	O
provides	_	_	O
bike	_	_	B-VAR
and	_	_	O
car	_	_	B-VAR
transportation	_	_	O
for	_	_	O
everyone	_	_	O
.	_	_	O
A	_	_	O
bike	_	_	B-VAR
can	_	_	O
take	_	_	O
3	_	_	B-PARAM
people	_	_	O
while	_	_	O
a	_	_	O
car	_	_	B-VAR
can	_	_	O
take	_	_	O
5	_	_	B-PARAM
people	_	_	O
.	_	_	O
Since	_	_	O
cars	_	_	B-VAR
are	_	_	O
more	_	_	O
expensive	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
40	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
vehicles	_	_	O
can	_	_	O
be	_	_	O
cars	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
village	_	_	O
needs	_	_	O
to	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
500	_	_	B-LIMIT
people	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
vehicle	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
bikes	_	_	I-OBJ_NAME
needed	_	_	O
?	_	_	O

An	_	_	O
industrial	_	_	O
tire	_	_	O
company	_	_	O
delivers	_	_	O
large	_	_	O
tires	_	_	O
for	_	_	O
equipment	_	_	O
to	_	_	O
remote	_	_	O
engineering	_	_	O
sites	_	_	O
either	_	_	O
by	_	_	O
cargo	_	_	B-VAR
planes	_	_	I-VAR
or	_	_	O
ultrawide	_	_	B-VAR
trucks	_	_	I-VAR
.	_	_	O
Each	_	_	O
cargo	_	_	B-VAR
plane	_	_	I-VAR
can	_	_	O
transport	_	_	O
10	_	_	B-PARAM
tires	_	_	O
per	_	_	O
trip	_	_	O
and	_	_	O
costs	_	_	O
$	_	_	O
1000	_	_	B-PARAM
.	_	_	O
Each	_	_	O
ultrawide	_	_	B-VAR
truck	_	_	I-VAR
can	_	_	O
transport	_	_	O
6	_	_	B-PARAM
tires	_	_	O
per	_	_	O
trip	_	_	O
and	_	_	O
costs	_	_	O
$	_	_	O
700	_	_	B-PARAM
.	_	_	O
The	_	_	O
company	_	_	O
needs	_	_	O
to	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
200	_	_	B-LIMIT
tires	_	_	O
and	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
$	_	_	O
22000	_	_	B-LIMIT
.	_	_	O
Because	_	_	O
most	_	_	O
remote	_	_	O
sites	_	_	O
do	_	_	O
n't	_	_	O
have	_	_	O
proper	_	_	O
airports	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
plane	_	_	B-VAR
trips	_	_	O
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
ultrawide	_	_	B-VAR
truck	_	_	I-VAR
trips	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
trips	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
done	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
trips	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
water	_	_	O
salesman	_	_	O
collects	_	_	O
water	_	_	O
from	_	_	O
a	_	_	O
glacier	_	_	O
and	_	_	O
transports	_	_	O
it	_	_	O
in	_	_	O
either	_	_	O
small	_	_	B-VAR
or	_	_	O
large	_	_	B-VAR
kegs	_	_	O
.	_	_	O
A	_	_	O
small	_	_	B-VAR
keg	_	_	I-VAR
can	_	_	O
hold	_	_	O
40	_	_	B-PARAM
liters	_	_	O
of	_	_	O
water	_	_	B-OBJ_NAME
while	_	_	O
a	_	_	O
large	_	_	B-VAR
keg	_	_	I-VAR
can	_	_	O
hold	_	_	O
100	_	_	B-PARAM
liters	_	_	O
of	_	_	O
water	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
salesman	_	_	O
has	_	_	O
available	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
small	_	_	B-VAR
kegs	_	_	I-VAR
and	_	_	O
10	_	_	B-LIMIT
large	_	_	B-VAR
kegs	_	_	I-VAR
.	_	_	O
Since	_	_	O
small	_	_	B-VAR
kegs	_	_	I-VAR
are	_	_	O
easier	_	_	O
to	_	_	O
carry	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-PARAM
as	_	_	O
may	_	_	O
small	_	_	B-VAR
kegs	_	_	I-VAR
must	_	_	O
be	_	_	O
used	_	_	O
than	_	_	O
large	_	_	B-VAR
kegs	_	_	I-VAR
.	_	_	O
If	_	_	O
he	_	_	O
can	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
25	_	_	B-LIMIT
kegs	_	_	O
total	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
kegs	_	_	O
must	_	_	O
be	_	_	O
large	_	_	B-VAR
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
use	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
glacial	_	_	I-OBJ_NAME
water	_	_	I-OBJ_NAME
he	_	_	O
can	_	_	O
transport	_	_	O
?	_	_	O

A	_	_	O
tropical	_	_	O
city	_	_	O
full	_	_	O
of	_	_	O
islands	_	_	O
sends	_	_	O
mail	_	_	O
either	_	_	O
by	_	_	O
submarine	_	_	B-VAR
or	_	_	O
by	_	_	O
boat	_	_	B-VAR
.	_	_	O
A	_	_	O
submarine	_	_	B-VAR
can	_	_	O
carry	_	_	O
100	_	_	B-PARAM
pieces	_	_	O
of	_	_	O
mail	_	_	O
per	_	_	O
trip	_	_	O
and	_	_	O
uses	_	_	O
30	_	_	B-PARAM
liters	_	_	O
of	_	_	O
gas	_	_	B-OBJ_NAME
.	_	_	O
A	_	_	O
boat	_	_	B-VAR
can	_	_	O
carry	_	_	O
80	_	_	B-PARAM
pieces	_	_	O
of	_	_	O
mail	_	_	O
per	_	_	O
trip	_	_	O
and	_	_	O
uses	_	_	O
25	_	_	B-PARAM
liters	_	_	O
of	_	_	O
gas	_	_	B-OBJ_NAME
.	_	_	O
There	_	_	O
can	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
6	_	_	B-LIMIT
submarine	_	_	B-VAR
trips	_	_	O
and	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
50	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
trips	_	_	O
must	_	_	O
be	_	_	O
by	_	_	O
boat	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
city	_	_	O
needs	_	_	O
to	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1000	_	_	B-LIMIT
pieces	_	_	O
of	_	_	O
mail	_	_	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
gas	_	_	I-OBJ_NAME
used	_	_	O
?	_	_	O

The	_	_	O
weather	_	_	O
is	_	_	O
freezing	_	_	O
and	_	_	O
the	_	_	O
fish	_	_	O
in	_	_	O
the	_	_	O
pond	_	_	O
need	_	_	O
to	_	_	O
be	_	_	O
transported	_	_	O
either	_	_	O
by	_	_	O
helicopter	_	_	B-VAR
or	_	_	O
car	_	_	B-VAR
.	_	_	O
A	_	_	O
helicopter	_	_	B-VAR
can	_	_	O
take	_	_	O
30	_	_	B-PARAM
fish	_	_	O
per	_	_	O
trip	_	_	O
and	_	_	O
takes	_	_	O
40	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
.	_	_	O
A	_	_	O
car	_	_	B-VAR
can	_	_	O
take	_	_	O
20	_	_	B-PARAM
fish	_	_	O
per	_	_	O
trip	_	_	O
and	_	_	O
takes	_	_	O
30	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
.	_	_	O
Since	_	_	O
helicopter	_	_	B-VAR
trips	_	_	O
are	_	_	O
expensive	_	_	O
,	_	_	O
there	_	_	O
can	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
5	_	_	B-LIMIT
helicopter	_	_	B-VAR
trips	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
60	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
trips	_	_	O
should	_	_	O
be	_	_	O
by	_	_	O
car	_	_	B-VAR
.	_	_	O
If	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
300	_	_	B-LIMIT
fish	_	_	O
need	_	_	O
to	_	_	O
transported	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
trip	_	_	O
should	_	_	O
be	_	_	O
taken	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
time	_	_	B-OBJ_NAME
needed	_	_	O
?	_	_	O

A	_	_	O
tourist	_	_	O
spot	_	_	O
in	_	_	O
the	_	_	O
mountains	_	_	O
allows	_	_	O
visitors	_	_	O
to	_	_	O
travel	_	_	O
to	_	_	O
the	_	_	O
top	_	_	O
either	_	_	O
by	_	_	O
hot	_	_	B-VAR
-	_	_	I-VAR
air	_	_	I-VAR
balloon	_	_	I-VAR
or	_	_	O
gondola	_	_	B-VAR
lift	_	_	I-VAR
.	_	_	O
A	_	_	O
hot	_	_	B-VAR
air	_	_	I-VAR
balloon	_	_	I-VAR
can	_	_	O
carry	_	_	O
4	_	_	B-PARAM
visitors	_	_	O
while	_	_	O
a	_	_	O
gondola	_	_	B-VAR
lift	_	_	I-VAR
can	_	_	O
carry	_	_	O
6	_	_	B-PARAM
visitors	_	_	O
.	_	_	O
Each	_	_	O
hot	_	_	B-VAR
air	_	_	I-VAR
balloon	_	_	I-VAR
produces	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
pollution	_	_	B-OBJ_NAME
while	_	_	O
each	_	_	O
gondola	_	_	B-VAR
lift	_	_	I-VAR
produces	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
pollution	_	_	B-OBJ_NAME
.	_	_	O
There	_	_	O
can	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
10	_	_	B-LIMIT
hot	_	_	B-VAR
-	_	_	I-VAR
air	_	_	I-VAR
balloon	_	_	I-VAR
rides	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
70	_	_	B-LIMIT
visitors	_	_	O
need	_	_	O
to	_	_	O
be	_	_	O
transported	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
transport	_	_	O
method	_	_	O
should	_	_	O
be	_	_	O
taken	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
pollution	_	_	B-OBJ_NAME
produced	_	_	O
?	_	_	O

A	_	_	O
factory	_	_	O
transports	_	_	O
rice	_	_	O
to	_	_	O
the	_	_	O
city	_	_	O
in	_	_	O
horse	_	_	O
-	_	_	O
drawn	_	_	O
carts	_	_	O
that	_	_	O
are	_	_	O
either	_	_	O
medium	_	_	B-VAR
or	_	_	O
large	_	_	B-VAR
size	_	_	O
.	_	_	O
A	_	_	O
medium	_	_	B-VAR
sized	_	_	I-VAR
cart	_	_	I-VAR
requires	_	_	O
2	_	_	B-PARAM
horses	_	_	O
and	_	_	O
can	_	_	O
carry	_	_	O
30	_	_	B-PARAM
kg	_	_	O
of	_	_	O
rice	_	_	B-OBJ_NAME
.	_	_	O
A	_	_	O
large	_	_	B-VAR
sized	_	_	I-VAR
cart	_	_	I-VAR
requires	_	_	O
4	_	_	B-PARAM
horses	_	_	O
and	_	_	O
can	_	_	O
carry	_	_	O
70	_	_	B-PARAM
kg	_	_	O
of	_	_	O
rice	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
factory	_	_	O
has	_	_	O
60	_	_	B-LIMIT
horses	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
Because	_	_	O
the	_	_	O
horses	_	_	O
do	_	_	O
n't	_	_	O
get	_	_	O
along	_	_	O
well	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
medium	_	_	B-VAR
sized	_	_	I-VAR
carts	_	_	I-VAR
must	_	_	B-CONST_DIR
be	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
large	_	_	B-VAR
sized	_	_	I-VAR
carts	_	_	I-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
medium	_	_	B-VAR
sized	_	_	I-VAR
carts	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
large	_	_	B-VAR
sized	_	_	I-VAR
carts	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
cart	_	_	O
size	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
rice	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
transported	_	_	O
?	_	_	O

A	_	_	O
dog	_	_	O
school	_	_	O
trains	_	_	O
labradors	_	_	B-VAR
and	_	_	O
golden	_	_	B-VAR
retrievers	_	_	I-VAR
to	_	_	O
deliver	_	_	O
newspaper	_	_	O
.	_	_	O
A	_	_	O
labrador	_	_	B-VAR
can	_	_	O
deliver	_	_	O
7	_	_	B-PARAM
newspapers	_	_	B-OBJ_NAME
at	_	_	O
a	_	_	O
time	_	_	O
and	_	_	O
requires	_	_	O
5	_	_	B-PARAM
small	_	_	O
bone	_	_	O
treats	_	_	O
for	_	_	O
service	_	_	O
.	_	_	O
A	_	_	O
golden	_	_	B-VAR
retriever	_	_	I-VAR
can	_	_	O
deliver	_	_	O
10	_	_	B-PARAM
newspapers	_	_	B-OBJ_NAME
at	_	_	O
a	_	_	O
time	_	_	O
and	_	_	O
requires	_	_	O
6	_	_	B-PARAM
small	_	_	O
bone	_	_	O
treats	_	_	O
per	_	_	O
service	_	_	O
.	_	_	O
The	_	_	O
school	_	_	O
only	_	_	B-CONST_DIR
has	_	_	O
1500	_	_	B-LIMIT
small	_	_	O
bone	_	_	O
treats	_	_	O
available	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
golden	_	_	B-VAR
retrievers	_	_	I-VAR
must	_	_	O
be	_	_	O
used	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
60	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
dogs	_	_	O
can	_	_	O
be	_	_	O
labradors	_	_	B-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
dog	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
newspapers	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
delivered	_	_	O
?	_	_	O

A	_	_	O
construction	_	_	O
company	_	_	O
in	_	_	O
the	_	_	O
tropics	_	_	O
uses	_	_	O
cows	_	_	B-VAR
and	_	_	O
elephants	_	_	B-VAR
to	_	_	O
carry	_	_	O
bricks	_	_	O
.	_	_	O
A	_	_	O
cow	_	_	B-VAR
can	_	_	O
carry	_	_	O
20	_	_	B-PARAM
bricks	_	_	O
on	_	_	O
its	_	_	O
back	_	_	O
while	_	_	O
an	_	_	O
elephant	_	_	B-VAR
can	_	_	O
carry	_	_	O
50	_	_	B-PARAM
bricks	_	_	O
on	_	_	O
its	_	_	O
back	_	_	O
.	_	_	O
To	_	_	O
avoid	_	_	O
having	_	_	O
elephants	_	_	B-VAR
create	_	_	O
too	_	_	O
much	_	_	O
traffic	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
elephant	_	_	B-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
cows	_	_	B-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
there	_	_	O
can	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
twice	_	_	B-PARAM
the	_	_	O
number	_	_	O
of	_	_	O
cows	_	_	B-VAR
as	_	_	O
elephants	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
company	_	_	O
needs	_	_	O
to	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1000	_	_	B-LIMIT
bricks	_	_	O
,	_	_	O
find	_	_	O
the	_	_	O
minimum	_	_	B-OBJ_DIR
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
animals	_	_	I-OBJ_NAME
,	_	_	O
cows	_	_	B-VAR
and	_	_	O
elephants	_	_	B-VAR
,	_	_	O
that	_	_	O
can	_	_	O
be	_	_	O
used	_	_	O
..	_	_	O

A	_	_	O
farmer	_	_	O
on	_	_	O
an	_	_	O
island	_	_	O
sends	_	_	O
corn	_	_	O
to	_	_	O
the	_	_	O
main	_	_	O
land	_	_	O
either	_	_	O
by	_	_	O
ferry	_	_	B-VAR
or	_	_	O
light	_	_	B-VAR
rail	_	_	I-VAR
.	_	_	O
Each	_	_	O
ferry	_	_	B-VAR
trip	_	_	I-VAR
can	_	_	O
take	_	_	O
20	_	_	B-PARAM
boxes	_	_	O
of	_	_	O
corn	_	_	O
while	_	_	O
each	_	_	O
light	_	_	B-VAR
rail	_	_	I-VAR
trip	_	_	O
can	_	_	O
take	_	_	O
15	_	_	B-PARAM
boxes	_	_	O
of	_	_	O
corn	_	_	O
.	_	_	O
Since	_	_	O
ferry	_	_	B-VAR
trips	_	_	O
are	_	_	O
slow	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
light	_	_	B-VAR
rail	_	_	I-VAR
trip	_	_	O
has	_	_	O
to	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
4	_	_	B-PARAM
times	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
ferry	_	_	B-VAR
trips	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
farmer	_	_	O
wants	_	_	O
to	_	_	O
send	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
500	_	_	B-LIMIT
boxes	_	_	O
of	_	_	O
corn	_	_	O
,	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
trips	_	_	I-OBJ_NAME
of	_	_	O
either	_	_	O
type	_	_	O
needed	_	_	O
.	_	_	O

A	_	_	O
factory	_	_	O
provides	_	_	O
rides	_	_	O
for	_	_	O
its	_	_	O
employees	_	_	O
in	_	_	O
either	_	_	O
taxis	_	_	B-VAR
or	_	_	O
company	_	_	B-VAR
cars	_	_	I-VAR
.	_	_	O
Each	_	_	O
taxi	_	_	B-VAR
ride	_	_	I-VAR
can	_	_	O
take	_	_	O
2	_	_	B-PARAM
employees	_	_	O
while	_	_	O
each	_	_	O
company	_	_	B-VAR
car	_	_	I-VAR
ride	_	_	I-VAR
can	_	_	O
take	_	_	O
3	_	_	B-PARAM
employees	_	_	O
.	_	_	O
Since	_	_	O
buying	_	_	O
and	_	_	O
maintaining	_	_	O
cars	_	_	O
is	_	_	O
expensive	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
60	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
rides	_	_	O
can	_	_	O
be	_	_	O
company	_	_	B-VAR
car	_	_	I-VAR
rides	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
there	_	_	O
has	_	_	O
to	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
company	_	_	B-VAR
car	_	_	I-VAR
rides	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
company	_	_	O
needs	_	_	O
to	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
500	_	_	B-LIMIT
employees	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
rides	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
done	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
taxi	_	_	I-OBJ_NAME
rides	_	_	I-OBJ_NAME
.	_	_	O

A	_	_	O
chemical	_	_	O
company	_	_	O
is	_	_	O
transporting	_	_	O
their	_	_	O
hydrogen	_	_	O
using	_	_	O
two	_	_	O
different	_	_	O
methods	_	_	O
,	_	_	O
high	_	_	B-VAR
pressure	_	_	I-VAR
tube	_	_	I-VAR
trailers	_	_	O
and	_	_	O
liquefied	_	_	B-VAR
hydrogen	_	_	I-VAR
tankers	_	_	I-VAR
.	_	_	O
The	_	_	O
first	_	_	O
method	_	_	O
is	_	_	O
a	_	_	O
high	_	_	B-VAR
-	_	_	I-VAR
pressure	_	_	I-VAR
tube	_	_	I-VAR
trailer	_	_	O
which	_	_	O
can	_	_	O
transport	_	_	O
50	_	_	B-PARAM
cubic	_	_	O
meters	_	_	O
each	_	_	O
per	_	_	O
trip	_	_	O
at	_	_	O
a	_	_	O
cost	_	_	O
of	_	_	O
$	_	_	O
500	_	_	B-PARAM
.	_	_	O
The	_	_	O
second	_	_	O
method	_	_	O
is	_	_	O
using	_	_	O
liquefied	_	_	B-VAR
hydrogen	_	_	I-VAR
tankers	_	_	I-VAR
which	_	_	O
can	_	_	O
transport	_	_	O
30	_	_	B-PARAM
cubic	_	_	O
meters	_	_	O
each	_	_	O
per	_	_	O
trip	_	_	O
at	_	_	O
a	_	_	O
cost	_	_	O
of	_	_	O
$	_	_	O
200	_	_	B-PARAM
.	_	_	O
The	_	_	O
company	_	_	O
needs	_	_	O
to	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1000	_	_	B-LIMIT
cubic	_	_	O
meters	_	_	O
of	_	_	O
hydrogen	_	_	O
and	_	_	O
they	_	_	O
have	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
3750	_	_	B-LIMIT
available	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
transports	_	_	O
done	_	_	O
by	_	_	O
the	_	_	O
high	_	_	B-VAR
pressure	_	_	I-VAR
tube	_	_	I-VAR
trailer	_	_	I-VAR
method	_	_	O
has	_	_	O
to	_	_	O
be	_	_	O
less	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
transports	_	_	O
done	_	_	O
by	_	_	O
the	_	_	O
liquefied	_	_	B-VAR
hydrogen	_	_	I-VAR
tanker	_	_	I-VAR
method	_	_	O
.	_	_	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	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
trips	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
grape	_	_	O
farmer	_	_	O
transports	_	_	O
his	_	_	O
grapes	_	_	O
in	_	_	O
either	_	_	O
small	_	_	B-VAR
crates	_	_	I-VAR
or	_	_	O
large	_	_	B-VAR
crates	_	_	I-VAR
.	_	_	O
A	_	_	O
small	_	_	B-VAR
crate	_	_	I-VAR
can	_	_	O
take	_	_	O
200	_	_	B-PARAM
grapes	_	_	B-OBJ_NAME
while	_	_	O
a	_	_	O
large	_	_	B-VAR
crate	_	_	I-VAR
can	_	_	O
take	_	_	O
500	_	_	B-PARAM
.	_	_	O
Because	_	_	O
his	_	_	O
customers	_	_	O
prefer	_	_	O
smaller	_	_	B-VAR
crates	_	_	I-VAR
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
small	_	_	B-VAR
crates	_	_	I-VAR
must	_	_	O
be	_	_	O
used	_	_	O
than	_	_	O
large	_	_	B-VAR
crates	_	_	I-VAR
.	_	_	O
The	_	_	O
farmer	_	_	O
has	_	_	O
available	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
small	_	_	B-VAR
crates	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
50	_	_	B-LIMIT
large	_	_	B-VAR
crates	_	_	I-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
his	_	_	O
truck	_	_	O
can	_	_	O
take	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
60	_	_	B-LIMIT
crates	_	_	O
total	_	_	O
and	_	_	O
he	_	_	O
must	_	_	O
use	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
large	_	_	B-VAR
crates	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
crate	_	_	O
should	_	_	O
he	_	_	O
use	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
grapes	_	_	I-OBJ_NAME
he	_	_	O
can	_	_	O
transport	_	_	O
?	_	_	O

A	_	_	O
shipping	_	_	O
company	_	_	O
need	_	_	O
to	_	_	O
transport	_	_	O
packages	_	_	O
by	_	_	O
either	_	_	O
truck	_	_	B-VAR
or	_	_	O
car	_	_	B-VAR
.	_	_	O
A	_	_	O
truck	_	_	B-VAR
can	_	_	O
transport	_	_	O
50	_	_	B-PARAM
packages	_	_	O
per	_	_	O
trip	_	_	O
while	_	_	O
a	_	_	O
car	_	_	B-VAR
can	_	_	O
transport	_	_	O
30	_	_	B-PARAM
packages	_	_	O
per	_	_	O
trip	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
a	_	_	O
truck	_	_	B-VAR
uses	_	_	O
20	_	_	B-PARAM
liters	_	_	O
of	_	_	O
gas	_	_	B-OBJ_NAME
per	_	_	O
trip	_	_	O
while	_	_	O
a	_	_	O
car	_	_	B-VAR
uses	_	_	O
15	_	_	B-PARAM
liters	_	_	O
of	_	_	O
gas	_	_	B-OBJ_NAME
per	_	_	O
trip	_	_	O
.	_	_	O
There	_	_	O
can	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
5	_	_	B-LIMIT
truck	_	_	B-VAR
trips	_	_	O
made	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
all	_	_	O
the	_	_	O
trips	_	_	O
must	_	_	O
be	_	_	O
made	_	_	O
by	_	_	O
car	_	_	B-VAR
.	_	_	O
The	_	_	O
company	_	_	O
needs	_	_	O
to	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
500	_	_	B-LIMIT
packages	_	_	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
gas	_	_	I-OBJ_NAME
consumed	_	_	O
?	_	_	O

There	_	_	O
has	_	_	O
been	_	_	O
a	_	_	O
horrible	_	_	O
accident	_	_	O
and	_	_	O
patients	_	_	O
need	_	_	O
to	_	_	O
be	_	_	O
taken	_	_	O
to	_	_	O
the	_	_	O
hospital	_	_	O
by	_	_	O
either	_	_	O
a	_	_	O
helicopter	_	_	B-VAR
or	_	_	O
bus	_	_	B-VAR
.	_	_	O
A	_	_	O
helicopter	_	_	B-VAR
can	_	_	O
transport	_	_	O
5	_	_	B-PARAM
patients	_	_	O
per	_	_	O
trip	_	_	O
and	_	_	O
takes	_	_	O
1	_	_	B-PARAM
hour	_	_	B-OBJ_NAME
.	_	_	O
On	_	_	O
the	_	_	O
other	_	_	O
hand	_	_	O
,	_	_	O
a	_	_	O
bus	_	_	B-VAR
can	_	_	O
transport	_	_	O
8	_	_	B-PARAM
patients	_	_	O
per	_	_	O
trip	_	_	O
and	_	_	O
takes	_	_	O
3	_	_	B-PARAM
hours	_	_	B-OBJ_NAME
.	_	_	O
At	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
120	_	_	B-LIMIT
patients	_	_	O
need	_	_	O
to	_	_	O
be	_	_	O
transported	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
trips	_	_	O
should	_	_	O
be	_	_	O
by	_	_	O
helicopter	_	_	B-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
there	_	_	O
can	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
10	_	_	B-LIMIT
bus	_	_	B-VAR
trips	_	_	O
.	_	_	O
How	_	_	O
should	_	_	O
the	_	_	O
patients	_	_	O
be	_	_	O
taken	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
time	_	_	I-OBJ_NAME
to	_	_	O
transport	_	_	O
the	_	_	O
patients	_	_	O
?	_	_	O

Employees	_	_	O
have	_	_	O
the	_	_	O
option	_	_	O
of	_	_	O
car	_	_	B-VAR
-	_	_	O
pooling	_	_	O
to	_	_	O
work	_	_	O
or	_	_	O
taking	_	_	O
the	_	_	O
company	_	_	O
bus	_	_	B-VAR
.	_	_	O
A	_	_	O
car	_	_	B-VAR
can	_	_	O
take	_	_	O
4	_	_	B-PARAM
employees	_	_	O
and	_	_	O
produces	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
pollution	_	_	B-OBJ_NAME
,	_	_	O
while	_	_	O
a	_	_	O
bus	_	_	B-VAR
can	_	_	O
take	_	_	O
20	_	_	B-PARAM
employees	_	_	O
and	_	_	O
produces	_	_	O
30	_	_	B-PARAM
units	_	_	O
of	_	_	O
pollution	_	_	B-OBJ_NAME
.	_	_	O
At	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
300	_	_	B-LIMIT
employees	_	_	O
need	_	_	O
to	_	_	O
be	_	_	O
transported	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
4	_	_	B-LIMIT
buses	_	_	B-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
pollution	_	_	B-OBJ_NAME
produced	_	_	O
.	_	_	O

A	_	_	O
snow	_	_	O
removal	_	_	O
company	_	_	O
removes	_	_	O
snow	_	_	O
from	_	_	O
neighborhoods	_	_	O
using	_	_	O
small	_	_	B-VAR
trucks	_	_	I-VAR
and	_	_	O
large	_	_	B-VAR
trucks	_	_	I-VAR
.	_	_	O
A	_	_	O
small	_	_	B-VAR
truck	_	_	I-VAR
requires	_	_	O
2	_	_	B-PARAM
people	_	_	O
to	_	_	O
shovel	_	_	O
the	_	_	O
snow	_	_	O
and	_	_	O
can	_	_	O
carry	_	_	O
30	_	_	B-PARAM
units	_	_	O
of	_	_	O
snow	_	_	B-OBJ_NAME
.	_	_	O
A	_	_	O
large	_	_	B-VAR
truck	_	_	I-VAR
require	_	_	O
4	_	_	B-PARAM
people	_	_	O
to	_	_	O
shovel	_	_	O
the	_	_	O
snow	_	_	O
and	_	_	O
car	_	_	O
carry	_	_	O
50	_	_	B-PARAM
units	_	_	O
of	_	_	O
snow	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
30	_	_	B-LIMIT
people	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
because	_	_	O
some	_	_	O
neighbourhood	_	_	O
do	_	_	O
n’t	_	_	O
allow	_	_	O
big	_	_	O
trucks	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
trucks	_	_	O
must	_	_	O
be	_	_	O
small	_	_	B-VAR
.	_	_	O
There	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-LIMIT
large	_	_	B-VAR
trucks	_	_	I-VAR
as	_	_	O
well	_	_	O
and	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
small	_	_	B-VAR
trucks	_	_	I-VAR
must	_	_	B-CONST_DIR
be	_	_	I-CONST_DIR
twice	_	_	B-PARAM
as	_	_	O
much	_	_	O
as	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
large	_	_	B-VAR
trucks	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
truck	_	_	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
snow	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
transported	_	_	O
?	_	_	O

A	_	_	O
magic	_	_	O
school	_	_	O
sends	_	_	O
letters	_	_	O
to	_	_	O
student	_	_	O
either	_	_	O
by	_	_	O
carrier	_	_	B-VAR
pigeons	_	_	I-VAR
or	_	_	O
owls	_	_	B-VAR
.	_	_	O
A	_	_	O
carrier	_	_	B-VAR
pigeon	_	_	I-VAR
can	_	_	O
carry	_	_	O
two	_	_	B-PARAM
letters	_	_	B-OBJ_NAME
at	_	_	O
a	_	_	O
time	_	_	O
and	_	_	O
requires	_	_	O
3	_	_	B-PARAM
treats	_	_	O
for	_	_	O
service	_	_	O
.	_	_	O
An	_	_	O
owl	_	_	B-VAR
can	_	_	O
carry	_	_	O
5	_	_	B-PARAM
letters	_	_	B-OBJ_NAME
at	_	_	O
a	_	_	O
time	_	_	O
and	_	_	O
requires	_	_	O
5	_	_	B-PARAM
treats	_	_	O
for	_	_	O
service	_	_	O
.	_	_	O
At	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
40	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
birds	_	_	O
can	_	_	O
be	_	_	O
owls	_	_	B-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
the	_	_	O
school	_	_	O
only	_	_	B-CONST_DIR
has	_	_	O
1000	_	_	B-LIMIT
treats	_	_	O
available	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
carrier	_	_	B-VAR
pigeons	_	_	I-VAR
must	_	_	O
be	_	_	O
uses	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
bird	_	_	O
can	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
letters	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
sent	_	_	O
.	_	_	O

An	_	_	O
international	_	_	O
shipping	_	_	O
company	_	_	O
uses	_	_	O
large	_	_	B-VAR
and	_	_	O
small	_	_	B-VAR
ships	_	_	I-VAR
to	_	_	O
transport	_	_	O
containers	_	_	O
around	_	_	O
the	_	_	O
world	_	_	O
.	_	_	O
A	_	_	O
large	_	_	B-VAR
ship	_	_	I-VAR
can	_	_	O
carry	_	_	O
500	_	_	B-PARAM
containers	_	_	O
while	_	_	O
a	_	_	O
small	_	_	B-VAR
ship	_	_	I-VAR
can	_	_	O
carry	_	_	O
200	_	_	B-PARAM
containers	_	_	O
.	_	_	O
Because	_	_	O
most	_	_	O
ports	_	_	O
are	_	_	O
small	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
large	_	_	B-VAR
ships	_	_	I-VAR
can	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
small	_	_	B-VAR
ships	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
company	_	_	O
is	_	_	O
under	_	_	O
contract	_	_	O
needs	_	_	O
to	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3000	_	_	B-LIMIT
containers	_	_	O
,	_	_	O
find	_	_	O
the	_	_	O
minimum	_	_	B-OBJ_DIR
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
ships	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
used	_	_	O
.	_	_	O

A	_	_	O
large	_	_	O
fishing	_	_	O
boat	_	_	O
sends	_	_	O
fish	_	_	O
back	_	_	O
to	_	_	O
shore	_	_	O
either	_	_	O
by	_	_	O
small	_	_	B-VAR
canoes	_	_	I-VAR
or	_	_	O
smaller	_	_	B-VAR
diesel	_	_	I-VAR
boats	_	_	I-VAR
.	_	_	O
A	_	_	O
canoe	_	_	B-VAR
can	_	_	O
carry	_	_	O
back	_	_	O
10	_	_	B-PARAM
fish	_	_	O
while	_	_	O
a	_	_	O
small	_	_	B-VAR
diesel	_	_	I-VAR
boat	_	_	I-VAR
can	_	_	O
carry	_	_	O
back	_	_	O
15	_	_	B-PARAM
fish	_	_	O
.	_	_	O
In	_	_	O
order	_	_	O
to	_	_	O
follow	_	_	O
environmental	_	_	O
rules	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
small	_	_	B-VAR
canoes	_	_	I-VAR
used	_	_	O
has	_	_	O
to	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
as	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
diesel	_	_	B-VAR
boats	_	_	I-VAR
uses	_	_	O
.	_	_	O
If	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1000	_	_	B-LIMIT
fish	_	_	O
need	_	_	O
to	_	_	O
be	_	_	O
transported	_	_	O
to	_	_	O
shore	_	_	O
,	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
canoes	_	_	I-OBJ_NAME
and	_	_	I-OBJ_NAME
diesel	_	_	I-OBJ_NAME
boats	_	_	I-OBJ_NAME
needed	_	_	O
.	_	_	O

A	_	_	O
volunteer	_	_	O
organization	_	_	O
transports	_	_	O
voters	_	_	O
to	_	_	O
the	_	_	O
polls	_	_	O
on	_	_	O
Election	_	_	O
Day	_	_	O
either	_	_	O
by	_	_	O
vans	_	_	B-VAR
or	_	_	O
cars	_	_	B-VAR
.	_	_	O
They	_	_	O
have	_	_	O
vans	_	_	B-VAR
which	_	_	O
can	_	_	O
carry	_	_	O
6	_	_	B-PARAM
people	_	_	O
and	_	_	O
cars	_	_	B-VAR
which	_	_	O
can	_	_	O
carry	_	_	O
3	_	_	B-PARAM
people	_	_	O
.	_	_	O
They	_	_	O
need	_	_	O
to	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
200	_	_	B-LIMIT
voters	_	_	O
to	_	_	O
the	_	_	O
polls	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
vehicles	_	_	O
can	_	_	O
be	_	_	O
vans	_	_	B-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
vehicle	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
cars	_	_	I-OBJ_NAME
used	_	_	O
?	_	_	O

A	_	_	O
school	_	_	O
employs	_	_	O
staff	_	_	B-VAR
and	_	_	O
substitute	_	_	B-VAR
teachers	_	_	I-VAR
.	_	_	O
Per	_	_	O
shift	_	_	O
,	_	_	O
staff	_	_	B-VAR
teachers	_	_	I-VAR
work	_	_	O
6	_	_	B-PARAM
hours	_	_	O
and	_	_	O
get	_	_	O
paid	_	_	O
$	_	_	O
300	_	_	B-PARAM
.	_	_	O
Per	_	_	O
shift	_	_	O
,	_	_	O
substitute	_	_	B-VAR
teachers	_	_	I-VAR
work	_	_	O
3	_	_	B-PARAM
hours	_	_	O
and	_	_	O
get	_	_	O
paid	_	_	O
$	_	_	O
100	_	_	B-PARAM
.	_	_	O
For	_	_	O
the	_	_	O
summer	_	_	O
term	_	_	O
,	_	_	O
the	_	_	O
school	_	_	O
requires	_	_	B-VAR
1000	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
teaching	_	_	O
availability	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
school	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
40000	_	_	B-LIMIT
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
teacher	_	_	O
should	_	_	O
be	_	_	O
hired	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
teachers	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
gem	_	_	O
factory	_	_	O
has	_	_	O
two	_	_	O
drills	_	_	O
,	_	_	O
a	_	_	O
high	_	_	B-VAR
intensity	_	_	I-VAR
one	_	_	O
and	_	_	O
a	_	_	O
low	_	_	B-VAR
intensity	_	_	I-VAR
one	_	_	O
.	_	_	O
Each	_	_	O
day	_	_	O
,	_	_	O
the	_	_	O
high	_	_	B-VAR
intensity	_	_	I-VAR
drill	_	_	I-VAR
can	_	_	O
process	_	_	O
50	_	_	B-PARAM
gems	_	_	O
and	_	_	O
requires	_	_	O
50	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	O
to	_	_	O
dissipate	_	_	O
heat	_	_	O
.	_	_	O
Each	_	_	O
day	_	_	O
,	_	_	O
the	_	_	O
low	_	_	B-VAR
intensity	_	_	I-VAR
drill	_	_	I-VAR
can	_	_	O
process	_	_	O
30	_	_	B-PARAM
gems	_	_	O
and	_	_	O
requires	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	O
to	_	_	O
dissipate	_	_	O
heat	_	_	O
.	_	_	O
Each	_	_	O
day	_	_	O
the	_	_	O
factory	_	_	O
must	_	_	O
process	_	_	B-CONST_DIR
800	_	_	B-LIMIT
gems	_	_	O
and	_	_	O
they	_	_	O
have	_	_	O
available	_	_	B-CONST_DIR
700	_	_	B-LIMIT
units	_	_	O
of	_	_	O
water	_	_	O
.	_	_	O
Since	_	_	O
the	_	_	O
high	_	_	B-VAR
intensity	_	_	I-VAR
drill	_	_	I-VAR
produces	_	_	O
a	_	_	O
lot	_	_	O
of	_	_	O
noise	_	_	O
pollution	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
40	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
drills	_	_	O
can	_	_	O
be	_	_	O
high	_	_	B-VAR
intensity	_	_	I-VAR
ones	_	_	O
.	_	_	O
Further	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
should	_	_	O
be	_	_	O
low	_	_	B-VAR
intensity	_	_	I-VAR
drills	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
drill	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
drills	_	_	I-OBJ_NAME
needed	_	_	O
?	_	_	O

A	_	_	O
sandwich	_	_	O
company	_	_	O
can	_	_	O
open	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
stores	_	_	O
,	_	_	O
a	_	_	O
dine	_	_	B-VAR
-	_	_	I-VAR
in	_	_	I-VAR
place	_	_	I-VAR
and	_	_	O
a	_	_	O
food	_	_	B-VAR
-	_	_	I-VAR
truck	_	_	I-VAR
.	_	_	O
A	_	_	O
dine	_	_	B-VAR
-	_	_	I-VAR
in	_	_	I-VAR
place	_	_	I-VAR
can	_	_	O
make	_	_	O
100	_	_	B-PARAM
sandwiches	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
requires	_	_	O
8	_	_	B-PARAM
employees	_	_	O
to	_	_	O
operate	_	_	O
.	_	_	O
A	_	_	O
food	_	_	B-VAR
-	_	_	I-VAR
truck	_	_	I-VAR
can	_	_	O
make	_	_	O
50	_	_	B-PARAM
sandwiches	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
requires	_	_	O
3	_	_	B-PARAM
employees	_	_	O
to	_	_	O
operate	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
500	_	_	B-LIMIT
sandwiches	_	_	O
per	_	_	O
day	_	_	O
but	_	_	O
they	_	_	O
only	_	_	O
have	_	_	O
available	_	_	B-CONST_DIR
35	_	_	B-LIMIT
employees	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
store	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
open	_	_	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

There	_	_	O
are	_	_	O
two	_	_	O
processes	_	_	O
,	_	_	O
process	_	_	B-VAR
A	_	_	I-VAR
and	_	_	O
process	_	_	B-VAR
B	_	_	I-VAR
,	_	_	O
to	_	_	O
plate	_	_	O
a	_	_	O
coin	_	_	O
with	_	_	O
gold	_	_	O
.	_	_	O
Process	_	_	B-VAR
A	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
gold	_	_	O
,	_	_	O
2	_	_	B-PARAM
wires	_	_	O
,	_	_	O
and	_	_	O
can	_	_	O
plate	_	_	O
5	_	_	B-PARAM
coins	_	_	B-OBJ_NAME
.	_	_	O
Process	_	_	B-VAR
B	_	_	I-VAR
requires	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
gold	_	_	O
,	_	_	O
3	_	_	B-PARAM
wires	_	_	O
,	_	_	O
and	_	_	O
can	_	_	O
plate	_	_	O
7	_	_	B-PARAM
coins	_	_	B-OBJ_NAME
.	_	_	O
There	_	_	O
are	_	_	O
500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
gold	_	_	O
and	_	_	O
300	_	_	B-LIMIT
wires	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
How	_	_	O
many	_	_	O
processes	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
be	_	_	O
run	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
coins	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
plated	_	_	O
?	_	_	O

A	_	_	O
woodshop	_	_	O
can	_	_	O
purchase	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
saws	_	_	O
,	_	_	O
a	_	_	O
miter	_	_	B-VAR
saw	_	_	I-VAR
and	_	_	O
a	_	_	O
circular	_	_	B-VAR
saw	_	_	I-VAR
.	_	_	O
A	_	_	O
miter	_	_	B-VAR
saw	_	_	I-VAR
can	_	_	O
cut	_	_	O
50	_	_	B-PARAM
planks	_	_	O
of	_	_	O
wood	_	_	O
and	_	_	O
produces	_	_	O
60	_	_	B-PARAM
units	_	_	O
of	_	_	O
sawdust	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
A	_	_	O
circular	_	_	B-VAR
saw	_	_	I-VAR
can	_	_	O
cut	_	_	O
70	_	_	B-PARAM
planks	_	_	O
of	_	_	O
wood	_	_	O
and	_	_	O
produces	_	_	O
100	_	_	B-PARAM
units	_	_	O
of	_	_	O
sawdust	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
The	_	_	O
woodshop	_	_	O
must	_	_	O
cut	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1500	_	_	B-LIMIT
planks	_	_	O
of	_	_	O
wood	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
to	_	_	O
avoid	_	_	O
too	_	_	O
much	_	_	O
pollution	_	_	O
in	_	_	O
the	_	_	O
woodshop	_	_	O
they	_	_	O
can	_	_	O
produce	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
2000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
sawdust	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
saw	_	_	O
should	_	_	O
be	_	_	O
purchased	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
saws	_	_	I-OBJ_NAME
needed	_	_	O
?	_	_	O

A	_	_	O
farmer	_	_	O
has	_	_	B-CONST_DIR
200	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
on	_	_	O
which	_	_	O
he	_	_	O
must	_	_	O
process	_	_	O
hay	_	_	O
using	_	_	O
either	_	_	O
a	_	_	O
windrower	_	_	B-VAR
or	_	_	O
hay	_	_	B-VAR
harvester	_	_	I-VAR
.	_	_	O
For	_	_	O
each	_	_	O
acre	_	_	O
of	_	_	O
land	_	_	O
,	_	_	O
the	_	_	O
windrower	_	_	B-VAR
can	_	_	O
process	_	_	O
10	_	_	B-PARAM
kg	_	_	O
of	_	_	O
hay	_	_	B-OBJ_NAME
while	_	_	O
the	_	_	O
hay	_	_	B-VAR
harvester	_	_	I-VAR
can	_	_	O
process	_	_	O
8	_	_	B-PARAM
kg	_	_	O
of	_	_	O
hay	_	_	B-OBJ_NAME
.	_	_	O
Per	_	_	O
acre	_	_	O
,	_	_	O
the	_	_	O
windrower	_	_	B-VAR
produces	_	_	O
5	_	_	B-PARAM
kg	_	_	O
of	_	_	O
methane	_	_	O
gas	_	_	O
and	_	_	O
requires	_	_	O
2	_	_	B-PARAM
kg	_	_	O
of	_	_	O
fuel	_	_	O
.	_	_	O
On	_	_	O
the	_	_	O
other	_	_	O
hand	_	_	O
,	_	_	O
the	_	_	O
hay	_	_	B-VAR
harvester	_	_	I-VAR
produces	_	_	O
3	_	_	B-PARAM
kg	_	_	O
of	_	_	O
methane	_	_	O
gas	_	_	O
per	_	_	O
acre	_	_	O
and	_	_	O
requires	_	_	O
1	_	_	B-PARAM
kg	_	_	O
of	_	_	O
fuel	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
300	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
fuel	_	_	O
available	_	_	B-CONST_DIR
and	_	_	O
the	_	_	O
farmer	_	_	O
can	_	_	O
produce	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
800	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
methane	_	_	O
gas	_	_	O
.	_	_	O
For	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
should	_	_	O
each	_	_	O
machine	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
hay	_	_	I-OBJ_NAME
processed	_	_	O
?	_	_	O

A	_	_	O
new	_	_	O
fast	_	_	O
food	_	_	O
place	_	_	O
makes	_	_	O
wraps	_	_	B-VAR
and	_	_	O
platters	_	_	B-VAR
.	_	_	O
Each	_	_	O
wrap	_	_	B-VAR
requires	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
meat	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
rice	_	_	O
.	_	_	O
Each	_	_	O
platter	_	_	B-VAR
requires	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
meant	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
rice	_	_	O
.	_	_	O
While	_	_	O
each	_	_	O
wrap	_	_	B-VAR
takes	_	_	O
10	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
to	_	_	O
make	_	_	O
,	_	_	O
each	_	_	O
platter	_	_	B-VAR
takes	_	_	O
8	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
to	_	_	O
make	_	_	O
.	_	_	O
The	_	_	O
fast	_	_	O
food	_	_	O
place	_	_	O
must	_	_	O
use	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
meat	_	_	O
and	_	_	O
2500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
rice	_	_	O
.	_	_	O
Since	_	_	O
wraps	_	_	B-VAR
are	_	_	O
easier	_	_	O
to	_	_	O
eat	_	_	O
on	_	_	O
the	_	_	O
go	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
wraps	_	_	B-VAR
need	_	_	O
to	_	_	O
be	_	_	O
made	_	_	O
as	_	_	O
platter	_	_	B-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
fast	_	_	O
food	_	_	O
place	_	_	O
make	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
production	_	_	I-OBJ_NAME
time	_	_	I-OBJ_NAME
?	_	_	O

An	_	_	O
amusement	_	_	O
park	_	_	O
is	_	_	O
installing	_	_	O
ticket	_	_	O
machines	_	_	O
,	_	_	O
both	_	_	O
cash	_	_	B-VAR
-	_	_	I-VAR
based	_	_	I-VAR
and	_	_	O
card	_	_	B-VAR
-	_	_	I-VAR
only	_	_	I-VAR
machines	_	_	O
.	_	_	O
A	_	_	O
cash	_	_	B-VAR
-	_	_	I-VAR
based	_	_	I-VAR
machine	_	_	I-VAR
can	_	_	O
process	_	_	O
20	_	_	B-PARAM
people	_	_	O
per	_	_	O
hour	_	_	O
while	_	_	O
a	_	_	O
card	_	_	B-VAR
-	_	_	I-VAR
only	_	_	I-VAR
machine	_	_	I-VAR
can	_	_	O
process	_	_	O
30	_	_	B-PARAM
people	_	_	O
per	_	_	O
hour	_	_	O
.	_	_	O
The	_	_	O
cash	_	_	B-VAR
-	_	_	I-VAR
based	_	_	I-VAR
machine	_	_	I-VAR
needs	_	_	O
4	_	_	B-PARAM
rolls	_	_	O
of	_	_	O
paper	_	_	O
per	_	_	O
hour	_	_	O
while	_	_	O
the	_	_	O
card	_	_	B-VAR
-	_	_	I-VAR
only	_	_	I-VAR
machine	_	_	I-VAR
requires	_	_	O
5	_	_	B-PARAM
rolls	_	_	O
of	_	_	O
paper	_	_	O
per	_	_	O
hour	_	_	O
.	_	_	O
The	_	_	O
amusement	_	_	O
park	_	_	O
needs	_	_	O
to	_	_	O
be	_	_	O
able	_	_	O
to	_	_	O
process	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
500	_	_	B-LIMIT
people	_	_	O
per	_	_	O
hour	_	_	O
but	_	_	O
can	_	_	O
use	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
90	_	_	B-LIMIT
rolls	_	_	O
of	_	_	O
paper	_	_	O
per	_	_	O
hour	_	_	O
.	_	_	O
Since	_	_	O
most	_	_	O
people	_	_	O
prefer	_	_	O
to	_	_	O
pay	_	_	O
by	_	_	O
cash	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
card	_	_	B-VAR
-	_	_	I-VAR
only	_	_	I-VAR
machines	_	_	I-VAR
must	_	_	B-CONST_DIR
not	_	_	I-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
cash	_	_	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
bought	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
machines	_	_	I-OBJ_NAME
in	_	_	O
the	_	_	O
park	_	_	O
?	_	_	O

A	_	_	O
honey	_	_	O
farmer	_	_	O
sells	_	_	O
his	_	_	O
honey	_	_	O
in	_	_	O
glass	_	_	B-VAR
and	_	_	O
plastic	_	_	B-VAR
jars	_	_	I-VAR
.	_	_	O
A	_	_	O
glass	_	_	B-VAR
jar	_	_	I-VAR
can	_	_	O
hold	_	_	O
250	_	_	B-PARAM
ml	_	_	O
of	_	_	O
honey	_	_	O
while	_	_	O
a	_	_	O
plastic	_	_	B-VAR
jar	_	_	I-VAR
can	_	_	O
hold	_	_	O
300	_	_	B-PARAM
ml	_	_	O
of	_	_	O
honey	_	_	O
.	_	_	O
Since	_	_	O
glass	_	_	B-VAR
jars	_	_	I-VAR
are	_	_	O
more	_	_	O
expensive	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-PARAM
as	_	_	O
many	_	_	O
plastic	_	_	B-VAR
jars	_	_	I-VAR
must	_	_	O
be	_	_	O
filled	_	_	O
as	_	_	O
glass	_	_	B-VAR
jars	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
glass	_	_	B-VAR
jars	_	_	I-VAR
should	_	_	O
be	_	_	O
filled	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
farmer	_	_	O
has	_	_	B-CONST_DIR
20000	_	_	B-LIMIT
ml	_	_	O
of	_	_	O
honey	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
jars	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
filled	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
bottles	_	_	I-OBJ_NAME
filled	_	_	O
?	_	_	O

A	_	_	O
bubble	_	_	O
tea	_	_	O
shop	_	_	O
sells	_	_	O
mango	_	_	O
and	_	_	O
lychee	_	_	B-VAR
bubble	_	_	I-VAR
tea	_	_	I-VAR
.	_	_	O
Each	_	_	O
mango	_	_	B-VAR
bubble	_	_	I-VAR
tea	_	_	I-VAR
requires	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
mango	_	_	O
juice	_	_	O
and	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
tea	_	_	B-OBJ_NAME
.	_	_	O
Each	_	_	O
lychee	_	_	B-VAR
bubble	_	_	I-VAR
tea	_	_	I-VAR
requires	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
lychee	_	_	O
juice	_	_	O
and	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
tea	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
shop	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
2000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
mango	_	_	O
juice	_	_	O
and	_	_	O
3000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
lychee	_	_	O
juice	_	_	O
.	_	_	O
At	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
40	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
bubble	_	_	O
teas	_	_	O
made	_	_	O
must	_	_	O
be	_	_	O
lychee	_	_	B-VAR
flavored	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
mango	_	_	B-VAR
bubble	_	_	I-VAR
tea	_	_	I-VAR
sells	_	_	O
better	_	_	O
and	_	_	O
thus	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
mango	_	_	B-VAR
bubble	_	_	I-VAR
teas	_	_	I-VAR
made	_	_	O
must	_	_	O
be	_	_	O
large	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
lychee	_	_	B-VAR
bubble	_	_	I-VAR
teas	_	_	I-VAR
made	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
bubble	_	_	O
tea	_	_	O
flavor	_	_	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
tea	_	_	I-OBJ_NAME
needed	_	_	O
?	_	_	O

A	_	_	O
city	_	_	O
employs	_	_	O
seasonal	_	_	B-VAR
and	_	_	O
permanent	_	_	B-VAR
snow	_	_	O
removers	_	_	O
.	_	_	O
A	_	_	O
seasonal	_	_	B-VAR
snow	_	_	I-VAR
remover	_	_	I-VAR
works	_	_	O
6	_	_	B-PARAM
hours	_	_	O
per	_	_	O
shift	_	_	O
and	_	_	O
gets	_	_	O
paid	_	_	O
$	_	_	O
120	_	_	B-PARAM
.	_	_	O
A	_	_	O
permanent	_	_	B-VAR
snow	_	_	I-VAR
remover	_	_	I-VAR
works	_	_	O
10	_	_	B-PARAM
hours	_	_	O
per	_	_	O
shift	_	_	O
and	_	_	O
gets	_	_	O
paid	_	_	O
$	_	_	O
250	_	_	B-PARAM
.	_	_	O
Currently	_	_	O
the	_	_	O
city	_	_	O
needs	_	_	B-CONST_DIR
300	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
snow	_	_	O
remover	_	_	O
labor	_	_	O
after	_	_	O
a	_	_	O
heavy	_	_	O
snowfall	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
city	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
6500	_	_	B-LIMIT
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
worker	_	_	O
should	_	_	O
be	_	_	O
hired	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
snow	_	_	I-OBJ_NAME
removers	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
high	_	_	O
rise	_	_	O
building	_	_	O
is	_	_	O
buying	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
furnaces	_	_	O
,	_	_	O
a	_	_	O
new	_	_	B-VAR
model	_	_	I-VAR
and	_	_	O
an	_	_	O
old	_	_	B-VAR
model	_	_	I-VAR
.	_	_	O
A	_	_	O
new	_	_	B-VAR
model	_	_	I-VAR
furnace	_	_	I-VAR
can	_	_	O
heat	_	_	O
10	_	_	B-PARAM
apartments	_	_	O
and	_	_	O
consumes	_	_	O
200	_	_	B-PARAM
kWh	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
An	_	_	O
old	_	_	B-VAR
model	_	_	I-VAR
can	_	_	O
heat	_	_	O
15	_	_	B-PARAM
apartments	_	_	O
and	_	_	O
consumes	_	_	O
250	_	_	B-PARAM
kWh	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
Since	_	_	O
the	_	_	O
old	_	_	B-VAR
model	_	_	I-VAR
is	_	_	O
harder	_	_	O
to	_	_	O
find	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
35	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
furnaces	_	_	O
can	_	_	O
be	_	_	O
the	_	_	O
old	_	_	B-VAR
model	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
new	_	_	B-VAR
model	_	_	I-VAR
furnaces	_	_	I-VAR
should	_	_	O
be	_	_	O
used	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
high	_	_	O
rise	_	_	O
needs	_	_	O
to	_	_	O
heat	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
200	_	_	B-LIMIT
apartments	_	_	O
and	_	_	O
has	_	_	O
3500	_	_	B-LIMIT
kWh	_	_	O
of	_	_	O
electricity	_	_	O
available	_	_	B-CONST_DIR
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
furnace	_	_	O
should	_	_	O
be	_	_	O
purchase	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
furnaces	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
cell	_	_	O
phone	_	_	O
company	_	_	O
is	_	_	O
building	_	_	O
rural	_	_	B-VAR
and	_	_	O
urban	_	_	B-VAR
factories	_	_	O
.	_	_	O
A	_	_	O
rural	_	_	B-VAR
factory	_	_	I-VAR
can	_	_	O
make	_	_	O
100	_	_	B-PARAM
phones	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
requires	_	_	O
8	_	_	B-PARAM
managers	_	_	O
.	_	_	O
An	_	_	O
urban	_	_	B-VAR
factory	_	_	I-VAR
can	_	_	O
make	_	_	O
200	_	_	B-PARAM
phones	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
requires	_	_	O
20	_	_	B-PARAM
managers	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
260	_	_	B-LIMIT
managers	_	_	O
and	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3000	_	_	B-LIMIT
phones	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
factory	_	_	O
type	_	_	O
should	_	_	O
be	_	_	O
built	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
factories	_	_	I-OBJ_NAME
?	_	_	O

An	_	_	O
ice	_	_	O
cream	_	_	O
store	_	_	O
can	_	_	O
buy	_	_	O
two	_	_	O
machines	_	_	O
,	_	_	O
a	_	_	O
counter	_	_	B-VAR
-	_	_	I-VAR
top	_	_	I-VAR
sized	_	_	I-VAR
one	_	_	O
and	_	_	O
a	_	_	O
fridge	_	_	B-VAR
sized	_	_	I-VAR
one	_	_	I-VAR
,	_	_	O
to	_	_	O
make	_	_	O
ice	_	_	O
cream	_	_	O
.	_	_	O
The	_	_	O
counter	_	_	B-VAR
-	_	_	I-VAR
top	_	_	I-VAR
sized	_	_	I-VAR
one	_	_	O
can	_	_	O
produce	_	_	O
80	_	_	B-PARAM
cones	_	_	O
worth	_	_	O
of	_	_	O
ice	_	_	O
cream	_	_	O
every	_	_	O
day	_	_	O
while	_	_	O
the	_	_	O
fridge	_	_	B-VAR
sizes	_	_	I-VAR
one	_	_	I-VAR
can	_	_	O
produce	_	_	O
150	_	_	B-PARAM
cones	_	_	O
worth	_	_	O
of	_	_	O
ice	_	_	O
cream	_	_	O
every	_	_	O
day	_	_	O
.	_	_	O
The	_	_	O
counter	_	_	B-VAR
-	_	_	I-VAR
top	_	_	I-VAR
sized	_	_	I-VAR
machine	_	_	O
outputs	_	_	O
50	_	_	B-PARAM
units	_	_	O
of	_	_	O
heat	_	_	O
while	_	_	O
the	_	_	O
fridge	_	_	B-VAR
sized	_	_	I-VAR
one	_	_	I-VAR
outputs	_	_	O
70	_	_	B-PARAM
units	_	_	O
of	_	_	O
heat	_	_	O
.	_	_	O
The	_	_	O
ice	_	_	O
cream	_	_	O
store	_	_	O
can	_	_	O
output	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
heat	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
must	_	_	O
produce	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1000	_	_	B-LIMIT
cones	_	_	O
worth	_	_	O
of	_	_	O
ice	_	_	O
cream	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
machine	_	_	O
should	_	_	O
they	_	_	O
buy	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
machines	_	_	I-OBJ_NAME
needed	_	_	O
?	_	_	O

There	_	_	O
are	_	_	O
two	_	_	O
specialized	_	_	O
containers	_	_	O
,	_	_	O
a	_	_	O
small	_	_	B-VAR
and	_	_	O
large	_	_	B-VAR
one	_	_	O
,	_	_	O
that	_	_	O
are	_	_	O
used	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
pharmaceutical	_	_	O
paste	_	_	O
.	_	_	O
The	_	_	O
small	_	_	B-VAR
container	_	_	I-VAR
requires	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	O
and	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
the	_	_	O
powdered	_	_	O
pill	_	_	O
to	_	_	O
make	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
the	_	_	O
paste	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
large	_	_	B-VAR
container	_	_	I-VAR
requires	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	O
and	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
the	_	_	O
powdered	_	_	O
pill	_	_	O
to	_	_	O
make	_	_	O
30	_	_	B-PARAM
units	_	_	O
of	_	_	O
the	_	_	O
paste	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
pharmacy	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
water	_	_	O
and	_	_	O
700	_	_	B-LIMIT
units	_	_	O
of	_	_	O
the	_	_	O
powdered	_	_	O
pill	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
container	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
paste	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
made	_	_	O
?	_	_	O

An	_	_	O
oil	_	_	O
and	_	_	O
gas	_	_	O
company	_	_	O
operates	_	_	B-CONST_DIR
on	_	_	I-CONST_DIR
300	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
where	_	_	O
they	_	_	O
use	_	_	O
oil	_	_	O
wells	_	_	O
of	_	_	O
small	_	_	B-VAR
and	_	_	O
large	_	_	B-VAR
size	_	_	O
.	_	_	O
Per	_	_	O
acre	_	_	O
of	_	_	O
land	_	_	O
,	_	_	O
a	_	_	O
small	_	_	B-VAR
oil	_	_	I-VAR
well	_	_	I-VAR
can	_	_	O
produce	_	_	O
2	_	_	B-PARAM
barrels	_	_	O
of	_	_	O
oil	_	_	B-OBJ_NAME
.	_	_	O
Per	_	_	O
acre	_	_	O
of	_	_	O
land	_	_	O
,	_	_	O
a	_	_	O
large	_	_	B-VAR
oil	_	_	I-VAR
well	_	_	I-VAR
can	_	_	O
produce	_	_	O
5	_	_	B-PARAM
barrels	_	_	O
of	_	_	O
oil	_	_	B-OBJ_NAME
.	_	_	O
However	_	_	O
,	_	_	O
a	_	_	O
small	_	_	B-VAR
oil	_	_	I-VAR
well	_	_	I-VAR
produces	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
pollution	_	_	O
and	_	_	O
requires	_	_	O
5	_	_	B-PARAM
drill	_	_	O
bits	_	_	O
per	_	_	O
acre	_	_	O
and	_	_	O
a	_	_	O
large	_	_	B-VAR
oil	_	_	I-VAR
well	_	_	I-VAR
produces	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
pollution	_	_	O
and	_	_	O
requires	_	_	O
10	_	_	B-PARAM
drill	_	_	O
bits	_	_	O
per	_	_	O
acre	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
2500	_	_	B-LIMIT
drill	_	_	O
bits	_	_	O
and	_	_	O
due	_	_	O
to	_	_	O
strict	_	_	O
environmental	_	_	O
laws	_	_	O
can	_	_	O
produce	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
4500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
pollution	_	_	O
.	_	_	O
For	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
should	_	_	O
each	_	_	O
oil	_	_	O
well	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
production	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
oil	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
bakery	_	_	O
makes	_	_	O
almond	_	_	B-VAR
and	_	_	O
pistachio	_	_	B-VAR
croissants	_	_	O
.	_	_	O
An	_	_	O
almond	_	_	B-VAR
croissant	_	_	I-VAR
requires	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
butter	_	_	O
and	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
flour	_	_	O
.	_	_	O
A	_	_	O
pistachio	_	_	B-VAR
croissant	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
butter	_	_	O
and	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
flour	_	_	O
.	_	_	O
The	_	_	O
bakery	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
600	_	_	B-LIMIT
units	_	_	O
of	_	_	O
butter	_	_	O
and	_	_	O
800	_	_	B-LIMIT
units	_	_	O
of	_	_	O
flour	_	_	O
.	_	_	O
Since	_	_	O
the	_	_	O
almond	_	_	B-VAR
croissant	_	_	I-VAR
is	_	_	O
more	_	_	O
popular	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
almond	_	_	B-VAR
croissants	_	_	I-VAR
should	_	_	O
be	_	_	O
made	_	_	O
as	_	_	O
pistachio	_	_	B-VAR
croissants	_	_	I-VAR
.	_	_	O
If	_	_	O
making	_	_	O
an	_	_	O
almond	_	_	B-VAR
croissant	_	_	I-VAR
takes	_	_	O
12	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
and	_	_	O
making	_	_	O
a	_	_	O
pistachio	_	_	B-VAR
croissant	_	_	I-VAR
takes	_	_	O
10	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
production	_	_	I-OBJ_NAME
time	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
burger	_	_	O
chain	_	_	O
is	_	_	O
buying	_	_	O
both	_	_	O
gas	_	_	B-VAR
and	_	_	O
electric	_	_	B-VAR
grills	_	_	O
to	_	_	O
make	_	_	O
burger	_	_	O
patties	_	_	O
.	_	_	O
A	_	_	O
gas	_	_	B-VAR
grill	_	_	I-VAR
can	_	_	O
cook	_	_	O
20	_	_	B-PARAM
patties	_	_	O
per	_	_	O
minute	_	_	O
while	_	_	O
an	_	_	O
electric	_	_	B-VAR
grill	_	_	I-VAR
can	_	_	O
cook	_	_	O
30	_	_	B-PARAM
patties	_	_	O
per	_	_	O
minute	_	_	O
.	_	_	O
The	_	_	O
gas	_	_	B-VAR
grill	_	_	I-VAR
requires	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
cooking	_	_	O
oil	_	_	O
per	_	_	O
minute	_	_	O
while	_	_	O
the	_	_	O
electric	_	_	B-VAR
grill	_	_	I-VAR
requires	_	_	O
25	_	_	B-PARAM
units	_	_	O
of	_	_	O
cooking	_	_	O
oil	_	_	O
per	_	_	O
minute	_	_	O
.	_	_	O
Since	_	_	O
the	_	_	O
gas	_	_	B-VAR
grill	_	_	I-VAR
patties	_	_	O
taste	_	_	O
better	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
electric	_	_	B-VAR
grills	_	_	I-VAR
must	_	_	O
be	_	_	O
less	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
gas	_	_	B-VAR
grills	_	_	I-VAR
.	_	_	O
Further	_	_	O
,	_	_	O
the	_	_	O
burger	_	_	O
chain	_	_	O
wants	_	_	O
to	_	_	O
be	_	_	O
able	_	_	O
to	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
150	_	_	B-LIMIT
patties	_	_	O
per	_	_	O
minute	_	_	O
and	_	_	O
use	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
140	_	_	B-LIMIT
units	_	_	O
of	_	_	O
cooking	_	_	O
oil	_	_	O
per	_	_	O
minute	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
grill	_	_	O
should	_	_	O
be	_	_	O
bought	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
grills	_	_	I-OBJ_NAME
in	_	_	O
the	_	_	O
store	_	_	O
?	_	_	O

A	_	_	O
cough	_	_	O
syrup	_	_	O
company	_	_	O
sells	_	_	O
cough	_	_	O
syrup	_	_	O
in	_	_	O
kids	_	_	B-VAR
and	_	_	O
adult	_	_	B-VAR
size	_	_	I-VAR
bottles	_	_	O
.	_	_	O
A	_	_	O
kids	_	_	B-VAR
size	_	_	I-VAR
bottle	_	_	I-VAR
can	_	_	O
hold	_	_	O
100	_	_	B-PARAM
ml	_	_	O
of	_	_	O
cough	_	_	O
syrup	_	_	O
while	_	_	O
an	_	_	O
adult	_	_	B-VAR
size	_	_	I-VAR
bottle	_	_	I-VAR
can	_	_	O
hold	_	_	O
300	_	_	B-PARAM
ml	_	_	O
of	_	_	O
cough	_	_	O
syrup	_	_	O
.	_	_	O
Since	_	_	O
there	_	_	O
is	_	_	O
no	_	_	O
difference	_	_	O
in	_	_	O
concentration	_	_	O
of	_	_	O
medical	_	_	O
ingredients	_	_	O
between	_	_	O
the	_	_	O
two	_	_	O
bottles	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
adult	_	_	B-VAR
size	_	_	I-VAR
bottle	_	_	I-VAR
must	_	_	O
be	_	_	O
made	_	_	O
as	_	_	O
kids	_	_	B-VAR
size	_	_	I-VAR
bottles	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
kids	_	_	B-VAR
size	_	_	I-VAR
bottles	_	_	I-VAR
must	_	_	O
be	_	_	O
made	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
company	_	_	O
has	_	_	O
25000	_	_	B-LIMIT
ml	_	_	O
of	_	_	O
cough	_	_	O
syrup	_	_	O
available	_	_	B-CONST_DIR
,	_	_	O
how	_	_	O
many	_	_	O
bottles	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
bottles	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
bakery	_	_	O
makes	_	_	O
fiber	_	_	O
supplemented	_	_	O
brownies	_	_	B-VAR
and	_	_	O
lemon	_	_	B-VAR
squares	_	_	I-VAR
.	_	_	O
Each	_	_	O
brownie	_	_	B-VAR
requires	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
chocolate	_	_	O
mix	_	_	O
and	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
fiber	_	_	B-OBJ_NAME
.	_	_	O
Each	_	_	O
lemon	_	_	B-VAR
square	_	_	I-VAR
requires	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
lemon	_	_	O
mix	_	_	O
and	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
fiber	_	_	B-OBJ_NAME
.	_	_	O
Lemon	_	_	B-VAR
squares	_	_	I-VAR
sell	_	_	O
much	_	_	O
faster	_	_	O
and	_	_	O
thus	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
lemon	_	_	B-VAR
squares	_	_	I-VAR
made	_	_	O
must	_	_	O
be	_	_	O
larger	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
brownies	_	_	B-VAR
made	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
to	_	_	O
please	_	_	O
all	_	_	O
customers	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
40	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
items	_	_	O
made	_	_	O
must	_	_	O
be	_	_	O
brownies	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
bakery	_	_	O
has	_	_	B-CONST_DIR
2500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
chocolate	_	_	O
mix	_	_	O
and	_	_	O
3300	_	_	B-LIMIT
units	_	_	O
of	_	_	O
lemon	_	_	O
mix	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
amount	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
fiber	_	_	I-OBJ_NAME
needed	_	_	O
?	_	_	O

A	_	_	O
clinic	_	_	O
employs	_	_	O
nurses	_	_	B-VAR
and	_	_	O
pharmacists	_	_	B-VAR
to	_	_	O
deliver	_	_	O
shots	_	_	O
to	_	_	O
patients	_	_	O
.	_	_	O
A	_	_	O
nurse	_	_	B-VAR
works	_	_	O
5	_	_	B-PARAM
hours	_	_	O
per	_	_	O
shift	_	_	O
while	_	_	O
a	_	_	O
pharmacist	_	_	B-VAR
works	_	_	O
7	_	_	B-PARAM
hours	_	_	O
per	_	_	O
shift	_	_	O
.	_	_	O
Nurses	_	_	B-VAR
are	_	_	O
paid	_	_	O
$	_	_	O
250	_	_	B-PARAM
per	_	_	O
shift	_	_	O
while	_	_	O
pharmacists	_	_	B-VAR
are	_	_	O
paid	_	_	O
$	_	_	O
300	_	_	B-PARAM
per	_	_	O
shift	_	_	O
.	_	_	O
Currently	_	_	O
,	_	_	O
the	_	_	O
clinic	_	_	O
needs	_	_	B-CONST_DIR
200	_	_	B-PARAM
hours	_	_	O
of	_	_	O
healthcare	_	_	O
labor	_	_	O
to	_	_	O
meet	_	_	O
needs	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
firm	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
9000	_	_	B-LIMIT
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
healthcare	_	_	O
worker	_	_	O
should	_	_	O
be	_	_	O
scheduled	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
workers	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
laundromat	_	_	O
can	_	_	O
buy	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
washing	_	_	O
machines	_	_	O
,	_	_	O
a	_	_	O
top	_	_	B-VAR
-	_	_	I-VAR
loading	_	_	I-VAR
model	_	_	I-VAR
and	_	_	O
a	_	_	O
front	_	_	B-VAR
-	_	_	I-VAR
loading	_	_	I-VAR
model	_	_	I-VAR
.	_	_	O
The	_	_	O
top	_	_	B-VAR
-	_	_	I-VAR
loading	_	_	I-VAR
model	_	_	I-VAR
can	_	_	O
wash	_	_	O
50	_	_	B-PARAM
items	_	_	O
per	_	_	O
day	_	_	O
while	_	_	O
the	_	_	O
front	_	_	B-VAR
-	_	_	I-VAR
loading	_	_	I-VAR
model	_	_	I-VAR
can	_	_	O
wash	_	_	O
75	_	_	B-PARAM
items	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
The	_	_	O
top	_	_	B-VAR
-	_	_	I-VAR
loading	_	_	I-VAR
model	_	_	I-VAR
consumes	_	_	O
85	_	_	B-PARAM
kWh	_	_	O
per	_	_	O
day	_	_	O
while	_	_	O
the	_	_	O
front	_	_	B-VAR
-	_	_	I-VAR
loading	_	_	I-VAR
model	_	_	I-VAR
consumes	_	_	O
100	_	_	B-PARAM
kWh	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
The	_	_	O
laundromat	_	_	O
must	_	_	O
be	_	_	O
able	_	_	O
to	_	_	O
wash	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5000	_	_	B-LIMIT
items	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
7000	_	_	B-LIMIT
kWh	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
Since	_	_	O
the	_	_	O
top	_	_	O
-	_	_	O
loading	_	_	O
machine	_	_	O
are	_	_	O
harder	_	_	O
to	_	_	O
use	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
40	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
machines	_	_	O
can	_	_	O
be	_	_	O
top	_	_	B-VAR
-	_	_	I-VAR
loading	_	_	I-VAR
.	_	_	O
Further	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
machines	_	_	O
should	_	_	O
be	_	_	O
front	_	_	B-VAR
-	_	_	I-VAR
loading	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
machine	_	_	O
should	_	_	O
the	_	_	O
laundromat	_	_	O
buy	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
washing	_	_	I-OBJ_NAME
machines	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
bank	_	_	O
can	_	_	O
build	_	_	O
small	_	_	B-VAR
and	_	_	O
large	_	_	B-VAR
branches	_	_	I-VAR
to	_	_	O
serve	_	_	O
their	_	_	O
customers	_	_	O
.	_	_	O
A	_	_	O
small	_	_	B-VAR
branch	_	_	I-VAR
can	_	_	O
serve	_	_	O
50	_	_	B-PARAM
customers	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
requires	_	_	O
10	_	_	B-PARAM
bank	_	_	O
tellers	_	_	O
.	_	_	O
A	_	_	O
large	_	_	B-VAR
branch	_	_	I-VAR
can	_	_	O
serve	_	_	O
100	_	_	B-PARAM
customers	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
requires	_	_	O
15	_	_	B-PARAM
bank	_	_	O
tellers	_	_	O
.	_	_	O
The	_	_	O
bank	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
200	_	_	B-LIMIT
bank	_	_	O
tellers	_	_	O
and	_	_	O
needs	_	_	O
to	_	_	O
be	_	_	O
able	_	_	O
to	_	_	O
serve	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1200	_	_	B-LIMIT
customers	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
branch	_	_	O
size	_	_	O
should	_	_	O
they	_	_	O
build	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
branches	_	_	I-OBJ_NAME
needed	_	_	O
?	_	_	O

A	_	_	O
shipping	_	_	O
company	_	_	O
can	_	_	O
purchase	_	_	O
regular	_	_	B-VAR
and	_	_	O
hybrid	_	_	B-VAR
vans	_	_	O
to	_	_	O
make	_	_	O
deliveries	_	_	O
.	_	_	O
A	_	_	O
regular	_	_	B-VAR
van	_	_	I-VAR
can	_	_	O
deliver	_	_	O
500	_	_	B-PARAM
packages	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
produces	_	_	O
200	_	_	B-PARAM
units	_	_	O
of	_	_	O
pollutants	_	_	O
.	_	_	O
A	_	_	O
hybrid	_	_	B-VAR
van	_	_	I-VAR
can	_	_	O
deliver	_	_	O
300	_	_	B-PARAM
packages	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
produces	_	_	O
100	_	_	B-PARAM
units	_	_	O
of	_	_	O
pollutants	_	_	O
.	_	_	O
Due	_	_	O
to	_	_	O
a	_	_	O
new	_	_	O
environmental	_	_	O
law	_	_	O
,	_	_	O
they	_	_	O
can	_	_	O
produce	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
7000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
pollutants	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
the	_	_	O
company	_	_	O
needs	_	_	O
to	_	_	O
be	_	_	O
able	_	_	O
to	_	_	O
deliver	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20000	_	_	B-LIMIT
packages	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
van	_	_	O
should	_	_	O
they	_	_	O
buy	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
vans	_	_	I-OBJ_NAME
needed	_	_	O
?	_	_	O

In	_	_	O
order	_	_	O
to	_	_	O
make	_	_	O
carbon	_	_	O
dioxide	_	_	O
,	_	_	O
wood	_	_	O
is	_	_	O
burned	_	_	O
using	_	_	O
two	_	_	O
processes	_	_	O
,	_	_	O
with	_	_	B-VAR
a	_	_	I-VAR
catalyst	_	_	I-VAR
and	_	_	O
without	_	_	B-VAR
a	_	_	I-VAR
catalyst	_	_	I-VAR
.	_	_	O
The	_	_	O
process	_	_	B-VAR
with	_	_	I-VAR
a	_	_	I-VAR
catalyst	_	_	I-VAR
requires	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
wood	_	_	O
and	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
oxygen	_	_	O
to	_	_	O
make	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
carbon	_	_	B-OBJ_NAME
dioxide	_	_	I-OBJ_NAME
.	_	_	O
The	_	_	O
process	_	_	B-VAR
without	_	_	I-VAR
a	_	_	I-VAR
catalyst	_	_	I-VAR
requires	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
wood	_	_	O
and	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
oxygen	_	_	O
to	_	_	O
make	_	_	O
18	_	_	B-PARAM
units	_	_	O
of	_	_	O
carbon	_	_	B-OBJ_NAME
dioxide	_	_	I-OBJ_NAME
.	_	_	O
There	_	_	O
are	_	_	O
300	_	_	B-LIMIT
units	_	_	O
of	_	_	O
wood	_	_	O
and	_	_	O
300	_	_	B-LIMIT
units	_	_	O
of	_	_	O
oxygen	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
process	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
carbon	_	_	I-OBJ_NAME
dioxide	_	_	I-OBJ_NAME
produced	_	_	O
?	_	_	O

A	_	_	O
tea	_	_	O
estate	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
500	_	_	B-LIMIT
acres	_	_	O
of	_	_	O
land	_	_	O
and	_	_	O
they	_	_	O
need	_	_	O
to	_	_	O
pick	_	_	O
the	_	_	O
tea	_	_	O
leaves	_	_	O
either	_	_	O
using	_	_	O
a	_	_	O
traditional	_	_	B-VAR
machine	_	_	I-VAR
or	_	_	O
modern	_	_	B-VAR
machine	_	_	I-VAR
.	_	_	O
For	_	_	O
each	_	_	O
acre	_	_	O
of	_	_	O
land	_	_	O
,	_	_	O
the	_	_	O
traditional	_	_	B-VAR
machine	_	_	I-VAR
can	_	_	O
pick	_	_	O
30	_	_	B-PARAM
kg	_	_	O
of	_	_	O
tea	_	_	B-OBJ_NAME
leaves	_	_	I-OBJ_NAME
,	_	_	O
creates	_	_	O
10	_	_	B-PARAM
kg	_	_	O
of	_	_	O
waste	_	_	O
,	_	_	O
and	_	_	O
requires	_	_	O
20	_	_	B-PARAM
liters	_	_	O
of	_	_	O
fuel	_	_	O
.	_	_	O
For	_	_	O
each	_	_	O
acre	_	_	O
of	_	_	O
land	_	_	O
,	_	_	O
the	_	_	O
modern	_	_	B-VAR
machine	_	_	I-VAR
can	_	_	O
pick	_	_	O
40	_	_	B-PARAM
kg	_	_	O
of	_	_	O
tea	_	_	B-OBJ_NAME
leaves	_	_	I-OBJ_NAME
,	_	_	O
creates	_	_	O
15	_	_	B-PARAM
kg	_	_	O
of	_	_	O
waste	_	_	O
,	_	_	O
and	_	_	O
requires	_	_	O
15	_	_	B-PARAM
liters	_	_	O
of	_	_	O
fuel	_	_	O
.	_	_	O
The	_	_	O
estate	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
9000	_	_	B-LIMIT
liters	_	_	O
of	_	_	O
fuel	_	_	O
can	_	_	O
handle	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
6000	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
waste	_	_	O
.	_	_	O
For	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
should	_	_	O
each	_	_	O
machine	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
tea	_	_	I-OBJ_NAME
leaves	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
picked	_	_	O
?	_	_	O

A	_	_	O
grilled	_	_	O
cheese	_	_	O
shop	_	_	O
sells	_	_	O
a	_	_	O
light	_	_	B-VAR
and	_	_	O
heavy	_	_	B-VAR
grilled	_	_	O
cheese	_	_	O
sandwich	_	_	O
.	_	_	O
A	_	_	O
light	_	_	B-VAR
grilled	_	_	I-VAR
cheese	_	_	I-VAR
sandwich	_	_	I-VAR
requires	_	_	O
2	_	_	B-PARAM
slices	_	_	O
of	_	_	O
bread	_	_	O
and	_	_	O
3	_	_	B-PARAM
slices	_	_	O
of	_	_	O
cheese	_	_	O
.	_	_	O
A	_	_	O
heavy	_	_	B-VAR
grilled	_	_	I-VAR
cheese	_	_	I-VAR
sandwich	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
slices	_	_	O
of	_	_	O
bread	_	_	O
and	_	_	O
5	_	_	B-PARAM
slices	_	_	O
of	_	_	O
cheese	_	_	O
.	_	_	O
Since	_	_	O
most	_	_	O
people	_	_	O
who	_	_	O
come	_	_	O
to	_	_	O
the	_	_	O
store	_	_	O
love	_	_	O
grilled	_	_	O
cheese	_	_	O
,	_	_	O
the	_	_	O
store	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
heavy	_	_	B-VAR
grilled	_	_	I-VAR
cheese	_	_	I-VAR
sandwiches	_	_	I-VAR
as	_	_	O
light	_	_	B-VAR
grilled	_	_	I-VAR
cheese	_	_	I-VAR
sandwiches	_	_	I-VAR
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
300	_	_	B-LIMIT
slices	_	_	O
of	_	_	O
bread	_	_	O
and	_	_	O
500	_	_	B-LIMIT
slices	_	_	O
of	_	_	O
cheese	_	_	O
.	_	_	O
If	_	_	O
a	_	_	O
light	_	_	B-VAR
grilled	_	_	I-VAR
cheese	_	_	I-VAR
sandwich	_	_	I-VAR
takes	_	_	O
10	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
to	_	_	O
make	_	_	O
and	_	_	O
a	_	_	O
heavy	_	_	B-VAR
grilled	_	_	I-VAR
cheese	_	_	I-VAR
sandwich	_	_	I-VAR
takes	_	_	O
15	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
to	_	_	O
make	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
production	_	_	I-OBJ_NAME
time	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
post	_	_	O
office	_	_	O
is	_	_	O
buying	_	_	O
stamping	_	_	O
machines	_	_	O
and	_	_	O
they	_	_	O
can	_	_	O
buy	_	_	O
a	_	_	O
dual	_	_	B-VAR
or	_	_	O
single	_	_	B-VAR
model	_	_	O
stamping	_	_	O
machine	_	_	O
.	_	_	O
A	_	_	O
dual	_	_	B-VAR
model	_	_	I-VAR
stamping	_	_	I-VAR
machine	_	_	O
can	_	_	O
stamp	_	_	O
50	_	_	B-PARAM
letters	_	_	O
per	_	_	O
minute	_	_	O
while	_	_	O
a	_	_	O
single	_	_	B-VAR
model	_	_	I-VAR
stamping	_	_	I-VAR
machine	_	_	O
can	_	_	O
stamp	_	_	O
30	_	_	B-PARAM
letters	_	_	O
per	_	_	O
minute	_	_	O
.	_	_	O
The	_	_	O
dual	_	_	B-VAR
model	_	_	I-VAR
stamping	_	_	I-VAR
machine	_	_	O
requires	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
glue	_	_	O
per	_	_	O
minute	_	_	O
while	_	_	O
the	_	_	O
single	_	_	B-VAR
model	_	_	I-VAR
stamping	_	_	I-VAR
machine	_	_	O
requires	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
glue	_	_	O
per	_	_	O
minute	_	_	O
.	_	_	O
Since	_	_	O
the	_	_	O
single	_	_	B-VAR
model	_	_	I-VAR
stamping	_	_	I-VAR
machine	_	_	O
is	_	_	O
quieter	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
single	_	_	B-VAR
model	_	_	I-VAR
stamping	_	_	I-VAR
machines	_	_	O
must	_	_	O
be	_	_	O
more	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
dual	_	_	B-VAR
model	_	_	I-VAR
stamping	_	_	I-VAR
machines	_	_	O
.	_	_	O
Further	_	_	O
,	_	_	O
the	_	_	O
post	_	_	O
office	_	_	O
wants	_	_	O
to	_	_	O
make	_	_	O
sure	_	_	O
they	_	_	O
can	_	_	O
stamp	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
300	_	_	B-LIMIT
letters	_	_	O
per	_	_	O
minute	_	_	O
and	_	_	O
use	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
135	_	_	B-LIMIT
units	_	_	O
of	_	_	O
glue	_	_	O
per	_	_	O
minute	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
stamping	_	_	O
machine	_	_	O
should	_	_	O
they	_	_	O
purchase	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
stamping	_	_	I-OBJ_NAME
machines	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
banana	_	_	O
company	_	_	O
sells	_	_	O
their	_	_	O
bananas	_	_	O
in	_	_	O
small	_	_	B-VAR
and	_	_	O
large	_	_	B-VAR
crates	_	_	O
.	_	_	O
A	_	_	O
small	_	_	B-VAR
crate	_	_	I-VAR
can	_	_	O
hold	_	_	O
20	_	_	B-PARAM
bananas	_	_	O
while	_	_	O
a	_	_	O
large	_	_	B-VAR
crate	_	_	I-VAR
can	_	_	O
hole	_	_	O
50	_	_	B-PARAM
bananas	_	_	O
.	_	_	O
Since	_	_	O
large	_	_	B-VAR
crates	_	_	I-VAR
are	_	_	O
more	_	_	O
manageable	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
large	_	_	B-VAR
crates	_	_	I-VAR
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-PARAM
the	_	_	O
number	_	_	O
of	_	_	O
small	_	_	B-VAR
crates	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
small	_	_	B-VAR
crates	_	_	I-VAR
should	_	_	O
be	_	_	O
used	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
500	_	_	B-LIMIT
bananas	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
crate	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
use	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
crates	_	_	I-OBJ_NAME
produced	_	_	O
?	_	_	O

A	_	_	O
crepe	_	_	O
store	_	_	O
sells	_	_	O
chocolate	_	_	O
and	_	_	O
peanut	_	_	B-VAR
butter	_	_	I-VAR
crepes	_	_	I-VAR
.	_	_	O
A	_	_	O
chocolate	_	_	B-VAR
crepe	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
chocolate	_	_	O
spread	_	_	O
and	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
crepe	_	_	B-OBJ_NAME
mix	_	_	I-OBJ_NAME
.	_	_	O
A	_	_	O
peanut	_	_	B-VAR
butter	_	_	I-VAR
crepe	_	_	I-VAR
requires	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
peanut	_	_	O
butter	_	_	O
spread	_	_	O
and	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
crepe	_	_	B-OBJ_NAME
mix	_	_	I-OBJ_NAME
.	_	_	O
Recently	_	_	O
,	_	_	O
the	_	_	O
peanut	_	_	B-VAR
butter	_	_	I-VAR
crepe	_	_	I-VAR
has	_	_	O
been	_	_	O
more	_	_	O
popular	_	_	O
and	_	_	O
therefore	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
peanut	_	_	B-VAR
butter	_	_	I-VAR
crepes	_	_	I-VAR
made	_	_	O
must	_	_	B-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
chocolate	_	_	B-VAR
crepes	_	_	I-VAR
made	_	_	O
.	_	_	O
However	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
25	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
crepes	_	_	O
made	_	_	O
should	_	_	O
be	_	_	O
chocolate	_	_	B-VAR
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
400	_	_	B-LIMIT
units	_	_	O
of	_	_	O
chocolate	_	_	O
spread	_	_	O
and	_	_	O
450	_	_	B-LIMIT
units	_	_	O
of	_	_	O
peanut	_	_	O
butter	_	_	O
spread	_	_	O
.	_	_	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
amount	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
crepe	_	_	I-OBJ_NAME
mix	_	_	I-OBJ_NAME
needed	_	_	O
?	_	_	O

A	_	_	O
fire	_	_	O
department	_	_	O
employs	_	_	O
regular	_	_	B-VAR
and	_	_	O
emergency	_	_	B-VAR
fire	_	_	I-VAR
fighters	_	_	O
.	_	_	O
A	_	_	O
regular	_	_	B-VAR
fire	_	_	I-VAR
fighter	_	_	I-VAR
works	_	_	O
10	_	_	B-PARAM
hours	_	_	O
per	_	_	O
shift	_	_	O
and	_	_	O
earns	_	_	O
$	_	_	O
300	_	_	B-PARAM
.	_	_	O
An	_	_	O
emergency	_	_	B-VAR
fire	_	_	I-VAR
fighter	_	_	I-VAR
works	_	_	O
6	_	_	B-PARAM
hours	_	_	O
per	_	_	O
shift	_	_	O
and	_	_	O
earns	_	_	O
$	_	_	O
100	_	_	B-PARAM
.	_	_	O
Due	_	_	O
to	_	_	O
wildfires	_	_	O
in	_	_	O
the	_	_	O
region	_	_	O
,	_	_	O
the	_	_	O
fire	_	_	O
department	_	_	O
needs	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
300	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
fire	_	_	O
fighter	_	_	O
time	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
fire	_	_	O
department	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
7000	_	_	B-LIMIT
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
fire	_	_	O
department	_	_	O
hire	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
fire	_	_	I-OBJ_NAME
fighters	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
mall	_	_	O
buys	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
hand	_	_	O
sanitizer	_	_	O
machines	_	_	O
,	_	_	O
a	_	_	O
motion	_	_	B-VAR
activated	_	_	I-VAR
one	_	_	O
and	_	_	O
a	_	_	O
manual	_	_	B-VAR
one	_	_	O
.	_	_	O
The	_	_	O
motion	_	_	B-VAR
activated	_	_	I-VAR
one	_	_	O
can	_	_	O
deliver	_	_	O
50	_	_	B-PARAM
drops	_	_	O
per	_	_	O
minute	_	_	O
and	_	_	O
consumes	_	_	O
30	_	_	B-PARAM
kWh	_	_	O
.	_	_	O
The	_	_	O
manual	_	_	B-VAR
one	_	_	O
can	_	_	O
deliver	_	_	O
75	_	_	B-PARAM
drops	_	_	O
per	_	_	O
minute	_	_	O
and	_	_	O
consumes	_	_	O
20	_	_	B-PARAM
kWh	_	_	O
.	_	_	O
Since	_	_	O
the	_	_	O
motion	_	_	B-VAR
activated	_	_	I-VAR
one	_	_	O
is	_	_	O
more	_	_	O
hygienic	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
40	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
machines	_	_	O
can	_	_	O
be	_	_	O
manual	_	_	B-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-LIMIT
should	_	_	O
be	_	_	O
motion	_	_	B-VAR
activated	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
mall	_	_	O
must	_	_	O
be	_	_	O
able	_	_	O
to	_	_	O
deliver	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1000	_	_	B-LIMIT
drops	_	_	O
per	_	_	O
minute	_	_	O
and	_	_	O
can	_	_	O
use	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
500	_	_	B-LIMIT
kWh	_	_	O
per	_	_	O
minute	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
machine	_	_	O
should	_	_	O
they	_	_	O
buy	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
machines	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
hot	_	_	O
dog	_	_	O
company	_	_	O
can	_	_	O
build	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
butcher	_	_	O
shops	_	_	O
,	_	_	O
a	_	_	O
small	_	_	B-VAR
shop	_	_	I-VAR
and	_	_	O
a	_	_	O
large	_	_	B-VAR
shop	_	_	I-VAR
.	_	_	O
A	_	_	O
small	_	_	B-VAR
shop	_	_	I-VAR
can	_	_	O
make	_	_	O
30	_	_	B-PARAM
hot	_	_	O
dogs	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
requires	_	_	O
2	_	_	B-PARAM
workers	_	_	O
.	_	_	O
A	_	_	O
large	_	_	B-VAR
shop	_	_	I-VAR
can	_	_	O
make	_	_	O
70	_	_	B-PARAM
hot	_	_	O
dogs	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
requires	_	_	O
4	_	_	B-PARAM
workers	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
500	_	_	B-LIMIT
hot	_	_	O
dogs	_	_	O
per	_	_	O
day	_	_	O
but	_	_	O
they	_	_	O
only	_	_	O
have	_	_	O
available	_	_	B-CONST_DIR
30	_	_	B-LIMIT
workers	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
butcher	_	_	O
shop	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
build	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
butcher	_	_	I-OBJ_NAME
shops	_	_	I-OBJ_NAME
?	_	_	O

An	_	_	O
airport	_	_	O
buys	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
vehicles	_	_	O
,	_	_	O
a	_	_	O
4	_	_	B-VAR
-	_	_	I-VAR
wheeler	_	_	I-VAR
and	_	_	O
3	_	_	B-VAR
-	_	_	I-VAR
wheeler	_	_	I-VAR
,	_	_	I-VAR
to	_	_	O
help	_	_	O
move	_	_	O
luggage	_	_	O
.	_	_	O
A	_	_	O
4	_	_	B-VAR
-	_	_	I-VAR
wheeler	_	_	I-VAR
vehicle	_	_	I-VAR
can	_	_	O
move	_	_	O
60	_	_	B-PARAM
luggage	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
produces	_	_	O
30	_	_	B-PARAM
units	_	_	O
of	_	_	O
pollutant	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
A	_	_	O
3	_	_	B-VAR
-	_	_	I-VAR
wheeler	_	_	I-VAR
vehicle	_	_	I-VAR
can	_	_	O
move	_	_	O
40	_	_	B-PARAM
luggage	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
produces	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
pollutant	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
The	_	_	O
airport	_	_	O
needs	_	_	O
to	_	_	O
be	_	_	O
able	_	_	O
to	_	_	O
move	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1000	_	_	B-LIMIT
luggage	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
To	_	_	O
avoid	_	_	O
over	_	_	O
-	_	_	O
polluting	_	_	O
the	_	_	O
airport	_	_	O
,	_	_	O
they	_	_	O
can	_	_	O
produce	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
430	_	_	B-LIMIT
units	_	_	O
of	_	_	O
pollutant	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
vehicle	_	_	O
should	_	_	O
the	_	_	O
airport	_	_	O
buy	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
vehicles	_	_	I-OBJ_NAME
needed	_	_	O
.	_	_	O

A	_	_	O
scientist	_	_	O
is	_	_	O
conducting	_	_	O
two	_	_	O
experiments	_	_	O
to	_	_	O
produce	_	_	O
electricity	_	_	O
,	_	_	O
experiment	_	_	B-VAR
alpha	_	_	I-VAR
and	_	_	O
experiment	_	_	B-VAR
beta	_	_	I-VAR
.	_	_	O
In	_	_	O
experiment	_	_	B-VAR
alpha	_	_	I-VAR
,	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
metal	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
acid	_	_	O
are	_	_	O
required	_	_	O
to	_	_	O
produce	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
electricity	_	_	B-OBJ_NAME
.	_	_	O
In	_	_	O
experiment	_	_	B-VAR
beta	_	_	I-VAR
,	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
metal	_	_	O
and	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
acid	_	_	O
are	_	_	O
required	_	_	O
to	_	_	O
produced	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
electricity	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
lab	_	_	O
has	_	_	O
800	_	_	B-LIMIT
units	_	_	O
of	_	_	O
metal	_	_	O
and	_	_	O
750	_	_	B-LIMIT
units	_	_	O
of	_	_	O
acid	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
experiment	_	_	O
should	_	_	O
the	_	_	O
scientist	_	_	O
conduct	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
electricity	_	_	I-OBJ_NAME
produced	_	_	O
?	_	_	O

A	_	_	O
man	_	_	O
fishes	_	_	O
in	_	_	B-CONST_DIR
a	_	_	I-CONST_DIR
250	_	_	B-LIMIT
acre	_	_	O
lake	_	_	O
and	_	_	O
can	_	_	O
catch	_	_	O
fish	_	_	O
either	_	_	O
using	_	_	O
a	_	_	O
net	_	_	B-VAR
or	_	_	O
fishing	_	_	B-VAR
line	_	_	I-VAR
.	_	_	O
For	_	_	O
each	_	_	O
acre	_	_	O
of	_	_	O
the	_	_	O
lake	_	_	O
,	_	_	O
using	_	_	O
a	_	_	O
net	_	_	B-VAR
will	_	_	O
catch	_	_	O
8	_	_	B-PARAM
fish	_	_	B-OBJ_NAME
and	_	_	O
requires	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
bait	_	_	O
but	_	_	O
also	_	_	O
causes	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
pain	_	_	O
for	_	_	O
the	_	_	O
fisherman	_	_	O
.	_	_	O
For	_	_	O
each	_	_	O
acre	_	_	O
of	_	_	O
the	_	_	O
lake	_	_	O
,	_	_	O
using	_	_	O
a	_	_	O
fishing	_	_	B-VAR
line	_	_	I-VAR
will	_	_	O
catch	_	_	O
5	_	_	B-PARAM
fish	_	_	B-OBJ_NAME
and	_	_	O
requires	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
bait	_	_	O
but	_	_	O
also	_	_	O
causes	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
pain	_	_	O
for	_	_	O
the	_	_	O
fisherman	_	_	O
.	_	_	O
The	_	_	O
fisherman	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
800	_	_	B-LIMIT
units	_	_	O
of	_	_	O
bait	_	_	O
and	_	_	O
can	_	_	O
tolerate	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
350	_	_	B-LIMIT
units	_	_	O
of	_	_	O
pain	_	_	O
.	_	_	O
For	_	_	O
how	_	_	O
many	_	_	O
acres	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
use	_	_	O
each	_	_	O
fishing	_	_	O
method	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
fish	_	_	I-OBJ_NAME
he	_	_	O
can	_	_	O
catch	_	_	O
?	_	_	O

A	_	_	O
coffee	_	_	O
shop	_	_	O
sells	_	_	O
mochas	_	_	B-VAR
and	_	_	O
regular	_	_	B-VAR
coffees	_	_	I-VAR
.	_	_	O
Each	_	_	O
mocha	_	_	B-VAR
requires	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
coffee	_	_	O
powder	_	_	O
and	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
milk	_	_	O
.	_	_	O
Each	_	_	O
regular	_	_	B-VAR
coffee	_	_	I-VAR
requires	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
coffee	_	_	O
powder	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
milk	_	_	O
.	_	_	O
The	_	_	O
shop	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
400	_	_	B-LIMIT
units	_	_	O
of	_	_	O
coffee	_	_	O
powder	_	_	O
and	_	_	O
500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
milk	_	_	O
.	_	_	O
Making	_	_	O
a	_	_	O
mocha	_	_	B-VAR
takes	_	_	O
5	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
and	_	_	O
making	_	_	O
a	_	_	O
regular	_	_	B-VAR
coffee	_	_	I-VAR
takes	_	_	O
3	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
.	_	_	O
Since	_	_	O
mochas	_	_	O
are	_	_	O
more	_	_	O
popular	_	_	O
among	_	_	O
people	_	_	O
,	_	_	O
the	_	_	O
shop	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
mochas	_	_	B-VAR
as	_	_	O
regular	_	_	B-VAR
coffees	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
make	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
production	_	_	I-OBJ_NAME
time	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
butcher	_	_	O
shop	_	_	O
is	_	_	O
buying	_	_	O
meat	_	_	O
slicers	_	_	O
for	_	_	O
their	_	_	O
shop	_	_	O
,	_	_	O
a	_	_	O
manual	_	_	B-VAR
and	_	_	O
automatic	_	_	B-VAR
slicer	_	_	O
.	_	_	O
The	_	_	O
manual	_	_	B-VAR
slicer	_	_	I-VAR
can	_	_	O
cut	_	_	O
5	_	_	B-PARAM
slices	_	_	O
per	_	_	O
minute	_	_	O
while	_	_	O
the	_	_	O
automatic	_	_	B-VAR
slicer	_	_	I-VAR
can	_	_	O
cut	_	_	O
8	_	_	B-PARAM
slices	_	_	O
per	_	_	O
minute	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
to	_	_	O
make	_	_	O
sure	_	_	O
all	_	_	O
the	_	_	O
parts	_	_	O
operate	_	_	O
smoothly	_	_	O
,	_	_	O
the	_	_	O
manual	_	_	B-VAR
slicer	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
grease	_	_	O
per	_	_	O
minute	_	_	O
while	_	_	O
the	_	_	O
automatic	_	_	B-VAR
slicer	_	_	I-VAR
requires	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
grease	_	_	O
per	_	_	O
minute	_	_	O
.	_	_	O
Since	_	_	O
the	_	_	O
automatic	_	_	B-VAR
slicer	_	_	I-VAR
does	_	_	O
not	_	_	O
need	_	_	O
someone	_	_	O
to	_	_	O
operate	_	_	O
it	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
manual	_	_	B-VAR
slicers	_	_	I-VAR
must	_	_	O
be	_	_	O
less	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
automatic	_	_	B-VAR
slicers	_	_	I-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
the	_	_	O
butcher	_	_	O
shop	_	_	O
needs	_	_	O
to	_	_	O
be	_	_	O
able	_	_	O
to	_	_	O
cut	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
slices	_	_	O
per	_	_	O
minute	_	_	O
but	_	_	O
can	_	_	O
use	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
35	_	_	B-LIMIT
units	_	_	O
of	_	_	O
grease	_	_	O
per	_	_	O
minute	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
slicer	_	_	O
should	_	_	O
the	_	_	O
butcher	_	_	O
shop	_	_	O
buy	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	B-OBJ_NAME
total	_	_	I-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
slicers	_	_	I-OBJ_NAME
in	_	_	O
the	_	_	O
shop	_	_	O
?	_	_	O

A	_	_	O
water	_	_	O
company	_	_	O
sells	_	_	O
water	_	_	O
in	_	_	O
glass	_	_	B-VAR
and	_	_	O
plastic	_	_	B-VAR
bottles	_	_	O
.	_	_	O
A	_	_	O
glass	_	_	B-VAR
bottle	_	_	I-VAR
can	_	_	O
hole	_	_	O
500	_	_	B-PARAM
ml	_	_	O
of	_	_	O
water	_	_	O
while	_	_	O
a	_	_	O
plastic	_	_	B-VAR
bottle	_	_	I-VAR
can	_	_	O
hold	_	_	O
750	_	_	B-PARAM
ml	_	_	O
of	_	_	O
water	_	_	O
.	_	_	O
Because	_	_	O
most	_	_	O
customer	_	_	O
prefer	_	_	O
plastic	_	_	B-VAR
bottles	_	_	I-VAR
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
plastic	_	_	B-VAR
bottles	_	_	I-VAR
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
glass	_	_	B-VAR
bottles	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
glass	_	_	B-VAR
bottles	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
250000	_	_	B-LIMIT
ml	_	_	O
of	_	_	O
water	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
bottle	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
bottles	_	_	I-OBJ_NAME
?	_	_	O

An	_	_	O
Indian	_	_	O
restaurant	_	_	O
makes	_	_	O
goat	_	_	B-VAR
and	_	_	O
chicken	_	_	B-VAR
curry	_	_	O
.	_	_	O
Each	_	_	O
bowl	_	_	O
of	_	_	O
goat	_	_	B-VAR
curry	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
goat	_	_	O
meat	_	_	O
and	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
the	_	_	O
curry	_	_	B-OBJ_NAME
base	_	_	I-OBJ_NAME
.	_	_	O
Each	_	_	O
bowl	_	_	O
of	_	_	O
chicken	_	_	B-VAR
curry	_	_	I-VAR
requires	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
chicken	_	_	O
meat	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
the	_	_	O
curry	_	_	B-OBJ_NAME
base	_	_	I-OBJ_NAME
.	_	_	O
The	_	_	O
restaurant	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
1500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
goat	_	_	O
meat	_	_	O
and	_	_	O
2000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
chicken	_	_	O
meat	_	_	O
.	_	_	O
At	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
25	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
bowls	_	_	O
made	_	_	O
must	_	_	O
be	_	_	O
chicken	_	_	B-VAR
curry	_	_	I-VAR
.	_	_	O
Since	_	_	O
goat	_	_	B-VAR
curry	_	_	I-VAR
is	_	_	O
more	_	_	O
popular	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
goat	_	_	B-VAR
curry	_	_	I-VAR
bowls	_	_	O
must	_	_	B-CONST_DIR
be	_	_	I-CONST_DIR
larger	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
chicken	_	_	B-VAR
curry	_	_	I-VAR
bowls	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
curry	_	_	O
bowl	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
amount	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
curry	_	_	I-OBJ_NAME
base	_	_	I-OBJ_NAME
used	_	_	O
?	_	_	O

An	_	_	O
accounting	_	_	O
firm	_	_	O
employs	_	_	O
part	_	_	B-VAR
time	_	_	I-VAR
workers	_	_	I-VAR
and	_	_	O
full	_	_	B-VAR
time	_	_	I-VAR
workers	_	_	I-VAR
.	_	_	O
Full	_	_	B-VAR
time	_	_	I-VAR
workers	_	_	I-VAR
work	_	_	O
8	_	_	B-PARAM
hours	_	_	O
per	_	_	O
shift	_	_	O
while	_	_	O
part	_	_	B-VAR
time	_	_	I-VAR
workers	_	_	I-VAR
work	_	_	O
4	_	_	B-PARAM
hours	_	_	O
per	_	_	O
shift	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
full	_	_	B-VAR
time	_	_	I-VAR
workers	_	_	I-VAR
are	_	_	O
paid	_	_	O
$	_	_	O
300	_	_	B-PARAM
per	_	_	O
shift	_	_	O
while	_	_	O
part	_	_	B-VAR
time	_	_	I-VAR
workers	_	_	I-VAR
are	_	_	O
paid	_	_	O
$	_	_	O
100	_	_	B-PARAM
per	_	_	O
shift	_	_	O
.	_	_	O
Currently	_	_	O
,	_	_	O
the	_	_	O
accounting	_	_	O
firm	_	_	O
has	_	_	O
a	_	_	O
project	_	_	O
requiring	_	_	B-CONST_DIR
500	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
labor	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
firm	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
15000	_	_	B-LIMIT
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
worker	_	_	O
should	_	_	O
be	_	_	O
scheduled	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
workers	_	_	I-OBJ_NAME
.	_	_	O

A	_	_	O
factory	_	_	O
has	_	_	O
two	_	_	O
machines	_	_	O
,	_	_	O
A	_	_	B-VAR
and	_	_	O
B.	_	_	B-VAR
Each	_	_	O
day	_	_	O
,	_	_	O
machine	_	_	B-VAR
A	_	_	I-VAR
can	_	_	O
make	_	_	O
30	_	_	B-PARAM
items	_	_	O
and	_	_	O
consumes	_	_	O
100	_	_	B-PARAM
kWh	_	_	O
.	_	_	O
Machine	_	_	B-VAR
B	_	_	I-VAR
can	_	_	O
make	_	_	O
50	_	_	B-PARAM
items	_	_	O
and	_	_	O
consumes	_	_	O
120	_	_	B-PARAM
kWh	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
The	_	_	O
factory	_	_	O
must	_	_	O
produce	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1000	_	_	B-LIMIT
items	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
has	_	_	O
3000	_	_	B-LIMIT
kWh	_	_	O
of	_	_	O
electricity	_	_	O
available	_	_	B-CONST_DIR
per	_	_	O
day	_	_	O
.	_	_	O
Since	_	_	O
there	_	_	O
are	_	_	O
not	_	_	O
many	_	_	O
workers	_	_	O
that	_	_	O
can	_	_	O
operate	_	_	O
both	_	_	O
machines	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
machines	_	_	O
must	_	_	O
be	_	_	O
of	_	_	O
type	_	_	O
B.	_	_	B-VAR
Further	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
machines	_	_	O
of	_	_	O
type	_	_	O
A	_	_	B-VAR
should	_	_	O
be	_	_	O
used	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
machine	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
machines	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
toy	_	_	O
company	_	_	O
can	_	_	O
build	_	_	O
two	_	_	O
factory	_	_	O
types	_	_	O
,	_	_	O
a	_	_	O
medium	_	_	B-VAR
sized	_	_	I-VAR
factory	_	_	I-VAR
and	_	_	O
a	_	_	O
small	_	_	B-VAR
factory	_	_	I-VAR
.	_	_	O
A	_	_	O
medium	_	_	B-VAR
sized	_	_	I-VAR
factory	_	_	I-VAR
can	_	_	O
make	_	_	O
50	_	_	B-PARAM
toys	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
requires	_	_	O
3	_	_	B-PARAM
operators	_	_	O
.	_	_	O
A	_	_	O
small	_	_	B-VAR
factory	_	_	I-VAR
can	_	_	O
make	_	_	O
35	_	_	B-PARAM
toys	_	_	O
per	_	_	O
day	_	_	O
and	_	_	O
requires	_	_	O
2	_	_	B-PARAM
operators	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
250	_	_	B-LIMIT
toys	_	_	O
per	_	_	O
day	_	_	O
but	_	_	O
they	_	_	O
only	_	_	O
have	_	_	O
available	_	_	B-CONST_DIR
16	_	_	B-LIMIT
operators	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
factory	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
build	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
factories	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
chemical	_	_	O
plant	_	_	O
can	_	_	O
buy	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
generators	_	_	O
,	_	_	O
generator	_	_	B-VAR
A	_	_	I-VAR
and	_	_	O
generator	_	_	B-VAR
B	_	_	I-VAR
,	_	_	O
which	_	_	O
use	_	_	O
two	_	_	O
different	_	_	O
processes	_	_	O
to	_	_	O
generate	_	_	O
hydrogen	_	_	O
.	_	_	O
Generator	_	_	B-VAR
A	_	_	I-VAR
uses	_	_	O
an	_	_	O
electrolysis	_	_	O
process	_	_	O
and	_	_	O
produces	_	_	O
40	_	_	B-PARAM
cubic	_	_	O
meters	_	_	O
of	_	_	O
hydrogen	_	_	O
as	_	_	O
well	_	_	O
as	_	_	O
300	_	_	B-PARAM
units	_	_	O
of	_	_	O
pollutants	_	_	O
every	_	_	O
day	_	_	O
.	_	_	O
Generator	_	_	B-VAR
B	_	_	I-VAR
uses	_	_	O
a	_	_	O
fermentation	_	_	O
process	_	_	O
to	_	_	O
produce	_	_	O
30	_	_	B-PARAM
cubic	_	_	O
meters	_	_	O
of	_	_	O
hydrogen	_	_	O
per	_	_	O
day	_	_	O
while	_	_	O
outputting	_	_	O
200	_	_	B-PARAM
units	_	_	O
of	_	_	O
pollutants	_	_	O
.	_	_	O
The	_	_	O
chemical	_	_	O
plant	_	_	O
must	_	_	O
make	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
1000	_	_	B-LIMIT
cubic	_	_	O
meters	_	_	O
of	_	_	O
hydrogen	_	_	O
per	_	_	O
day	_	_	O
but	_	_	O
due	_	_	O
to	_	_	O
environmental	_	_	O
restrictions	_	_	O
they	_	_	O
can	_	_	O
produce	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
3000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
pollutant	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
generator	_	_	O
should	_	_	O
they	_	_	O
buy	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
generators	_	_	I-OBJ_NAME
needed	_	_	O
?	_	_	O

There	_	_	O
are	_	_	O
two	_	_	O
chemical	_	_	O
reactions	_	_	O
,	_	_	O
chemical	_	_	B-VAR
reaction	_	_	I-VAR
A	_	_	I-VAR
and	_	_	O
chemical	_	_	B-VAR
reaction	_	_	I-VAR
B.	_	_	I-VAR
Chemical	_	_	B-VAR
reaction	_	_	I-VAR
A	_	_	I-VAR
requires	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
rare	_	_	O
inert	_	_	O
gas	_	_	O
and	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
treated	_	_	O
water	_	_	O
to	_	_	O
produce	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
a	_	_	O
rare	_	_	B-OBJ_NAME
compound	_	_	I-OBJ_NAME
.	_	_	O
Chemical	_	_	B-VAR
reaction	_	_	I-VAR
B	_	_	I-VAR
requires	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
rare	_	_	O
inert	_	_	O
gas	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
treater	_	_	O
water	_	_	O
to	_	_	O
produce	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
a	_	_	O
rare	_	_	B-OBJ_NAME
compound	_	_	I-OBJ_NAME
.	_	_	O
There	_	_	O
are	_	_	O
1000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
the	_	_	O
rare	_	_	O
inert	_	_	O
gas	_	_	O
and	_	_	O
800	_	_	B-LIMIT
units	_	_	O
of	_	_	O
treated	_	_	O
water	_	_	O
available	_	_	B-CONST_DIR
in	_	_	O
the	_	_	O
lab	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
reactions	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
be	_	_	O
done	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
rare	_	_	I-OBJ_NAME
compound	_	_	I-OBJ_NAME
produced	_	_	O
?	_	_	O

A	_	_	O
mining	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
a	_	_	O
total	_	_	O
of	_	_	O
100	_	_	B-LIMIT
square	_	_	O
miles	_	_	O
of	_	_	O
mining	_	_	O
sites	_	_	O
and	_	_	O
considering	_	_	O
the	_	_	O
use	_	_	O
of	_	_	O
two	_	_	O
mining	_	_	O
techniques	_	_	O
:	_	_	O
heap	_	_	B-VAR
leaching	_	_	I-VAR
and	_	_	O
vat	_	_	B-VAR
leaching	_	_	I-VAR
.	_	_	O
For	_	_	O
each	_	_	O
square	_	_	O
mile	_	_	O
of	_	_	O
land	_	_	O
,	_	_	O
heap	_	_	B-VAR
leaching	_	_	I-VAR
technique	_	_	O
can	_	_	O
have	_	_	O
a	_	_	O
daily	_	_	O
production	_	_	O
of	_	_	O
3	_	_	B-PARAM
tons	_	_	O
of	_	_	O
rare	_	_	B-OBJ_NAME
earth	_	_	I-OBJ_NAME
oxide	_	_	I-OBJ_NAME
per	_	_	O
square	_	_	O
miles	_	_	O
but	_	_	O
it	_	_	O
also	_	_	O
creates	_	_	O
8	_	_	B-PARAM
tons	_	_	O
of	_	_	O
polluted	_	_	O
wastewater	_	_	O
and	_	_	O
requires	_	_	O
10	_	_	B-PARAM
extraction	_	_	O
machines	_	_	O
.	_	_	O
On	_	_	O
the	_	_	O
other	_	_	O
hand	_	_	O
,	_	_	O
vat	_	_	B-VAR
leaching	_	_	I-VAR
technique	_	_	O
produces	_	_	O
5	_	_	B-PARAM
tons	_	_	O
of	_	_	O
rare	_	_	B-OBJ_NAME
earth	_	_	I-OBJ_NAME
oxide	_	_	I-OBJ_NAME
per	_	_	O
square	_	_	O
miles	_	_	O
per	_	_	O
day	_	_	O
while	_	_	O
creating	_	_	O
17	_	_	B-PARAM
tons	_	_	O
of	_	_	O
polluted	_	_	O
wastewater	_	_	O
and	_	_	O
requiring	_	_	O
20	_	_	B-PARAM
extraction	_	_	O
machines	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
100	_	_	B-LIMIT
machines	_	_	O
available	_	_	B-CONST_DIR
and	_	_	O
due	_	_	O
to	_	_	O
environmental	_	_	O
regulations	_	_	O
,	_	_	O
the	_	_	O
amount	_	_	O
of	_	_	O
polluted	_	_	O
wastewater	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
90	_	_	B-LIMIT
tons	_	_	O
daily	_	_	O
.	_	_	O
Find	_	_	O
the	_	_	O
proportion	_	_	O
of	_	_	O
lands	_	_	O
that	_	_	O
use	_	_	O
each	_	_	O
mining	_	_	O
technique	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
daily	_	_	O
production	_	_	O
of	_	_	O
rare	_	_	B-OBJ_NAME
earth	_	_	I-OBJ_NAME
oxide	_	_	I-OBJ_NAME
.	_	_	O

A	_	_	O
small	_	_	O
chocolate	_	_	O
shop	_	_	O
makes	_	_	O
milk	_	_	B-VAR
chocolate	_	_	I-VAR
and	_	_	O
dark	_	_	B-VAR
chocolate	_	_	I-VAR
bars	_	_	I-VAR
.	_	_	O
Milk	_	_	B-VAR
chocolate	_	_	I-VAR
bars	_	_	I-VAR
require	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
cocoa	_	_	O
and	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
milk	_	_	O
.	_	_	O
Dark	_	_	B-VAR
chocolate	_	_	I-VAR
bars	_	_	I-VAR
require	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
cocoa	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
milk	_	_	O
.	_	_	O
The	_	_	O
shop	_	_	O
has	_	_	O
2000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
cocoa	_	_	O
and	_	_	O
1750	_	_	B-LIMIT
units	_	_	O
of	_	_	O
milk	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
In	_	_	O
addition	_	_	O
since	_	_	O
milk	_	_	B-VAR
chocolate	_	_	I-VAR
sells	_	_	O
better	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
2	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
milk	_	_	B-VAR
chocolate	_	_	I-VAR
bars	_	_	I-VAR
need	_	_	O
to	_	_	O
be	_	_	O
made	_	_	O
as	_	_	O
dark	_	_	B-VAR
chocolate	_	_	I-VAR
bars	_	_	I-VAR
.	_	_	O
If	_	_	O
making	_	_	O
a	_	_	O
milk	_	_	B-VAR
chocolate	_	_	I-VAR
bar	_	_	I-VAR
takes	_	_	O
15	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
and	_	_	O
making	_	_	O
a	_	_	O
dark	_	_	B-VAR
chocolate	_	_	I-VAR
bar	_	_	I-VAR
takes	_	_	O
12	_	_	B-PARAM
mins	_	_	B-OBJ_NAME
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
make	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
total	_	_	B-OBJ_NAME
production	_	_	I-OBJ_NAME
time	_	_	I-OBJ_NAME
?	_	_	O

An	_	_	O
office	_	_	O
is	_	_	O
buying	_	_	O
printers	_	_	O
for	_	_	O
their	_	_	O
headquarters	_	_	O
,	_	_	O
a	_	_	O
premium	_	_	B-VAR
model	_	_	I-VAR
and	_	_	O
regular	_	_	B-VAR
model	_	_	I-VAR
.	_	_	O
The	_	_	O
premium	_	_	B-VAR
model	_	_	I-VAR
can	_	_	O
print	_	_	O
30	_	_	B-PARAM
pages	_	_	O
per	_	_	O
minute	_	_	O
while	_	_	O
the	_	_	O
regular	_	_	B-VAR
model	_	_	I-VAR
can	_	_	O
print	_	_	O
20	_	_	B-PARAM
pages	_	_	O
per	_	_	O
minute	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
the	_	_	O
premium	_	_	B-VAR
model	_	_	I-VAR
requires	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
ink	_	_	O
per	_	_	O
minute	_	_	O
while	_	_	O
the	_	_	O
regular	_	_	B-VAR
model	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
ink	_	_	O
per	_	_	O
minute	_	_	O
.	_	_	O
The	_	_	O
office	_	_	O
wants	_	_	O
to	_	_	O
make	_	_	O
sure	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
200	_	_	B-LIMIT
pages	_	_	O
can	_	_	O
be	_	_	O
printed	_	_	O
per	_	_	O
minute	_	_	O
and	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
35	_	_	B-LIMIT
units	_	_	O
of	_	_	O
ink	_	_	O
are	_	_	O
used	_	_	O
per	_	_	O
minute	_	_	O
.	_	_	O
Since	_	_	O
the	_	_	O
premium	_	_	B-VAR
model	_	_	I-VAR
is	_	_	O
more	_	_	O
user	_	_	O
friendly	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
regular	_	_	B-VAR
printers	_	_	I-VAR
must	_	_	O
be	_	_	O
less	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
premium	_	_	B-VAR
printers	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
printer	_	_	O
should	_	_	O
be	_	_	O
bought	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
printers	_	_	I-OBJ_NAME
in	_	_	O
the	_	_	O
office	_	_	O
?	_	_	O

A	_	_	O
vine	_	_	O
company	_	_	O
sells	_	_	O
vine	_	_	O
in	_	_	O
vintage	_	_	B-VAR
and	_	_	O
regular	_	_	B-VAR
bottles	_	_	I-VAR
.	_	_	O
A	_	_	O
vintage	_	_	B-VAR
bottle	_	_	I-VAR
can	_	_	O
hold	_	_	O
500	_	_	B-PARAM
ml	_	_	O
of	_	_	O
vine	_	_	O
while	_	_	O
a	_	_	O
regular	_	_	B-VAR
bottle	_	_	I-VAR
can	_	_	O
hold	_	_	O
750	_	_	B-PARAM
ml	_	_	O
of	_	_	O
vine	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
100000	_	_	B-LIMIT
ml	_	_	O
of	_	_	O
vine	_	_	O
.	_	_	O
Because	_	_	O
vintage	_	_	B-VAR
bottles	_	_	I-VAR
are	_	_	O
mostly	_	_	O
bought	_	_	O
by	_	_	O
collectors	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
regular	_	_	B-VAR
bottles	_	_	I-VAR
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
4	_	_	B-PARAM
times	_	_	O
as	_	_	O
much	_	_	O
as	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
vintage	_	_	B-VAR
bottles	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
vintage	_	_	B-VAR
bottles	_	_	I-VAR
must	_	_	O
be	_	_	O
made	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
bottles	_	_	I-OBJ_NAME
produced	_	_	O
?	_	_	O

A	_	_	O
candy	_	_	O
company	_	_	O
is	_	_	O
making	_	_	O
peach	_	_	B-VAR
flavored	_	_	I-VAR
candy	_	_	I-VAR
and	_	_	O
cherry	_	_	B-VAR
flavored	_	_	I-VAR
candy	_	_	I-VAR
.	_	_	O
Each	_	_	O
pack	_	_	O
of	_	_	O
peach	_	_	B-VAR
flavored	_	_	I-VAR
candy	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
peach	_	_	O
flavoring	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
special	_	_	B-OBJ_NAME
syrup	_	_	I-OBJ_NAME
.	_	_	O
Each	_	_	O
pack	_	_	O
of	_	_	O
cherry	_	_	B-VAR
flavored	_	_	I-VAR
candy	_	_	I-VAR
requires	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
cherry	_	_	O
flavoring	_	_	O
and	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
special	_	_	B-OBJ_NAME
syrup	_	_	I-OBJ_NAME
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
3000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
peach	_	_	O
flavoring	_	_	O
and	_	_	O
4000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
cherry	_	_	O
flavoring	_	_	O
.	_	_	O
Peach	_	_	B-VAR
candy	_	_	I-VAR
is	_	_	O
much	_	_	O
more	_	_	O
popular	_	_	O
and	_	_	O
thus	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
peach	_	_	B-VAR
candy	_	_	I-VAR
packs	_	_	O
must	_	_	O
be	_	_	O
larger	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
cherry	_	_	B-VAR
candy	_	_	I-VAR
packs	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
pack	_	_	O
must	_	_	O
be	_	_	O
cherry	_	_	B-VAR
flavored	_	_	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
special	_	_	I-OBJ_NAME
syrup	_	_	I-OBJ_NAME
used	_	_	O
?	_	_	O

A	_	_	O
patient	_	_	O
in	_	_	O
the	_	_	O
hospital	_	_	O
can	_	_	O
take	_	_	O
two	_	_	O
pills	_	_	O
,	_	_	O
Pill	_	_	B-VAR
1	_	_	I-VAR
and	_	_	O
Pill	_	_	B-VAR
2	_	_	I-VAR
.	_	_	O
Per	_	_	O
pill	_	_	O
,	_	_	O
pill	_	_	B-VAR
1	_	_	I-VAR
provides	_	_	O
0.2	_	_	B-PARAM
units	_	_	O
of	_	_	O
pain	_	_	O
medication	_	_	O
and	_	_	O
0.3	_	_	B-PARAM
units	_	_	O
of	_	_	O
anxiety	_	_	O
medication	_	_	O
.	_	_	O
Per	_	_	O
pill	_	_	O
,	_	_	O
pill	_	_	B-VAR
2	_	_	I-VAR
provides	_	_	O
0.6	_	_	B-PARAM
units	_	_	O
of	_	_	O
pain	_	_	O
medication	_	_	O
and	_	_	O
0.2	_	_	B-PARAM
units	_	_	O
of	_	_	O
anxiety	_	_	O
medication	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
pill	_	_	B-VAR
1	_	_	I-VAR
causes	_	_	O
0.3	_	_	B-PARAM
units	_	_	O
of	_	_	O
discharge	_	_	B-OBJ_NAME
while	_	_	O
pill	_	_	B-VAR
2	_	_	I-VAR
causes	_	_	O
0.1	_	_	B-PARAM
units	_	_	O
of	_	_	O
discharge	_	_	B-OBJ_NAME
.	_	_	O
At	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
6	_	_	B-LIMIT
units	_	_	O
of	_	_	O
pain	_	_	O
medication	_	_	O
can	_	_	O
be	_	_	O
provided	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-LIMIT
units	_	_	O
of	_	_	O
anxiety	_	_	O
medication	_	_	O
must	_	_	O
be	_	_	O
provided	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
pills	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
patient	_	_	O
be	_	_	O
given	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
discharge	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
man	_	_	O
on	_	_	O
a	_	_	O
strict	_	_	O
diet	_	_	O
only	_	_	O
drinks	_	_	O
meal	_	_	O
replacement	_	_	O
drinks	_	_	O
from	_	_	O
two	_	_	O
brands	_	_	O
,	_	_	O
alpha	_	_	B-VAR
and	_	_	O
omega	_	_	B-VAR
.	_	_	O
The	_	_	O
alpha	_	_	B-VAR
brand	_	_	I-VAR
drink	_	_	I-VAR
contains	_	_	O
30	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
20	_	_	B-PARAM
grams	_	_	O
of	_	_	O
sugar	_	_	B-OBJ_NAME
,	_	_	O
and	_	_	O
350	_	_	B-PARAM
calories	_	_	O
per	_	_	O
bottle	_	_	O
.	_	_	O
The	_	_	O
omega	_	_	B-VAR
brand	_	_	I-VAR
drink	_	_	I-VAR
contains	_	_	O
20	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
15	_	_	B-PARAM
grams	_	_	O
of	_	_	O
sugar	_	_	B-OBJ_NAME
,	_	_	O
and	_	_	O
300	_	_	B-PARAM
calories	_	_	O
per	_	_	O
bottle	_	_	O
.	_	_	O
The	_	_	O
man	_	_	O
wants	_	_	O
to	_	_	O
get	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
2000	_	_	B-LIMIT
calories	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
because	_	_	O
the	_	_	O
omega	_	_	B-VAR
brand	_	_	I-VAR
drink	_	_	I-VAR
contains	_	_	O
tiny	_	_	O
amounts	_	_	O
of	_	_	O
caffeine	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
35	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
drink	_	_	O
should	_	_	O
be	_	_	O
omega	_	_	B-VAR
brand	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
bottles	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
drink	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
sugar	_	_	B-OBJ_NAME
intake	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
summer	_	_	O
camps	_	_	O
does	_	_	O
science	_	_	O
experiments	_	_	O
in	_	_	O
two	_	_	O
pre	_	_	O
filled	_	_	O
beakers	_	_	O
,	_	_	O
beaker	_	_	B-VAR
1	_	_	I-VAR
and	_	_	O
beaker	_	_	B-VAR
2	_	_	I-VAR
.	_	_	O
Beaker	_	_	B-VAR
1	_	_	I-VAR
uses	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
flour	_	_	O
and	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
special	_	_	O
liquid	_	_	O
to	_	_	O
make	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
slime	_	_	B-OBJ_NAME
.	_	_	O
Beaker	_	_	B-VAR
2	_	_	I-VAR
uses	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
flour	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
special	_	_	O
liquid	_	_	O
to	_	_	O
make	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
slime	_	_	B-OBJ_NAME
.	_	_	O
However	_	_	O
,	_	_	O
beaker	_	_	B-VAR
1	_	_	I-VAR
creates	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
waste	_	_	O
while	_	_	O
beaker	_	_	B-VAR
2	_	_	I-VAR
creates	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
waste	_	_	O
.	_	_	O
The	_	_	O
summer	_	_	O
camp	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
150	_	_	B-LIMIT
units	_	_	O
of	_	_	O
flour	_	_	O
and	_	_	O
100	_	_	B-LIMIT
units	_	_	O
of	_	_	O
special	_	_	O
liquid	_	_	O
.	_	_	O
If	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
units	_	_	O
of	_	_	O
waste	_	_	O
can	_	_	O
be	_	_	O
produced	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
beaker	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
slime	_	_	I-OBJ_NAME
produced	_	_	O
?	_	_	O

An	_	_	O
dog	_	_	O
hospital	_	_	O
has	_	_	B-CONST_DIR
2000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
tooth	_	_	O
medication	_	_	O
to	_	_	O
make	_	_	O
both	_	_	O
small	_	_	B-VAR
and	_	_	O
large	_	_	B-VAR
bones	_	_	I-VAR
.	_	_	O
A	_	_	O
small	_	_	B-VAR
bone	_	_	I-VAR
requires	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
tooth	_	_	O
medication	_	_	O
and	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
meat	_	_	B-OBJ_NAME
.	_	_	O
A	_	_	O
large	_	_	B-VAR
bone	_	_	I-VAR
requires	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
tooth	_	_	O
medication	_	_	O
and	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
meat	_	_	B-OBJ_NAME
.	_	_	O
Since	_	_	O
most	_	_	O
dogs	_	_	O
prefer	_	_	O
the	_	_	O
small	_	_	B-VAR
bones	_	_	I-VAR
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
bones	_	_	O
made	_	_	O
must	_	_	O
be	_	_	O
small	_	_	B-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
the	_	_	O
hospital	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
large	_	_	B-VAR
bones	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
bone	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
meat	_	_	I-OBJ_NAME
needed	_	_	O
?	_	_	O

A	_	_	O
scientist	_	_	O
in	_	_	O
the	_	_	O
arctic	_	_	O
needs	_	_	O
to	_	_	O
get	_	_	O
enough	_	_	O
vitamin	_	_	O
D	_	_	O
and	_	_	O
vitamin	_	_	O
C	_	_	O
in	_	_	O
his	_	_	O
diet	_	_	O
by	_	_	O
drinking	_	_	O
orange	_	_	B-VAR
and	_	_	O
apple	_	_	B-VAR
juice	_	_	I-VAR
.	_	_	O
Each	_	_	O
box	_	_	O
of	_	_	O
orange	_	_	B-VAR
juice	_	_	I-VAR
contains	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	B-OBJ_NAME
D	_	_	I-OBJ_NAME
and	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
C.	_	_	O
Each	_	_	O
box	_	_	O
of	_	_	O
apple	_	_	B-VAR
juice	_	_	I-VAR
contains	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	B-OBJ_NAME
D	_	_	I-OBJ_NAME
and	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
C.	_	_	O
Since	_	_	O
the	_	_	O
scientist	_	_	O
prefers	_	_	O
apple	_	_	B-VAR
juice	_	_	I-VAR
,	_	_	O
he	_	_	O
must	_	_	O
drink	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
apple	_	_	B-VAR
juice	_	_	I-VAR
boxes	_	_	O
and	_	_	O
orange	_	_	B-VAR
juice	_	_	I-VAR
boxes	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
he	_	_	O
must	_	_	O
also	_	_	O
drink	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-LIMIT
orange	_	_	B-VAR
juice	_	_	I-VAR
boxes	_	_	O
.	_	_	O
To	_	_	O
avoid	_	_	O
a	_	_	O
vitamin	_	_	O
C	_	_	O
overdose	_	_	O
,	_	_	O
the	_	_	O
scientist	_	_	O
can	_	_	O
consume	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
300	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamin	_	_	O
C.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
juice	_	_	O
box	_	_	O
should	_	_	O
he	_	_	O
drink	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
total	_	_	B-OBJ_NAME
vitamin	_	_	I-OBJ_NAME
D	_	_	I-OBJ_NAME
intake	_	_	O
?	_	_	O

A	_	_	O
cleaning	_	_	O
company	_	_	O
uses	_	_	O
a	_	_	O
cleansing	_	_	B-VAR
chemical	_	_	I-VAR
and	_	_	O
odor	_	_	B-VAR
-	_	_	I-VAR
removing	_	_	I-VAR
chemical	_	_	I-VAR
to	_	_	O
clean	_	_	O
a	_	_	O
house	_	_	O
.	_	_	O
Each	_	_	O
unit	_	_	O
of	_	_	O
the	_	_	O
cleansing	_	_	B-VAR
chemical	_	_	I-VAR
takes	_	_	O
4	_	_	B-PARAM
units	_	_	B-OBJ_NAME
to	_	_	O
be	_	_	O
effective	_	_	O
while	_	_	O
each	_	_	O
unit	_	_	O
of	_	_	O
the	_	_	O
odor	_	_	B-VAR
-	_	_	I-VAR
removing	_	_	I-VAR
chemical	_	_	I-VAR
takes	_	_	O
6	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
to	_	_	O
be	_	_	O
effective	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
must	_	_	O
use	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
units	_	_	O
of	_	_	O
the	_	_	O
cleansing	_	_	B-VAR
chemical	_	_	I-VAR
.	_	_	O
In	_	_	O
total	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
300	_	_	B-LIMIT
units	_	_	O
of	_	_	O
chemicals	_	_	O
can	_	_	O
be	_	_	O
used	_	_	O
per	_	_	O
house	_	_	O
.	_	_	O
Further	_	_	O
,	_	_	O
because	_	_	O
the	_	_	O
cleansing	_	_	B-VAR
chemical	_	_	I-VAR
is	_	_	O
strong	_	_	O
,	_	_	O
there	_	_	O
can	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
twice	_	_	B-PARAM
the	_	_	O
amount	_	_	O
of	_	_	O
cleansing	_	_	B-VAR
chemical	_	_	I-VAR
as	_	_	O
odor	_	_	B-VAR
-	_	_	I-VAR
removing	_	_	I-VAR
chemical	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
units	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
time	_	_	I-OBJ_NAME
it	_	_	O
takes	_	_	O
for	_	_	O
a	_	_	O
house	_	_	O
to	_	_	O
be	_	_	O
cleaned	_	_	O
?	_	_	O

A	_	_	O
drug	_	_	O
company	_	_	O
is	_	_	O
making	_	_	O
allergy	_	_	O
pills	_	_	O
and	_	_	O
fever	_	_	O
reducing	_	_	O
pills	_	_	O
in	_	_	O
two	_	_	O
factories	_	_	O
,	_	_	O
factory	_	_	B-VAR
1	_	_	I-VAR
and	_	_	O
factory	_	_	B-VAR
2	_	_	I-VAR
.	_	_	O
Factory	_	_	B-VAR
1	_	_	I-VAR
produces	_	_	O
20	_	_	B-PARAM
allergy	_	_	O
pills	_	_	O
and	_	_	O
15	_	_	B-PARAM
fever	_	_	O
reducing	_	_	O
pills	_	_	O
per	_	_	O
hour	_	_	O
.	_	_	O
Factory	_	_	B-VAR
2	_	_	I-VAR
produces	_	_	O
10	_	_	B-PARAM
allergy	_	_	O
pills	_	_	O
and	_	_	O
30	_	_	B-PARAM
fever	_	_	O
reducing	_	_	O
pills	_	_	O
per	_	_	O
hour	_	_	O
.	_	_	O
Factory	_	_	B-VAR
1	_	_	I-VAR
is	_	_	O
much	_	_	O
more	_	_	O
efficient	_	_	O
and	_	_	O
only	_	_	O
requires	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
a	_	_	O
rare	_	_	O
compound	_	_	O
while	_	_	O
factory	_	_	B-VAR
2	_	_	I-VAR
requires	_	_	O
30	_	_	B-PARAM
units	_	_	O
of	_	_	O
a	_	_	O
rare	_	_	O
compound	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
only	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
1000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
the	_	_	O
rare	_	_	O
compound	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
company	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
700	_	_	B-LIMIT
allergy	_	_	O
pills	_	_	O
and	_	_	O
600	_	_	B-LIMIT
fever	_	_	O
reducing	_	_	O
pills	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
hours	_	_	O
should	_	_	O
each	_	_	O
factory	_	_	O
be	_	_	O
run	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
time	_	_	I-OBJ_NAME
needed	_	_	O
?	_	_	O

A	_	_	O
doctor	_	_	O
recommends	_	_	O
her	_	_	O
patient	_	_	O
eat	_	_	O
more	_	_	O
fish	_	_	B-VAR
and	_	_	O
chicken	_	_	B-VAR
to	_	_	O
increase	_	_	O
her	_	_	O
protein	_	_	O
and	_	_	O
iron	_	_	O
intake	_	_	O
.	_	_	O
Each	_	_	O
fish	_	_	B-VAR
meal	_	_	I-VAR
contains	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
iron	_	_	O
.	_	_	O
Each	_	_	O
chicken	_	_	B-VAR
meal	_	_	I-VAR
contains	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
iron	_	_	O
.	_	_	O
The	_	_	O
patient	_	_	O
needs	_	_	O
to	_	_	O
consume	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
130	_	_	B-LIMIT
units	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
120	_	_	B-LIMIT
units	_	_	O
of	_	_	O
iron	_	_	O
.	_	_	O
Since	_	_	O
the	_	_	O
chicken	_	_	B-VAR
meal	_	_	I-VAR
is	_	_	O
less	_	_	O
expensive	_	_	O
,	_	_	O
the	_	_	O
patient	_	_	O
prefers	_	_	O
to	_	_	O
consume	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-PARAM
as	_	_	O
many	_	_	O
chicken	_	_	B-VAR
meals	_	_	I-VAR
as	_	_	O
fish	_	_	B-VAR
meals	_	_	I-VAR
.	_	_	O
If	_	_	O
each	_	_	O
fish	_	_	B-VAR
meal	_	_	I-VAR
contains	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	B-OBJ_NAME
and	_	_	O
each	_	_	O
chicken	_	_	B-VAR
meal	_	_	I-VAR
contains	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	B-OBJ_NAME
,	_	_	O
how	_	_	O
many	_	_	O
meals	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
she	_	_	O
eat	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
her	_	_	O
fat	_	_	B-OBJ_NAME
intake	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
pharmaceutical	_	_	O
company	_	_	O
makes	_	_	O
skin	_	_	O
cream	_	_	O
in	_	_	O
batches	_	_	O
,	_	_	O
a	_	_	O
regular	_	_	B-VAR
batch	_	_	I-VAR
and	_	_	O
premium	_	_	B-VAR
batch	_	_	I-VAR
,	_	_	O
to	_	_	O
sell	_	_	O
to	_	_	O
hospitals	_	_	O
.	_	_	O
The	_	_	O
regular	_	_	B-VAR
batch	_	_	I-VAR
requires	_	_	O
50	_	_	B-PARAM
units	_	_	O
of	_	_	O
medicinal	_	_	O
ingredients	_	_	O
and	_	_	O
40	_	_	B-PARAM
units	_	_	O
of	_	_	O
rehydration	_	_	O
product	_	_	O
.	_	_	O
A	_	_	O
premium	_	_	B-VAR
batch	_	_	I-VAR
requires	_	_	O
40	_	_	B-PARAM
units	_	_	O
of	_	_	O
medicinal	_	_	O
ingredients	_	_	O
and	_	_	O
60	_	_	B-PARAM
units	_	_	O
of	_	_	O
rehydration	_	_	O
product	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
3000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
medicinal	_	_	O
ingredients	_	_	O
and	_	_	O
3500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
rehydration	_	_	O
product	_	_	O
.	_	_	O
Since	_	_	O
the	_	_	O
premium	_	_	B-VAR
batch	_	_	I-VAR
sells	_	_	O
better	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
regular	_	_	B-VAR
batches	_	_	I-VAR
must	_	_	O
be	_	_	O
less	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
premium	_	_	B-VAR
batches	_	_	I-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
the	_	_	O
company	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
regular	_	_	B-VAR
batches	_	_	I-VAR
.	_	_	O
If	_	_	O
a	_	_	O
regular	_	_	B-VAR
batch	_	_	I-VAR
can	_	_	O
treat	_	_	O
50	_	_	B-PARAM
people	_	_	B-OBJ_NAME
and	_	_	O
a	_	_	O
premium	_	_	B-VAR
batch	_	_	I-VAR
can	_	_	O
treat	_	_	O
30	_	_	B-PARAM
people	_	_	B-OBJ_NAME
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
batch	_	_	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
clinic	_	_	O
takes	_	_	O
patient	_	_	O
blood	_	_	O
pressure	_	_	O
either	_	_	O
using	_	_	O
an	_	_	O
automatic	_	_	B-VAR
machine	_	_	I-VAR
or	_	_	O
a	_	_	O
manual	_	_	B-VAR
machine	_	_	I-VAR
.	_	_	O
The	_	_	O
automatic	_	_	B-VAR
machine	_	_	I-VAR
takes	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
per	_	_	O
patient	_	_	O
while	_	_	O
the	_	_	O
manual	_	_	B-VAR
machine	_	_	I-VAR
takes	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
per	_	_	O
patient	_	_	O
.	_	_	O
Since	_	_	O
the	_	_	O
automatic	_	_	B-VAR
machine	_	_	I-VAR
frequently	_	_	O
breaks	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-PARAM
as	_	_	O
many	_	_	O
patients	_	_	O
must	_	_	O
have	_	_	O
their	_	_	O
blood	_	_	O
pressure	_	_	O
taken	_	_	O
by	_	_	O
the	_	_	O
manual	_	_	B-VAR
machine	_	_	I-VAR
than	_	_	O
the	_	_	O
automatic	_	_	B-VAR
machine	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
patient	_	_	O
can	_	_	O
be	_	_	O
processed	_	_	O
by	_	_	O
the	_	_	O
automatic	_	_	B-VAR
machine	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
clinic	_	_	O
is	_	_	O
open	_	_	B-CONST_DIR
for	_	_	O
20000	_	_	B-LIMIT
minutes	_	_	O
,	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
patients	_	_	I-OBJ_NAME
whose	_	_	O
blood	_	_	O
pressure	_	_	O
can	_	_	O
be	_	_	O
taken	_	_	O
.	_	_	O

A	_	_	O
patient	_	_	O
with	_	_	O
a	_	_	O
sore	_	_	O
throat	_	_	O
can	_	_	O
drink	_	_	O
two	_	_	O
syrups	_	_	O
,	_	_	O
syrup	_	_	B-VAR
1	_	_	I-VAR
and	_	_	O
syrup	_	_	B-VAR
2	_	_	I-VAR
for	_	_	O
treatment	_	_	O
.	_	_	O
Per	_	_	O
serving	_	_	O
,	_	_	O
syrup	_	_	B-VAR
1	_	_	I-VAR
delivers	_	_	O
0.5	_	_	B-PARAM
units	_	_	O
of	_	_	O
medicine	_	_	O
to	_	_	O
the	_	_	O
throat	_	_	O
and	_	_	O
0.4	_	_	B-PARAM
units	_	_	O
of	_	_	O
medicine	_	_	O
to	_	_	O
the	_	_	O
lungs	_	_	O
.	_	_	O
Per	_	_	O
serving	_	_	O
,	_	_	O
syrup	_	_	B-VAR
2	_	_	I-VAR
delivers	_	_	O
0.2	_	_	B-PARAM
units	_	_	O
of	_	_	O
medicine	_	_	O
to	_	_	O
the	_	_	O
throat	_	_	O
and	_	_	O
0.5	_	_	B-PARAM
units	_	_	O
of	_	_	O
medicine	_	_	O
to	_	_	O
the	_	_	O
lungs	_	_	O
.	_	_	O
Furthermore	_	_	O
,	_	_	O
syrup	_	_	B-VAR
1	_	_	I-VAR
contains	_	_	O
0.5	_	_	B-PARAM
units	_	_	O
of	_	_	O
sugar	_	_	B-OBJ_NAME
while	_	_	O
syrup	_	_	B-VAR
2	_	_	I-VAR
contains	_	_	O
0.3	_	_	B-PARAM
units	_	_	O
of	_	_	O
sugar	_	_	B-OBJ_NAME
per	_	_	O
serving	_	_	O
.	_	_	O
The	_	_	O
patient	_	_	O
can	_	_	O
get	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
5	_	_	B-LIMIT
units	_	_	O
of	_	_	O
medicine	_	_	O
for	_	_	O
the	_	_	O
throat	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
4	_	_	B-LIMIT
units	_	_	O
of	_	_	O
medicine	_	_	O
to	_	_	O
the	_	_	O
lungs	_	_	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
sailor	_	_	O
can	_	_	O
eat	_	_	O
either	_	_	O
a	_	_	O
crab	_	_	B-VAR
cakes	_	_	I-VAR
or	_	_	O
a	_	_	O
lobster	_	_	B-VAR
roll	_	_	I-VAR
for	_	_	O
his	_	_	O
meals	_	_	O
.	_	_	O
He	_	_	O
needs	_	_	O
to	_	_	O
ensure	_	_	O
he	_	_	O
gets	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
80	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamin	_	_	O
A	_	_	O
and	_	_	O
100	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamin	_	_	O
C.	_	_	O
Each	_	_	O
crab	_	_	B-VAR
cake	_	_	I-VAR
contains	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
A	_	_	O
and	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
C.	_	_	O
Each	_	_	O
lobster	_	_	B-VAR
roll	_	_	I-VAR
contains	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
A	_	_	O
and	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
C.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
since	_	_	O
lobster	_	_	O
is	_	_	O
more	_	_	O
expensive	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
40	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
his	_	_	O
meals	_	_	O
should	_	_	O
be	_	_	O
lobster	_	_	B-VAR
rolls	_	_	I-VAR
.	_	_	O
If	_	_	O
each	_	_	O
crab	_	_	B-VAR
cake	_	_	I-VAR
contains	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
unsaturated	_	_	B-OBJ_NAME
fat	_	_	I-OBJ_NAME
and	_	_	O
each	_	_	O
lobster	_	_	B-VAR
roll	_	_	I-VAR
contains	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
unsaturated	_	_	B-OBJ_NAME
fat	_	_	I-OBJ_NAME
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
eat	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
unsaturated	_	_	B-OBJ_NAME
fat	_	_	I-OBJ_NAME
intake	_	_	O
?	_	_	O

A	_	_	O
science	_	_	O
show	_	_	O
preforms	_	_	O
two	_	_	O
different	_	_	O
demonstrations	_	_	O
,	_	_	O
demonstration	_	_	B-VAR
1	_	_	I-VAR
and	_	_	O
demonstration	_	_	B-VAR
2	_	_	I-VAR
.	_	_	O
In	_	_	O
demonstration	_	_	B-VAR
1	_	_	I-VAR
,	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
mint	_	_	O
and	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
the	_	_	O
active	_	_	O
ingredient	_	_	O
is	_	_	O
used	_	_	O
to	_	_	O
make	_	_	O
25	_	_	B-PARAM
units	_	_	O
of	_	_	O
minty	_	_	B-OBJ_NAME
foam	_	_	I-OBJ_NAME
.	_	_	O
In	_	_	O
demonstration	_	_	B-VAR
2	_	_	I-VAR
,	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
mint	_	_	O
and	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
the	_	_	O
active	_	_	O
ingredient	_	_	O
is	_	_	O
used	_	_	O
to	_	_	O
make	_	_	O
18	_	_	B-PARAM
units	_	_	O
of	_	_	O
minty	_	_	B-OBJ_NAME
foam	_	_	I-OBJ_NAME
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
demonstration	_	_	B-VAR
1	_	_	I-VAR
creates	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
black	_	_	O
tar	_	_	O
while	_	_	O
demonstration	_	_	B-VAR
2	_	_	I-VAR
creates	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
black	_	_	O
tar	_	_	O
.	_	_	O
The	_	_	O
show	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
120	_	_	B-LIMIT
units	_	_	O
of	_	_	O
mint	_	_	O
and	_	_	O
100	_	_	B-LIMIT
units	_	_	O
of	_	_	O
active	_	_	O
ingredients	_	_	O
.	_	_	O
If	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
50	_	_	B-LIMIT
units	_	_	O
of	_	_	O
black	_	_	O
tar	_	_	O
can	_	_	O
be	_	_	O
produced	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
demonstration	_	_	O
should	_	_	O
be	_	_	O
done	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
minty	_	_	I-OBJ_NAME
foam	_	_	I-OBJ_NAME
produced	_	_	O
?	_	_	O

A	_	_	O
lab	_	_	O
has	_	_	O
20000	_	_	B-LIMIT
mg	_	_	O
of	_	_	O
mRNA	_	_	O
anti	_	_	O
-	_	_	O
viral	_	_	O
available	_	_	B-CONST_DIR
to	_	_	O
make	_	_	O
children	_	_	B-VAR
's	_	_	I-VAR
and	_	_	O
adult	_	_	B-VAR
vaccines	_	_	I-VAR
.	_	_	O
Each	_	_	O
children	_	_	B-VAR
's	_	_	I-VAR
vaccine	_	_	I-VAR
contains	_	_	O
50	_	_	B-PARAM
mg	_	_	O
of	_	_	O
mRNA	_	_	O
and	_	_	O
50	_	_	B-PARAM
mg	_	_	O
of	_	_	O
fever	_	_	B-OBJ_NAME
suppressant	_	_	I-OBJ_NAME
.	_	_	O
Each	_	_	O
adult	_	_	B-VAR
vaccine	_	_	I-VAR
contains	_	_	O
75	_	_	B-PARAM
mg	_	_	O
of	_	_	O
mRNA	_	_	O
and	_	_	O
75	_	_	B-PARAM
mg	_	_	O
of	_	_	O
fever	_	_	B-OBJ_NAME
suppressant	_	_	I-OBJ_NAME
.	_	_	O
Since	_	_	O
adult	_	_	B-VAR
vaccines	_	_	I-VAR
are	_	_	O
more	_	_	O
essential	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
70	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
vaccines	_	_	O
should	_	_	O
be	_	_	O
adult	_	_	B-VAR
vaccines	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
children	_	_	B-VAR
's	_	_	I-VAR
vaccines	_	_	I-VAR
should	_	_	O
be	_	_	O
made	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
vaccine	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
fever	_	_	I-OBJ_NAME
suppressant	_	_	I-OBJ_NAME
used	_	_	O
?	_	_	O

A	_	_	O
parent	_	_	O
feeds	_	_	O
their	_	_	O
baby	_	_	O
two	_	_	O
flavors	_	_	O
of	_	_	O
baby	_	_	O
food	_	_	O
,	_	_	O
apple	_	_	B-VAR
and	_	_	O
carrot	_	_	B-VAR
,	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
meet	_	_	O
the	_	_	O
babies	_	_	O
fat	_	_	O
and	_	_	O
folate	_	_	O
requirements	_	_	O
.	_	_	O
Each	_	_	O
serving	_	_	O
of	_	_	O
apple	_	_	B-VAR
flavored	_	_	I-VAR
baby	_	_	I-VAR
food	_	_	O
contains	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	B-OBJ_NAME
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
folate	_	_	O
.	_	_	O
Each	_	_	O
serving	_	_	O
of	_	_	O
carrot	_	_	B-VAR
flavored	_	_	I-VAR
baby	_	_	I-VAR
food	_	_	O
contains	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	B-OBJ_NAME
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
folate	_	_	O
.	_	_	O
The	_	_	O
baby	_	_	O
does	_	_	O
not	_	_	O
like	_	_	O
the	_	_	O
carrot	_	_	B-VAR
flavor	_	_	I-VAR
,	_	_	O
and	_	_	O
therefore	_	_	O
he	_	_	O
must	_	_	B-CONST_DIR
eat	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
apple	_	_	B-VAR
flavored	_	_	I-VAR
baby	_	_	I-VAR
food	_	_	I-VAR
as	_	_	O
carrot	_	_	B-VAR
flavored	_	_	I-VAR
baby	_	_	I-VAR
food	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
he	_	_	O
must	_	_	O
eat	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
2	_	_	B-LIMIT
servings	_	_	O
of	_	_	O
carrot	_	_	B-VAR
flavored	_	_	I-VAR
baby	_	_	I-VAR
food	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
baby	_	_	O
can	_	_	O
consume	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
units	_	_	O
of	_	_	O
folate	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
servings	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
eat	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
fat	_	_	B-OBJ_NAME
intake	_	_	I-OBJ_NAME
?	_	_	O

Both	_	_	O
fertilizer	_	_	B-VAR
and	_	_	O
seeds	_	_	B-VAR
need	_	_	O
to	_	_	O
be	_	_	O
added	_	_	O
to	_	_	O
a	_	_	O
lawn	_	_	O
.	_	_	O
One	_	_	O
unit	_	_	O
of	_	_	O
fertilizer	_	_	B-VAR
takes	_	_	O
0.5	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
to	_	_	O
be	_	_	O
effective	_	_	O
while	_	_	O
one	_	_	O
unit	_	_	O
of	_	_	O
seeds	_	_	B-VAR
takes	_	_	O
1.5	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
to	_	_	O
be	_	_	O
effective	_	_	O
.	_	_	O
There	_	_	O
can	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
300	_	_	B-LIMIT
units	_	_	O
of	_	_	O
fertilizer	_	_	B-VAR
and	_	_	O
seeds	_	_	B-VAR
combined	_	_	O
added	_	_	O
to	_	_	O
the	_	_	O
lawn	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
units	_	_	O
of	_	_	O
fertilizer	_	_	B-VAR
need	_	_	O
to	_	_	O
be	_	_	O
added	_	_	O
.	_	_	O
Since	_	_	O
the	_	_	O
lawn	_	_	O
is	_	_	O
really	_	_	O
patchy	_	_	O
,	_	_	O
there	_	_	O
can	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
twice	_	_	B-PARAM
the	_	_	O
amount	_	_	O
of	_	_	O
fertilizer	_	_	B-VAR
as	_	_	O
seeds	_	_	B-VAR
.	_	_	O
How	_	_	O
many	_	_	O
units	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
added	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
time	_	_	I-OBJ_NAME
it	_	_	O
takes	_	_	O
for	_	_	O
the	_	_	O
lawn	_	_	O
to	_	_	O
be	_	_	O
ready	_	_	O
?	_	_	O

A	_	_	O
pharmacy	_	_	O
has	_	_	O
two	_	_	O
factories	_	_	O
,	_	_	O
factory	_	_	B-VAR
1	_	_	I-VAR
and	_	_	O
factory	_	_	B-VAR
2	_	_	I-VAR
,	_	_	O
where	_	_	O
they	_	_	O
make	_	_	O
acne	_	_	O
cream	_	_	O
and	_	_	O
anti	_	_	O
-	_	_	O
bacterial	_	_	O
cream	_	_	O
.	_	_	O
Factory	_	_	B-VAR
1	_	_	I-VAR
produces	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
acne	_	_	O
cream	_	_	O
and	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
anti	_	_	O
-	_	_	O
bacterial	_	_	O
cream	_	_	O
per	_	_	O
hour	_	_	O
.	_	_	O
Factory	_	_	B-VAR
2	_	_	I-VAR
produces	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
acne	_	_	O
cream	_	_	O
and	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
anti	_	_	O
-	_	_	O
bacterial	_	_	O
cream	_	_	O
per	_	_	O
hour	_	_	O
.	_	_	O
Factory	_	_	B-VAR
1	_	_	I-VAR
requires	_	_	O
30	_	_	B-PARAM
units	_	_	O
of	_	_	O
base	_	_	O
gel	_	_	O
per	_	_	O
hour	_	_	O
while	_	_	O
factory	_	_	B-VAR
2	_	_	I-VAR
requires	_	_	O
45	_	_	B-PARAM
units	_	_	O
of	_	_	O
base	_	_	O
gel	_	_	O
per	_	_	O
hour	_	_	O
.	_	_	O
The	_	_	O
pharmacy	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
5000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
base	_	_	O
gel	_	_	O
.	_	_	O
Further	_	_	O
,	_	_	O
they	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
800	_	_	B-LIMIT
units	_	_	O
of	_	_	O
acne	_	_	O
cream	_	_	O
and	_	_	O
1000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
anti	_	_	O
-	_	_	O
bacterial	_	_	O
cream	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
hours	_	_	O
should	_	_	O
each	_	_	O
factory	_	_	O
be	_	_	O
run	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
time	_	_	I-OBJ_NAME
needed	_	_	O
?	_	_	O

A	_	_	O
doctor	_	_	O
recommends	_	_	O
that	_	_	O
a	_	_	O
man	_	_	O
eat	_	_	O
burgers	_	_	B-VAR
and	_	_	O
pizza	_	_	B-VAR
in	_	_	O
order	_	_	O
to	_	_	O
put	_	_	O
on	_	_	O
weight	_	_	O
.	_	_	O
Each	_	_	O
burger	_	_	B-VAR
contains	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	O
and	_	_	O
300	_	_	B-PARAM
calories	_	_	O
.	_	_	O
Each	_	_	O
slice	_	_	O
of	_	_	O
pizza	_	_	B-VAR
contains	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
fat	_	_	O
and	_	_	O
250	_	_	B-PARAM
calories	_	_	O
.	_	_	O
The	_	_	O
man	_	_	O
must	_	_	O
get	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
130	_	_	B-LIMIT
units	_	_	O
of	_	_	O
fat	_	_	O
and	_	_	O
3000	_	_	B-LIMIT
calories	_	_	O
.	_	_	O
Further	_	_	O
,	_	_	O
each	_	_	O
burger	_	_	B-VAR
contains	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
cholesterol	_	_	B-OBJ_NAME
while	_	_	O
each	_	_	O
slice	_	_	O
of	_	_	O
pizza	_	_	B-VAR
contains	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
cholesterol	_	_	B-OBJ_NAME
.	_	_	O
Since	_	_	O
burgers	_	_	B-VAR
are	_	_	O
slightly	_	_	O
more	_	_	O
expensive	_	_	O
,	_	_	O
the	_	_	O
man	_	_	O
decides	_	_	O
to	_	_	O
eat	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-PARAM
as	_	_	O
many	_	_	O
slices	_	_	O
of	_	_	O
pizza	_	_	B-VAR
as	_	_	O
burgers	_	_	B-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
eat	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
cholesterol	_	_	B-OBJ_NAME
intake	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
clinic	_	_	O
makes	_	_	O
batches	_	_	O
of	_	_	O
vitamin	_	_	B-VAR
shots	_	_	I-VAR
and	_	_	O
pills	_	_	B-VAR
.	_	_	O
Each	_	_	O
batch	_	_	O
of	_	_	O
vitamin	_	_	B-VAR
shots	_	_	I-VAR
requires	_	_	O
30	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
C	_	_	O
and	_	_	O
40	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
D.	_	_	O
Each	_	_	O
batch	_	_	O
of	_	_	O
vitamin	_	_	B-VAR
pills	_	_	I-VAR
requires	_	_	O
50	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
C	_	_	O
and	_	_	O
30	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
D.	_	_	O
Since	_	_	O
pills	_	_	O
are	_	_	O
more	_	_	O
popular	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
batches	_	_	O
of	_	_	O
vitamin	_	_	B-VAR
pills	_	_	I-VAR
must	_	_	O
be	_	_	O
larger	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
batches	_	_	O
of	_	_	O
vitamin	_	_	B-VAR
shots	_	_	I-VAR
.	_	_	O
Further	_	_	O
,	_	_	O
the	_	_	O
clinic	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
10	_	_	B-LIMIT
batches	_	_	O
of	_	_	O
vitamin	_	_	B-VAR
shots	_	_	I-VAR
.	_	_	O
The	_	_	O
clinic	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
1200	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamin	_	_	O
C	_	_	O
and	_	_	O
1500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamin	_	_	O
D.	_	_	O
If	_	_	O
each	_	_	O
batch	_	_	O
of	_	_	O
vitamin	_	_	B-VAR
shots	_	_	I-VAR
can	_	_	O
supply	_	_	O
10	_	_	B-PARAM
people	_	_	B-OBJ_NAME
and	_	_	O
each	_	_	O
batch	_	_	O
of	_	_	O
vitamin	_	_	B-VAR
pills	_	_	I-VAR
can	_	_	O
supply	_	_	O
7	_	_	B-PARAM
people	_	_	B-OBJ_NAME
,	_	_	O
how	_	_	O
many	_	_	O
batches	_	_	O
of	_	_	O
each	_	_	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
supplied	_	_	O
?	_	_	O

A	_	_	O
doctor	_	_	O
's	_	_	O
office	_	_	O
takes	_	_	O
the	_	_	O
temperature	_	_	O
of	_	_	O
patients	_	_	O
one	_	_	O
by	_	_	O
one	_	_	O
either	_	_	O
by	_	_	O
using	_	_	O
an	_	_	O
electronic	_	_	B-VAR
or	_	_	O
regular	_	_	B-VAR
thermometer	_	_	I-VAR
.	_	_	O
The	_	_	O
electronic	_	_	B-VAR
thermometer	_	_	I-VAR
takes	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
reading	_	_	O
while	_	_	O
the	_	_	O
regular	_	_	B-VAR
thermometer	_	_	I-VAR
takes	_	_	O
2	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
reading	_	_	O
.	_	_	O
Since	_	_	O
the	_	_	O
electronic	_	_	B-VAR
thermometer	_	_	I-VAR
is	_	_	O
more	_	_	O
accurate	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-PARAM
as	_	_	O
many	_	_	O
patients	_	_	O
should	_	_	O
have	_	_	O
their	_	_	O
temperature	_	_	O
checked	_	_	O
by	_	_	O
the	_	_	O
electronic	_	_	B-VAR
thermometer	_	_	I-VAR
than	_	_	O
the	_	_	O
regular	_	_	B-VAR
thermometer	_	_	I-VAR
.	_	_	O
Since	_	_	O
the	_	_	O
electronic	_	_	B-VAR
thermometer	_	_	I-VAR
has	_	_	O
a	_	_	O
cooldown	_	_	O
time	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
patients	_	_	O
should	_	_	O
have	_	_	O
their	_	_	O
temperature	_	_	O
checked	_	_	O
by	_	_	O
a	_	_	O
regular	_	_	B-VAR
thermometer	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
office	_	_	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
whose	_	_	O
temperature	_	_	O
can	_	_	O
be	_	_	O
taken	_	_	O
?	_	_	O

A	_	_	O
patient	_	_	O
can	_	_	O
be	_	_	O
hooked	_	_	O
up	_	_	O
to	_	_	O
two	_	_	O
machines	_	_	O
to	_	_	O
have	_	_	O
medicine	_	_	O
delivered	_	_	O
,	_	_	O
machine	_	_	B-VAR
1	_	_	I-VAR
and	_	_	O
machine	_	_	B-VAR
2	_	_	I-VAR
.	_	_	O
Machine	_	_	B-VAR
1	_	_	I-VAR
delivers	_	_	O
0.5	_	_	B-PARAM
units	_	_	O
of	_	_	O
medicine	_	_	O
to	_	_	O
the	_	_	O
heart	_	_	O
per	_	_	O
minute	_	_	O
and	_	_	O
0.8	_	_	B-PARAM
units	_	_	O
of	_	_	O
medicine	_	_	O
per	_	_	O
minute	_	_	O
to	_	_	O
the	_	_	O
brain	_	_	O
.	_	_	O
Machine	_	_	B-VAR
2	_	_	I-VAR
delivers	_	_	O
0.3	_	_	B-PARAM
units	_	_	O
of	_	_	O
medicine	_	_	O
per	_	_	O
minute	_	_	O
to	_	_	O
the	_	_	O
heart	_	_	O
and	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
medicine	_	_	O
per	_	_	O
minute	_	_	O
to	_	_	O
the	_	_	O
brain	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
however	_	_	O
,	_	_	O
machine	_	_	B-VAR
1	_	_	I-VAR
creates	_	_	O
0.3	_	_	B-PARAM
units	_	_	O
of	_	_	O
waste	_	_	B-OBJ_NAME
per	_	_	O
minute	_	_	O
while	_	_	O
machine	_	_	B-VAR
2	_	_	I-VAR
creates	_	_	O
0.5	_	_	B-PARAM
units	_	_	O
of	_	_	O
waste	_	_	B-OBJ_NAME
per	_	_	O
minute	_	_	O
.	_	_	O
If	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
8	_	_	B-LIMIT
units	_	_	O
of	_	_	O
medicine	_	_	O
can	_	_	O
be	_	_	O
received	_	_	O
by	_	_	O
the	_	_	O
heart	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
4	_	_	B-LIMIT
units	_	_	O
of	_	_	O
medicine	_	_	O
should	_	_	O
be	_	_	O
received	_	_	O
by	_	_	O
the	_	_	O
brain	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
minutes	_	_	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
waste	_	_	I-OBJ_NAME
produced	_	_	O
?	_	_	O

A	_	_	O
travelling	_	_	O
salesman	_	_	O
only	_	_	O
eats	_	_	O
ramen	_	_	B-VAR
and	_	_	O
fries	_	_	B-VAR
.	_	_	O
Each	_	_	O
pack	_	_	O
of	_	_	O
ramen	_	_	B-VAR
contains	_	_	O
400	_	_	B-PARAM
calories	_	_	O
,	_	_	O
20	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
and	_	_	O
100	_	_	B-PARAM
mg	_	_	O
of	_	_	O
sodium	_	_	B-OBJ_NAME
.	_	_	O
Each	_	_	O
pack	_	_	O
of	_	_	O
fries	_	_	B-VAR
contains	_	_	O
300	_	_	B-PARAM
calories	_	_	O
,	_	_	O
10	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
and	_	_	O
75	_	_	B-PARAM
mg	_	_	O
of	_	_	O
sodium	_	_	B-OBJ_NAME
.	_	_	O
Since	_	_	O
fries	_	_	B-VAR
are	_	_	O
easier	_	_	O
to	_	_	O
eat	_	_	O
while	_	_	O
driving	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
his	_	_	O
meals	_	_	O
can	_	_	O
be	_	_	O
ramen	_	_	B-VAR
.	_	_	O
The	_	_	O
salesman	_	_	O
wants	_	_	O
to	_	_	O
ensure	_	_	O
he	_	_	O
eats	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3000	_	_	B-LIMIT
calories	_	_	O
and	_	_	O
80	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
protein	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
eat	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
sodium	_	_	B-OBJ_NAME
intake	_	_	O
?	_	_	O

A	_	_	O
science	_	_	O
store	_	_	O
makes	_	_	O
two	_	_	O
boxes	_	_	O
,	_	_	O
a	_	_	O
cheap	_	_	B-VAR
and	_	_	O
expensive	_	_	B-VAR
box	_	_	I-VAR
.	_	_	O
The	_	_	O
cheap	_	_	B-VAR
box	_	_	I-VAR
contains	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
metal	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
acid	_	_	O
which	_	_	O
can	_	_	O
be	_	_	O
mixed	_	_	O
to	_	_	O
create	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
foam	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
expensive	_	_	B-VAR
box	_	_	I-VAR
contains	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
metal	_	_	O
and	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
acid	_	_	O
which	_	_	O
can	_	_	O
be	_	_	O
mixed	_	_	O
to	_	_	O
create	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
foam	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
cheap	_	_	B-VAR
box	_	_	I-VAR
however	_	_	O
gives	_	_	O
off	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
heat	_	_	O
while	_	_	O
the	_	_	O
expensive	_	_	B-VAR
box	_	_	I-VAR
gives	_	_	O
off	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
heat	_	_	O
.	_	_	O
The	_	_	O
science	_	_	O
store	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
200	_	_	B-LIMIT
units	_	_	O
of	_	_	O
metal	_	_	O
and	_	_	O
300	_	_	B-LIMIT
units	_	_	O
of	_	_	O
acid	_	_	O
.	_	_	O
If	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
50	_	_	B-LIMIT
units	_	_	O
of	_	_	O
heat	_	_	O
can	_	_	O
be	_	_	O
given	_	_	O
off	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
box	_	_	O
should	_	_	O
the	_	_	O
store	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
foam	_	_	I-OBJ_NAME
produced	_	_	O
?	_	_	O

A	_	_	O
pharmacy	_	_	O
has	_	_	B-CONST_DIR
3000	_	_	B-LIMIT
mg	_	_	O
of	_	_	O
morphine	_	_	O
to	_	_	O
make	_	_	O
painkillers	_	_	B-VAR
and	_	_	O
sleeping	_	_	B-VAR
pills	_	_	I-VAR
.	_	_	O
Each	_	_	O
painkiller	_	_	B-VAR
pill	_	_	I-VAR
requires	_	_	O
10	_	_	B-PARAM
mg	_	_	O
of	_	_	O
morphine	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
digestive	_	_	B-OBJ_NAME
medicine	_	_	I-OBJ_NAME
.	_	_	O
Each	_	_	O
sleeping	_	_	B-VAR
pill	_	_	I-VAR
requires	_	_	O
6	_	_	B-PARAM
mg	_	_	O
of	_	_	O
morphine	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
digestive	_	_	B-OBJ_NAME
medicine	_	_	I-OBJ_NAME
.	_	_	O
The	_	_	O
pharmacy	_	_	O
needs	_	_	O
to	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
painkiller	_	_	B-VAR
pills	_	_	I-VAR
.	_	_	O
Since	_	_	O
sleeping	_	_	B-VAR
pills	_	_	I-VAR
are	_	_	O
more	_	_	O
popular	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
70	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
pills	_	_	O
should	_	_	O
be	_	_	O
sleeping	_	_	B-VAR
pills	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
pharmacy	_	_	O
make	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
digestive	_	_	I-OBJ_NAME
medicine	_	_	I-OBJ_NAME
needed	_	_	O
?	_	_	O

A	_	_	O
boy	_	_	O
needs	_	_	O
to	_	_	O
get	_	_	O
enough	_	_	O
magnesium	_	_	O
and	_	_	O
zinc	_	_	O
in	_	_	O
his	_	_	O
diet	_	_	O
by	_	_	O
eating	_	_	O
chewable	_	_	O
gummies	_	_	B-VAR
and	_	_	O
taking	_	_	O
pills	_	_	B-VAR
.	_	_	O
Each	_	_	O
gummy	_	_	B-VAR
contains	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
magnesium	_	_	O
and	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
zinc	_	_	B-OBJ_NAME
.	_	_	O
Each	_	_	O
pill	_	_	B-VAR
contains	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
magnesium	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
zinc	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
boy	_	_	O
must	_	_	O
take	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
pills	_	_	B-VAR
.	_	_	O
Since	_	_	O
he	_	_	O
prefers	_	_	O
gummies	_	_	B-VAR
more	_	_	O
,	_	_	O
he	_	_	O
must	_	_	O
eat	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	O
the	_	_	O
amount	_	_	O
of	_	_	O
gummies	_	_	B-VAR
as	_	_	O
pills	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
boy	_	_	O
can	_	_	O
consume	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
200	_	_	B-LIMIT
units	_	_	O
of	_	_	O
magnesium	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
eat	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
zinc	_	_	B-OBJ_NAME
intake	_	_	O
?	_	_	O

A	_	_	O
patient	_	_	O
takes	_	_	O
anxiety	_	_	B-VAR
medication	_	_	I-VAR
and	_	_	O
anti	_	_	B-VAR
-	_	_	I-VAR
depressants	_	_	I-VAR
one	_	_	I-VAR
after	_	_	O
the	_	_	O
other	_	_	O
.	_	_	O
Each	_	_	O
unit	_	_	O
of	_	_	O
anxiety	_	_	B-VAR
medication	_	_	I-VAR
takes	_	_	O
3	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
to	_	_	O
be	_	_	O
effective	_	_	O
while	_	_	O
each	_	_	O
unit	_	_	O
of	_	_	O
anti	_	_	B-VAR
-	_	_	I-VAR
depressant	_	_	I-VAR
takes	_	_	O
5	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
to	_	_	O
be	_	_	O
effective	_	_	O
.	_	_	O
The	_	_	O
patient	_	_	O
must	_	_	O
take	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
units	_	_	O
of	_	_	O
medication	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
should	_	_	O
be	_	_	O
anxiety	_	_	B-VAR
medication	_	_	I-VAR
.	_	_	O
Since	_	_	O
the	_	_	O
anxiety	_	_	B-VAR
medication	_	_	I-VAR
is	_	_	O
strong	_	_	O
,	_	_	O
the	_	_	O
patient	_	_	O
can	_	_	O
take	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
twice	_	_	B-PARAM
the	_	_	O
amount	_	_	O
of	_	_	O
anxiety	_	_	B-VAR
medication	_	_	I-VAR
as	_	_	O
anti	_	_	B-VAR
-	_	_	I-VAR
depressants	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
units	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
patient	_	_	O
take	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
time	_	_	I-OBJ_NAME
it	_	_	O
take	_	_	O
for	_	_	O
the	_	_	O
medication	_	_	O
to	_	_	O
be	_	_	O
effective	_	_	O
?	_	_	O

A	_	_	O
pharmacy	_	_	O
makes	_	_	O
eye	_	_	O
cream	_	_	O
and	_	_	O
foot	_	_	O
cream	_	_	O
using	_	_	O
two	_	_	O
different	_	_	O
machines	_	_	O
,	_	_	O
machine	_	_	B-VAR
1	_	_	I-VAR
and	_	_	O
machine	_	_	B-VAR
2	_	_	I-VAR
.	_	_	O
Machine	_	_	B-VAR
1	_	_	I-VAR
can	_	_	O
make	_	_	O
30	_	_	B-PARAM
ml	_	_	O
of	_	_	O
eye	_	_	O
cream	_	_	O
and	_	_	O
60	_	_	B-PARAM
ml	_	_	O
of	_	_	O
foot	_	_	O
cream	_	_	O
per	_	_	O
hour	_	_	O
.	_	_	O
Machine	_	_	B-VAR
2	_	_	I-VAR
can	_	_	O
make	_	_	O
45	_	_	B-PARAM
ml	_	_	O
of	_	_	O
eye	_	_	O
cream	_	_	O
and	_	_	O
30	_	_	B-PARAM
ml	_	_	O
of	_	_	O
foot	_	_	O
cream	_	_	O
per	_	_	O
hour	_	_	O
.	_	_	O
Furthermore	_	_	O
,	_	_	O
machine	_	_	B-VAR
1	_	_	I-VAR
requires	_	_	O
20	_	_	B-PARAM
ml	_	_	O
of	_	_	O
distilled	_	_	O
water	_	_	O
per	_	_	O
hour	_	_	O
while	_	_	O
machine	_	_	B-VAR
2	_	_	I-VAR
requires	_	_	O
15	_	_	B-PARAM
ml	_	_	O
of	_	_	O
distilled	_	_	O
water	_	_	O
per	_	_	O
hour	_	_	O
.	_	_	O
The	_	_	O
pharmacy	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
1200	_	_	B-LIMIT
ml	_	_	O
of	_	_	O
distilled	_	_	O
water	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
pharmacy	_	_	O
needs	_	_	O
to	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1300	_	_	B-LIMIT
ml	_	_	O
of	_	_	O
eye	_	_	O
cream	_	_	O
and	_	_	O
1500	_	_	B-LIMIT
ml	_	_	O
of	_	_	O
foot	_	_	O
cream	_	_	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
time	_	_	I-OBJ_NAME
needed	_	_	O
?	_	_	O

A	_	_	O
woman	_	_	O
eats	_	_	O
cashews	_	_	B-VAR
and	_	_	O
almonds	_	_	B-VAR
to	_	_	O
get	_	_	O
her	_	_	O
calorie	_	_	O
and	_	_	O
protein	_	_	O
intake	_	_	O
.	_	_	O
A	_	_	O
serving	_	_	O
of	_	_	O
almonds	_	_	B-VAR
contains	_	_	O
200	_	_	B-PARAM
calories	_	_	O
and	_	_	O
20	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
.	_	_	O
A	_	_	O
serving	_	_	O
of	_	_	O
cashews	_	_	B-VAR
contains	_	_	O
300	_	_	B-PARAM
calories	_	_	O
and	_	_	O
25	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
.	_	_	O
The	_	_	O
woman	_	_	O
decides	_	_	O
to	_	_	O
eat	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-PARAM
as	_	_	O
many	_	_	O
servings	_	_	O
of	_	_	O
almonds	_	_	B-VAR
as	_	_	O
cashews	_	_	B-VAR
.	_	_	O
Furthermore	_	_	O
,	_	_	O
a	_	_	O
serving	_	_	O
of	_	_	O
almonds	_	_	B-VAR
contains	_	_	O
15	_	_	B-PARAM
grams	_	_	O
of	_	_	O
fat	_	_	B-OBJ_NAME
while	_	_	O
a	_	_	O
serving	_	_	O
of	_	_	O
cashews	_	_	B-VAR
contains	_	_	O
12	_	_	B-PARAM
grams	_	_	O
of	_	_	O
fat	_	_	B-OBJ_NAME
.	_	_	O
If	_	_	O
the	_	_	O
woman	_	_	O
needs	_	_	O
to	_	_	O
consume	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10000	_	_	B-LIMIT
calories	_	_	O
and	_	_	O
800	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
protein	_	_	O
this	_	_	O
week	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
servings	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
she	_	_	O
eat	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
her	_	_	O
fat	_	_	B-OBJ_NAME
intake	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
company	_	_	O
make	_	_	O
both	_	_	O
liquid	_	_	B-VAR
and	_	_	O
foam	_	_	B-VAR
hand	_	_	I-VAR
sanitizer	_	_	I-VAR
.	_	_	O
Liquid	_	_	B-VAR
hand	_	_	I-VAR
sanitizer	_	_	I-VAR
requires	_	_	O
40	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	O
and	_	_	O
50	_	_	B-PARAM
units	_	_	O
of	_	_	O
alcohol	_	_	O
.	_	_	O
Foam	_	_	B-VAR
hand	_	_	I-VAR
sanitizer	_	_	I-VAR
requires	_	_	O
60	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	O
and	_	_	O
40	_	_	B-PARAM
units	_	_	O
of	_	_	O
alcohol	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
2000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
water	_	_	O
and	_	_	O
2100	_	_	B-LIMIT
units	_	_	O
of	_	_	O
alcohol	_	_	O
.	_	_	O
The	_	_	O
number	_	_	O
of	_	_	O
foam	_	_	B-VAR
hand	_	_	I-VAR
sanitizers	_	_	I-VAR
made	_	_	O
must	_	_	B-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
liquid	_	_	B-VAR
hand	_	_	I-VAR
sanitizers	_	_	I-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
liquid	_	_	B-VAR
hand	_	_	I-VAR
sanitizers	_	_	I-VAR
can	_	_	O
be	_	_	O
made	_	_	O
.	_	_	O
If	_	_	O
each	_	_	O
liquid	_	_	B-VAR
hand	_	_	I-VAR
sanitizer	_	_	I-VAR
can	_	_	O
clean	_	_	O
30	_	_	B-PARAM
hands	_	_	B-OBJ_NAME
and	_	_	O
each	_	_	O
foam	_	_	B-VAR
hand	_	_	I-VAR
sanitizer	_	_	I-VAR
can	_	_	O
clean	_	_	O
20	_	_	B-PARAM
hands	_	_	B-OBJ_NAME
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
hands	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
cleaned	_	_	O
?	_	_	O

A	_	_	O
clinic	_	_	O
is	_	_	O
conducting	_	_	O
a	_	_	O
throat	_	_	B-VAR
or	_	_	O
nasal	_	_	B-VAR
swabs	_	_	I-VAR
on	_	_	O
each	_	_	O
patient	_	_	O
.	_	_	O
A	_	_	O
throat	_	_	B-VAR
swab	_	_	I-VAR
takes	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
while	_	_	O
a	_	_	O
nasal	_	_	B-VAR
swab	_	_	I-VAR
takes	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
.	_	_	O
The	_	_	O
clinic	_	_	O
must	_	_	O
administer	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
nasal	_	_	B-VAR
swabs	_	_	I-VAR
.	_	_	O
Since	_	_	O
the	_	_	O
nasal	_	_	B-VAR
swab	_	_	I-VAR
is	_	_	O
more	_	_	O
uncomfortable	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
4	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
throat	_	_	B-VAR
swabs	_	_	I-VAR
must	_	_	O
be	_	_	O
done	_	_	O
as	_	_	O
nasal	_	_	B-VAR
swabs	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
clinic	_	_	O
is	_	_	O
only	_	_	B-CONST_DIR
operational	_	_	O
for	_	_	O
20000	_	_	B-LIMIT
minutes	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
swab	_	_	O
should	_	_	O
be	_	_	O
done	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
patients	_	_	I-OBJ_NAME
seen	_	_	O
?	_	_	O

A	_	_	O
patient	_	_	O
in	_	_	O
the	_	_	O
hospital	_	_	O
can	_	_	O
take	_	_	O
two	_	_	O
different	_	_	O
pain	_	_	O
killers	_	_	O
,	_	_	O
pain	_	_	B-VAR
killer	_	_	I-VAR
1	_	_	I-VAR
and	_	_	O
pain	_	_	B-VAR
killer	_	_	I-VAR
2	_	_	I-VAR
.	_	_	O
Per	_	_	O
dose	_	_	O
,	_	_	O
pain	_	_	B-VAR
killer	_	_	I-VAR
1	_	_	I-VAR
delivers	_	_	O
0.5	_	_	B-PARAM
units	_	_	O
of	_	_	O
medicine	_	_	O
to	_	_	O
the	_	_	O
legs	_	_	O
and	_	_	O
0.8	_	_	B-PARAM
units	_	_	O
of	_	_	O
medicine	_	_	O
to	_	_	O
the	_	_	O
back	_	_	B-OBJ_NAME
.	_	_	O
Per	_	_	O
dose	_	_	O
,	_	_	O
pain	_	_	B-VAR
killer	_	_	I-VAR
2	_	_	I-VAR
delivers	_	_	O
0.7	_	_	B-PARAM
units	_	_	O
of	_	_	O
medicine	_	_	O
to	_	_	O
the	_	_	O
legs	_	_	O
and	_	_	O
0.4	_	_	B-PARAM
units	_	_	O
of	_	_	O
medicine	_	_	O
to	_	_	O
the	_	_	O
back	_	_	B-OBJ_NAME
.	_	_	O
In	_	_	O
,	_	_	O
addition	_	_	O
pain	_	_	B-VAR
killer	_	_	I-VAR
1	_	_	I-VAR
deliver	_	_	O
0.3	_	_	B-PARAM
units	_	_	O
of	_	_	O
sleeping	_	_	O
medicine	_	_	O
and	_	_	O
pain	_	_	B-VAR
killer	_	_	I-VAR
2	_	_	I-VAR
delivers	_	_	O
0.6	_	_	B-PARAM
units	_	_	O
of	_	_	O
sleeping	_	_	O
medicine	_	_	O
.	_	_	O
At	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
8	_	_	B-LIMIT
units	_	_	O
of	_	_	O
sleep	_	_	O
medicine	_	_	O
should	_	_	O
be	_	_	O
delivered	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
4	_	_	B-LIMIT
units	_	_	O
of	_	_	O
medicine	_	_	O
should	_	_	O
be	_	_	O
delivered	_	_	O
to	_	_	O
the	_	_	O
legs	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
doses	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
taken	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
medicine	_	_	I-OBJ_NAME
delivered	_	_	I-OBJ_NAME
to	_	_	I-OBJ_NAME
the	_	_	I-OBJ_NAME
back	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
zookeeper	_	_	O
feeds	_	_	O
a	_	_	O
gorilla	_	_	O
with	_	_	O
bananas	_	_	B-VAR
and	_	_	O
mangoes	_	_	B-VAR
.	_	_	O
Each	_	_	O
banana	_	_	B-VAR
contains	_	_	O
80	_	_	B-PARAM
calories	_	_	O
,	_	_	O
20	_	_	B-PARAM
grams	_	_	O
of	_	_	O
potassium	_	_	O
,	_	_	O
and	_	_	O
10	_	_	B-PARAM
grams	_	_	O
of	_	_	O
sugar	_	_	B-OBJ_NAME
.	_	_	O
Each	_	_	O
mango	_	_	B-VAR
contains	_	_	O
100	_	_	B-PARAM
calories	_	_	O
,	_	_	O
15	_	_	B-PARAM
grams	_	_	O
of	_	_	O
potassium	_	_	O
,	_	_	O
and	_	_	O
8	_	_	B-PARAM
grams	_	_	O
of	_	_	O
sugar	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
gorilla	_	_	O
must	_	_	O
consume	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
4000	_	_	B-LIMIT
calories	_	_	O
and	_	_	O
150	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
potassium	_	_	O
.	_	_	O
Since	_	_	O
the	_	_	O
gorilla	_	_	O
prefers	_	_	O
bananas	_	_	B-VAR
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
33	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
fruits	_	_	O
he	_	_	O
eats	_	_	O
can	_	_	O
be	_	_	O
mangoes	_	_	B-VAR
.	_	_	O
If	_	_	O
excess	_	_	O
sugar	_	_	O
makes	_	_	O
the	_	_	O
gorilla	_	_	O
aggressive	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
fruit	_	_	O
should	_	_	O
he	_	_	O
consume	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
sugar	_	_	B-OBJ_NAME
intake	_	_	O
?	_	_	O

In	_	_	O
a	_	_	O
science	_	_	O
club	_	_	O
,	_	_	O
there	_	_	O
are	_	_	O
two	_	_	O
tables	_	_	O
that	_	_	O
can	_	_	O
be	_	_	O
set	_	_	O
up	_	_	O
to	_	_	O
make	_	_	O
slime	_	_	O
.	_	_	O
At	_	_	O
table	_	_	B-VAR
1	_	_	I-VAR
,	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
powder	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
glue	_	_	O
are	_	_	O
used	_	_	O
to	_	_	O
make	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
slime	_	_	B-OBJ_NAME
.	_	_	O
At	_	_	O
table	_	_	B-VAR
2	_	_	I-VAR
,	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
powder	_	_	O
and	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
glue	_	_	O
are	_	_	O
used	_	_	O
to	_	_	O
make	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
slime	_	_	B-OBJ_NAME
.	_	_	O
However	_	_	O
,	_	_	O
table	_	_	B-VAR
1	_	_	I-VAR
produces	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
mess	_	_	O
while	_	_	O
table	_	_	B-VAR
2	_	_	I-VAR
produces	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
mess	_	_	O
.	_	_	O
The	_	_	O
science	_	_	O
club	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
100	_	_	B-LIMIT
units	_	_	O
of	_	_	O
powder	_	_	O
and	_	_	O
90	_	_	B-LIMIT
units	_	_	O
of	_	_	O
glue	_	_	O
.	_	_	O
If	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
units	_	_	O
of	_	_	O
mess	_	_	O
can	_	_	O
be	_	_	O
made	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
table	_	_	O
should	_	_	O
be	_	_	O
set	_	_	O
up	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
slime	_	_	I-OBJ_NAME
produced	_	_	O
?	_	_	O

A	_	_	O
pharmaceutical	_	_	O
company	_	_	O
has	_	_	B-CONST_DIR
800	_	_	B-LIMIT
units	_	_	O
of	_	_	O
painkiller	_	_	O
medicine	_	_	O
and	_	_	O
makes	_	_	O
daytime	_	_	B-VAR
and	_	_	O
nighttime	_	_	B-VAR
painkiller	_	_	I-VAR
.	_	_	O
A	_	_	O
daytime	_	_	B-VAR
pill	_	_	I-VAR
has	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
painkiller	_	_	O
medicine	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
sleep	_	_	B-OBJ_NAME
medicine	_	_	I-OBJ_NAME
.	_	_	O
A	_	_	O
nighttime	_	_	B-VAR
pill	_	_	I-VAR
has	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
painkiller	_	_	O
medicine	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
sleep	_	_	B-OBJ_NAME
medicine	_	_	I-OBJ_NAME
.	_	_	O
Since	_	_	O
some	_	_	O
people	_	_	O
do	_	_	O
n’t	_	_	O
want	_	_	O
the	_	_	O
sleeping	_	_	O
effect	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
40	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
pills	_	_	O
must	_	_	O
be	_	_	O
daytime	_	_	B-VAR
pills	_	_	I-VAR
.	_	_	O
However	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
200	_	_	B-LIMIT
nighttime	_	_	B-VAR
pills	_	_	I-VAR
must	_	_	O
be	_	_	O
made	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
pill	_	_	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
sleep	_	_	I-OBJ_NAME
medicine	_	_	I-OBJ_NAME
required	_	_	O
?	_	_	O

A	_	_	O
competitive	_	_	O
eater	_	_	O
challenges	_	_	O
himself	_	_	O
to	_	_	O
eat	_	_	O
slices	_	_	O
of	_	_	O
cheesecake	_	_	B-VAR
and	_	_	O
caramel	_	_	B-VAR
cake	_	_	I-VAR
.	_	_	O
Each	_	_	O
slice	_	_	O
of	_	_	O
cheesecake	_	_	B-VAR
contains	_	_	O
200	_	_	B-PARAM
calories	_	_	O
and	_	_	O
40	_	_	B-PARAM
grams	_	_	O
of	_	_	O
sugar	_	_	B-OBJ_NAME
.	_	_	O
Each	_	_	O
slice	_	_	O
of	_	_	O
caramel	_	_	B-VAR
cake	_	_	I-VAR
contains	_	_	O
250	_	_	B-PARAM
calories	_	_	O
and	_	_	O
50	_	_	B-PARAM
grams	_	_	O
of	_	_	O
sugar	_	_	B-OBJ_NAME
.	_	_	O
He	_	_	O
prefers	_	_	O
cheesecake	_	_	B-VAR
and	_	_	O
decides	_	_	O
to	_	_	O
eat	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
slices	_	_	O
of	_	_	O
cheesecake	_	_	B-VAR
as	_	_	O
caramel	_	_	B-VAR
cake	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
he	_	_	O
must	_	_	O
also	_	_	O
eat	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-LIMIT
slices	_	_	O
of	_	_	O
caramel	_	_	B-VAR
cake	_	_	I-VAR
.	_	_	O
If	_	_	O
he	_	_	O
can	_	_	O
consume	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
10000	_	_	B-LIMIT
calories	_	_	O
in	_	_	O
one	_	_	O
day	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
slices	_	_	O
of	_	_	O
each	_	_	O
cake	_	_	O
should	_	_	O
he	_	_	O
eat	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
amount	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
sugar	_	_	I-OBJ_NAME
he	_	_	O
consumes	_	_	O
?	_	_	O

Both	_	_	O
sulfate	_	_	B-VAR
and	_	_	O
ginger	_	_	B-VAR
need	_	_	O
to	_	_	O
be	_	_	O
added	_	_	O
to	_	_	O
a	_	_	O
shampoo	_	_	O
.	_	_	O
One	_	_	O
unit	_	_	O
of	_	_	O
sulfate	_	_	B-VAR
takes	_	_	O
0.5	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
to	_	_	O
be	_	_	O
effective	_	_	O
while	_	_	O
one	_	_	O
unit	_	_	O
of	_	_	O
ginger	_	_	B-VAR
takes	_	_	O
0.75	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
to	_	_	O
be	_	_	O
effective	_	_	O
.	_	_	O
The	_	_	O
shampoo	_	_	O
must	_	_	O
contain	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
units	_	_	O
of	_	_	O
sulfates	_	_	B-VAR
and	_	_	O
a	_	_	O
total	_	_	B-CONST_DIR
of	_	_	O
400	_	_	B-LIMIT
units	_	_	O
of	_	_	O
both	_	_	O
ingredient	_	_	O
.	_	_	O
Since	_	_	O
too	_	_	O
much	_	_	O
sulfate	_	_	B-VAR
can	_	_	O
damage	_	_	O
the	_	_	O
hair	_	_	O
,	_	_	O
there	_	_	O
can	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
twice	_	_	B-PARAM
the	_	_	O
amount	_	_	O
of	_	_	O
sulfate	_	_	B-VAR
as	_	_	O
ginger	_	_	B-VAR
in	_	_	O
the	_	_	O
shampoo	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
units	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
added	_	_	O
to	_	_	O
the	_	_	O
shampoo	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
time	_	_	I-OBJ_NAME
it	_	_	O
takes	_	_	O
for	_	_	O
the	_	_	O
mixture	_	_	O
to	_	_	O
be	_	_	O
effective	_	_	O
?	_	_	O
(	_	_	O
Note	_	_	O
:	_	_	O
one	_	_	O
must	_	_	O
be	_	_	O
added	_	_	O
before	_	_	O
the	_	_	O
other	_	_	O
)	_	_	O

A	_	_	O
pharmaceutical	_	_	O
company	_	_	O
has	_	_	O
two	_	_	O
labs	_	_	O
,	_	_	O
lab	_	_	B-VAR
1	_	_	I-VAR
and	_	_	O
lab	_	_	B-VAR
2	_	_	I-VAR
,	_	_	O
where	_	_	O
they	_	_	O
make	_	_	O
heart	_	_	O
and	_	_	O
lung	_	_	O
medication	_	_	O
in	_	_	O
pill	_	_	O
form	_	_	O
.	_	_	O
At	_	_	O
lab	_	_	B-VAR
1	_	_	I-VAR
,	_	_	O
they	_	_	O
can	_	_	O
produce	_	_	O
20	_	_	B-PARAM
heart	_	_	O
medication	_	_	O
pills	_	_	O
and	_	_	O
30	_	_	B-PARAM
lung	_	_	O
medication	_	_	O
pills	_	_	O
per	_	_	O
hour	_	_	O
.	_	_	O
At	_	_	O
lab	_	_	B-VAR
2	_	_	I-VAR
,	_	_	O
they	_	_	O
can	_	_	O
produce	_	_	O
30	_	_	B-PARAM
heart	_	_	O
medication	_	_	O
pills	_	_	O
and	_	_	O
40	_	_	B-PARAM
lung	_	_	O
medication	_	_	O
pills	_	_	O
per	_	_	O
hour	_	_	O
.	_	_	O
Each	_	_	O
session	_	_	O
at	_	_	O
lab	_	_	B-VAR
1	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
hours	_	_	O
of	_	_	O
worker	_	_	O
labor	_	_	O
while	_	_	O
each	_	_	O
session	_	_	O
at	_	_	O
lab	_	_	B-VAR
2	_	_	I-VAR
requires	_	_	O
5	_	_	B-PARAM
hours	_	_	O
of	_	_	O
worker	_	_	O
labor	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
1500	_	_	B-LIMIT
worker	_	_	O
hours	_	_	O
available	_	_	B-CONST_DIR
and	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20000	_	_	B-LIMIT
heart	_	_	O
medication	_	_	O
pills	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30000	_	_	B-LIMIT
lung	_	_	O
medication	_	_	O
pills	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
hours	_	_	O
at	_	_	O
each	_	_	O
lab	_	_	O
should	_	_	O
be	_	_	O
run	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
time	_	_	I-OBJ_NAME
needed	_	_	O
?	_	_	O

A	_	_	O
doctor	_	_	O
suggests	_	_	O
that	_	_	O
his	_	_	O
patient	_	_	O
eat	_	_	O
oranges	_	_	B-VAR
and	_	_	O
grapefruit	_	_	B-VAR
to	_	_	O
meet	_	_	O
his	_	_	O
vitamin	_	_	O
C	_	_	O
and	_	_	O
vitamin	_	_	O
A	_	_	O
requirements	_	_	O
.	_	_	O
One	_	_	O
orange	_	_	B-VAR
contains	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
C	_	_	O
,	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
A	_	_	O
,	_	_	O
and	_	_	O
5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
sugar	_	_	B-OBJ_NAME
.	_	_	O
One	_	_	O
grapefruit	_	_	B-VAR
contains	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
C	_	_	O
,	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
A	_	_	O
,	_	_	O
and	_	_	O
6	_	_	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
80	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamin	_	_	O
C	_	_	O
and	_	_	O
70	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamin	_	_	O
A.	_	_	O
Since	_	_	O
the	_	_	O
patent	_	_	O
prefers	_	_	O
oranges	_	_	B-VAR
,	_	_	O
he	_	_	O
must	_	_	O
eat	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
2	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
oranges	_	_	B-VAR
as	_	_	O
grapefruit	_	_	B-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
eat	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
sugar	_	_	B-OBJ_NAME
intake	_	_	O
?	_	_	O

A	_	_	O
university	_	_	O
research	_	_	O
lab	_	_	O
can	_	_	O
make	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
diabetes	_	_	O
medicine	_	_	O
,	_	_	O
medicine	_	_	B-VAR
A	_	_	I-VAR
and	_	_	O
medicine	_	_	B-VAR
B.	_	_	I-VAR
Per	_	_	O
dose	_	_	O
,	_	_	O
medicine	_	_	B-VAR
A	_	_	I-VAR
takes	_	_	O
30	_	_	B-PARAM
units	_	_	O
of	_	_	O
imported	_	_	O
material	_	_	O
and	_	_	O
50	_	_	B-PARAM
units	_	_	O
of	_	_	O
mRNA	_	_	O
to	_	_	O
make	_	_	O
.	_	_	O
Per	_	_	O
dose	_	_	O
,	_	_	O
medicine	_	_	B-VAR
B	_	_	I-VAR
takes	_	_	O
40	_	_	B-PARAM
units	_	_	O
of	_	_	O
imported	_	_	O
material	_	_	O
and	_	_	O
30	_	_	B-PARAM
units	_	_	O
of	_	_	O
mRNA	_	_	O
to	_	_	O
take	_	_	O
.	_	_	O
The	_	_	O
lab	_	_	O
has	_	_	O
available	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
300	_	_	B-LIMIT
units	_	_	O
of	_	_	O
imported	_	_	O
material	_	_	O
and	_	_	O
400	_	_	B-LIMIT
units	_	_	O
of	_	_	O
mRNA	_	_	O
.	_	_	O
The	_	_	O
lab	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
5	_	_	B-LIMIT
doses	_	_	O
of	_	_	O
medicine	_	_	B-VAR
A	_	_	I-VAR
and	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
doses	_	_	O
of	_	_	O
medicine	_	_	B-VAR
B	_	_	I-VAR
must	_	_	O
be	_	_	O
larger	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
dosed	_	_	O
of	_	_	O
medicine	_	_	B-VAR
A.	_	_	I-VAR
If	_	_	O
one	_	_	O
dose	_	_	O
of	_	_	O
medicine	_	_	B-VAR
A	_	_	I-VAR
can	_	_	O
treat	_	_	O
12	_	_	B-PARAM
people	_	_	B-OBJ_NAME
and	_	_	O
one	_	_	O
dose	_	_	O
of	_	_	O
medicine	_	_	B-VAR
B	_	_	I-VAR
can	_	_	O
treat	_	_	O
8	_	_	B-PARAM
people	_	_	B-OBJ_NAME
,	_	_	O
how	_	_	O
many	_	_	O
doses	_	_	O
of	_	_	O
each	_	_	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
popup	_	_	O
clinic	_	_	O
is	_	_	O
doing	_	_	O
virus	_	_	O
testing	_	_	O
with	_	_	O
either	_	_	O
spit	_	_	B-VAR
tests	_	_	I-VAR
or	_	_	O
swabs	_	_	B-VAR
.	_	_	O
A	_	_	O
spit	_	_	B-VAR
test	_	_	I-VAR
takes	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
administer	_	_	O
while	_	_	O
a	_	_	O
swab	_	_	B-VAR
takes	_	_	O
15	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
administer	_	_	O
.	_	_	O
Since	_	_	O
the	_	_	O
spit	_	_	B-VAR
test	_	_	I-VAR
is	_	_	O
more	_	_	O
accurate	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-PARAM
as	_	_	O
many	_	_	O
spit	_	_	B-VAR
tests	_	_	I-VAR
should	_	_	O
be	_	_	O
given	_	_	O
as	_	_	O
swabs	_	_	B-VAR
.	_	_	O
However	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
swabs	_	_	B-VAR
must	_	_	O
be	_	_	O
administers	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
popup	_	_	O
clinic	_	_	O
operates	_	_	B-CONST_DIR
for	_	_	I-CONST_DIR
8000	_	_	B-LIMIT
minutes	_	_	O
,	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
tests	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
administered	_	_	O
.	_	_	O

A	_	_	O
patient	_	_	O
is	_	_	O
undergoing	_	_	O
radiation	_	_	O
treatment	_	_	O
involving	_	_	O
two	_	_	O
beams	_	_	O
,	_	_	O
Beam	_	_	B-VAR
1	_	_	I-VAR
and	_	_	O
Beam	_	_	B-VAR
2	_	_	I-VAR
.	_	_	O
Beam	_	_	B-VAR
1	_	_	I-VAR
delivers	_	_	O
a	_	_	O
dose	_	_	O
of	_	_	O
0.3	_	_	B-PARAM
units	_	_	O
of	_	_	O
medicine	_	_	O
per	_	_	O
minute	_	_	O
to	_	_	O
the	_	_	O
benign	_	_	O
area	_	_	O
of	_	_	O
the	_	_	O
pancreas	_	_	B-OBJ_NAME
and	_	_	O
0.2	_	_	B-PARAM
units	_	_	O
of	_	_	O
medicine	_	_	O
per	_	_	O
minute	_	_	O
to	_	_	O
the	_	_	O
benign	_	_	O
area	_	_	O
of	_	_	O
the	_	_	O
skin	_	_	O
.	_	_	O
Beam	_	_	B-VAR
2	_	_	I-VAR
delivers	_	_	O
0.2	_	_	B-PARAM
units	_	_	O
of	_	_	O
medicine	_	_	O
per	_	_	O
minute	_	_	O
to	_	_	O
the	_	_	O
benign	_	_	O
area	_	_	O
of	_	_	O
the	_	_	O
pancreas	_	_	B-OBJ_NAME
and	_	_	O
0.1	_	_	B-PARAM
units	_	_	O
of	_	_	O
medicine	_	_	O
per	_	_	O
minute	_	_	O
to	_	_	O
the	_	_	O
benign	_	_	O
area	_	_	O
of	_	_	O
the	_	_	O
skin	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
beam	_	_	B-VAR
1	_	_	I-VAR
delivers	_	_	O
0.6	_	_	B-PARAM
units	_	_	O
of	_	_	O
medicine	_	_	O
per	_	_	O
minute	_	_	O
to	_	_	O
the	_	_	O
tumor	_	_	O
and	_	_	O
beam	_	_	B-VAR
2	_	_	I-VAR
delivers	_	_	O
0.4	_	_	B-PARAM
units	_	_	O
of	_	_	O
medicine	_	_	O
per	_	_	O
minute	_	_	O
to	_	_	O
the	_	_	O
tumor	_	_	O
.	_	_	O
At	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
4	_	_	B-LIMIT
units	_	_	O
of	_	_	O
medicine	_	_	O
should	_	_	O
be	_	_	O
received	_	_	O
by	_	_	O
the	_	_	O
skin	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-LIMIT
units	_	_	O
of	_	_	O
medicine	_	_	O
should	_	_	O
be	_	_	O
delivered	_	_	O
to	_	_	O
the	_	_	O
tumor	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
minutes	_	_	O
of	_	_	O
each	_	_	O
beam	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
radiation	_	_	I-OBJ_NAME
received	_	_	I-OBJ_NAME
by	_	_	I-OBJ_NAME
the	_	_	I-OBJ_NAME
pancreas	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
body	_	_	O
builder	_	_	O
buys	_	_	O
pre	_	_	O
prepared	_	_	O
meals	_	_	O
,	_	_	O
a	_	_	O
turkey	_	_	B-VAR
dinner	_	_	I-VAR
and	_	_	O
a	_	_	O
tuna	_	_	B-VAR
salad	_	_	I-VAR
sandwich	_	_	I-VAR
.	_	_	O
The	_	_	O
turkey	_	_	B-VAR
dinner	_	_	I-VAR
contains	_	_	O
20	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
30	_	_	B-PARAM
grams	_	_	O
of	_	_	O
carbs	_	_	O
,	_	_	O
and	_	_	O
12	_	_	B-PARAM
grams	_	_	O
of	_	_	O
fat	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
tuna	_	_	B-VAR
salad	_	_	I-VAR
sandwich	_	_	I-VAR
contains	_	_	O
18	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
25	_	_	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
bodybuilder	_	_	O
wants	_	_	O
to	_	_	O
get	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
150	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
protein	_	_	O
and	_	_	O
200	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
carbs	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
because	_	_	O
the	_	_	O
turkey	_	_	B-VAR
dinner	_	_	I-VAR
is	_	_	O
expensive	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
40	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
meals	_	_	O
should	_	_	O
be	_	_	O
turkey	_	_	B-VAR
dinner	_	_	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
chemistry	_	_	O
teacher	_	_	O
teaches	_	_	O
her	_	_	O
students	_	_	O
two	_	_	O
experiments	_	_	O
,	_	_	O
experiment	_	_	B-VAR
1	_	_	I-VAR
and	_	_	O
experiment	_	_	B-VAR
2	_	_	I-VAR
.	_	_	O
In	_	_	O
experiment	_	_	B-VAR
1	_	_	I-VAR
,	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
the	_	_	O
red	_	_	O
liquid	_	_	O
and	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
the	_	_	O
blue	_	_	O
liquid	_	_	O
mix	_	_	O
to	_	_	O
create	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
green	_	_	B-OBJ_NAME
gas	_	_	I-OBJ_NAME
.	_	_	O
In	_	_	O
experiment	_	_	B-VAR
2	_	_	I-VAR
,	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
the	_	_	O
red	_	_	O
liquid	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
the	_	_	O
blue	_	_	O
liquid	_	_	O
mix	_	_	O
to	_	_	O
create	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
the	_	_	O
green	_	_	B-OBJ_NAME
gas	_	_	I-OBJ_NAME
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
experiment	_	_	B-VAR
1	_	_	I-VAR
produces	_	_	O
1	_	_	B-PARAM
units	_	_	O
of	_	_	O
smelly	_	_	O
gas	_	_	O
while	_	_	O
experiment	_	_	B-VAR
2	_	_	I-VAR
produces	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
smelly	_	_	O
gas	_	_	O
.	_	_	O
The	_	_	O
lab	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
80	_	_	B-LIMIT
units	_	_	O
of	_	_	O
red	_	_	O
liquid	_	_	O
and	_	_	O
70	_	_	B-LIMIT
units	_	_	O
of	_	_	O
blue	_	_	O
liquid	_	_	O
.	_	_	O
If	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
10	_	_	B-LIMIT
units	_	_	O
of	_	_	O
smelly	_	_	O
gas	_	_	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	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
green	_	_	I-OBJ_NAME
gas	_	_	I-OBJ_NAME
produced	_	_	O
?	_	_	O

A	_	_	O
lab	_	_	O
has	_	_	B-CONST_DIR
1000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
medicinal	_	_	O
ingredients	_	_	O
to	_	_	O
make	_	_	O
two	_	_	O
pills	_	_	O
,	_	_	O
a	_	_	O
large	_	_	B-VAR
pill	_	_	I-VAR
and	_	_	O
a	_	_	O
small	_	_	B-VAR
pill	_	_	I-VAR
.	_	_	O
A	_	_	O
large	_	_	B-VAR
pill	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
medicinal	_	_	O
ingredients	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
filler	_	_	B-OBJ_NAME
.	_	_	O
A	_	_	O
small	_	_	B-VAR
pill	_	_	I-VAR
requires	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
medicinal	_	_	O
ingredients	_	_	O
and	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
filler	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
lab	_	_	O
has	_	_	O
to	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
large	_	_	B-VAR
pills	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
since	_	_	O
small	_	_	B-VAR
pills	_	_	I-VAR
are	_	_	O
more	_	_	O
popular	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
60	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
total	_	_	O
number	_	_	O
of	_	_	O
pills	_	_	O
must	_	_	O
be	_	_	O
small	_	_	B-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
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
filler	_	_	I-OBJ_NAME
material	_	_	O
needed	_	_	O
?	_	_	O

Both	_	_	O
chorine	_	_	B-VAR
and	_	_	O
water	_	_	B-VAR
softener	_	_	I-VAR
need	_	_	O
to	_	_	O
be	_	_	O
added	_	_	O
to	_	_	O
a	_	_	O
pool	_	_	O
.	_	_	O
One	_	_	O
unit	_	_	O
of	_	_	O
chlorine	_	_	B-VAR
takes	_	_	O
1	_	_	B-PARAM
minute	_	_	B-OBJ_NAME
to	_	_	O
be	_	_	O
effective	_	_	O
while	_	_	O
one	_	_	O
unit	_	_	O
of	_	_	O
water	_	_	B-VAR
softener	_	_	I-VAR
takes	_	_	O
2	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
to	_	_	O
be	_	_	O
effective	_	_	O
.	_	_	O
Because	_	_	O
too	_	_	O
much	_	_	O
chlorine	_	_	B-VAR
can	_	_	O
burn	_	_	O
your	_	_	O
eyes	_	_	O
,	_	_	O
there	_	_	O
has	_	_	O
to	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
half	_	_	B-PARAM
as	_	_	O
much	_	_	O
chlorine	_	_	B-VAR
as	_	_	O
water	_	_	B-VAR
softener	_	_	I-VAR
in	_	_	O
the	_	_	O
pool	_	_	O
.	_	_	O
If	_	_	O
there	_	_	O
has	_	_	O
to	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
200	_	_	B-LIMIT
units	_	_	O
of	_	_	O
chlorine	_	_	B-VAR
in	_	_	O
the	_	_	O
water	_	_	O
and	_	_	O
a	_	_	B-CONST_DIR
total	_	_	I-CONST_DIR
of	_	_	I-CONST_DIR
500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
chemicals	_	_	O
in	_	_	O
the	_	_	O
water	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
units	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
added	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
time	_	_	I-OBJ_NAME
it	_	_	O
takes	_	_	O
for	_	_	O
the	_	_	O
pool	_	_	O
to	_	_	O
be	_	_	O
ready	_	_	O
?	_	_	O
(	_	_	O
Note	_	_	O
:	_	_	O
chlorine	_	_	O
must	_	_	O
be	_	_	O
added	_	_	O
before	_	_	O
water	_	_	O
softener	_	_	O
or	_	_	O
vice	_	_	O
versa	_	_	O
)	_	_	O
.	_	_	O

A	_	_	O
drug	_	_	O
company	_	_	O
is	_	_	O
making	_	_	O
pain	_	_	O
killers	_	_	O
and	_	_	O
sleeping	_	_	O
pills	_	_	O
using	_	_	O
two	_	_	O
processes	_	_	O
,	_	_	O
process	_	_	B-VAR
1	_	_	I-VAR
and	_	_	O
process	_	_	B-VAR
2	_	_	I-VAR
.	_	_	O
Process	_	_	B-VAR
1	_	_	I-VAR
produces	_	_	O
35	_	_	B-PARAM
units	_	_	O
of	_	_	O
pain	_	_	O
killers	_	_	O
and	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
sleeping	_	_	O
pills	_	_	O
per	_	_	O
hour	_	_	O
.	_	_	O
Process	_	_	B-VAR
2	_	_	I-VAR
produces	_	_	O
50	_	_	B-PARAM
units	_	_	O
of	_	_	O
pain	_	_	O
killers	_	_	O
and	_	_	O
30	_	_	B-PARAM
units	_	_	O
of	_	_	O
sleeping	_	_	O
pills	_	_	O
per	_	_	O
hour	_	_	O
.	_	_	O
Process	_	_	B-VAR
1	_	_	I-VAR
requires	_	_	O
50	_	_	B-PARAM
units	_	_	O
of	_	_	O
preliminary	_	_	O
material	_	_	O
while	_	_	O
process	_	_	B-VAR
2	_	_	I-VAR
requires	_	_	O
60	_	_	B-PARAM
units	_	_	O
of	_	_	O
preliminary	_	_	O
material	_	_	O
.	_	_	O
The	_	_	O
drug	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
2000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
preliminary	_	_	O
material	_	_	O
and	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1200	_	_	B-LIMIT
units	_	_	O
of	_	_	O
pain	_	_	O
killers	_	_	O
and	_	_	O
1200	_	_	B-LIMIT
units	_	_	O
of	_	_	O
sleeping	_	_	O
pills	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
process	_	_	O
should	_	_	O
be	_	_	O
run	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
time	_	_	I-OBJ_NAME
needed	_	_	O
?	_	_	O

A	_	_	O
dietician	_	_	O
recommends	_	_	O
her	_	_	O
client	_	_	O
eat	_	_	O
blueberries	_	_	B-VAR
and	_	_	O
strawberries	_	_	B-VAR
to	_	_	O
meet	_	_	O
her	_	_	O
anti	_	_	O
-	_	_	O
oxidant	_	_	O
and	_	_	O
mineral	_	_	O
requirement	_	_	O
.	_	_	O
A	_	_	O
pack	_	_	O
of	_	_	O
blueberries	_	_	B-VAR
contains	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
anti	_	_	O
-	_	_	O
oxidants	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
minerals	_	_	O
.	_	_	O
A	_	_	O
pack	_	_	O
of	_	_	O
strawberries	_	_	B-VAR
contains	_	_	O
1	_	_	B-PARAM
unit	_	_	O
of	_	_	O
anti	_	_	O
-	_	_	O
oxidants	_	_	O
and	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
minerals	_	_	O
.	_	_	O
The	_	_	O
client	_	_	O
must	_	_	O
get	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
90	_	_	B-LIMIT
units	_	_	O
of	_	_	O
anti	_	_	O
-	_	_	O
oxidants	_	_	O
and	_	_	O
100	_	_	B-LIMIT
units	_	_	O
of	_	_	O
minerals	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
because	_	_	O
blueberries	_	_	B-VAR
are	_	_	O
not	_	_	O
in	_	_	O
season	_	_	O
,	_	_	O
the	_	_	O
dietician	_	_	O
recommend	_	_	O
she	_	_	O
eats	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
packs	_	_	O
of	_	_	O
strawberries	_	_	B-VAR
as	_	_	O
blueberries	_	_	B-VAR
.	_	_	O
If	_	_	O
a	_	_	O
pack	_	_	O
of	_	_	O
blueberries	_	_	B-VAR
contains	_	_	O
5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
sugar	_	_	B-OBJ_NAME
and	_	_	O
a	_	_	O
pack	_	_	O
of	_	_	O
strawberries	_	_	B-VAR
contains	_	_	O
7	_	_	B-PARAM
grams	_	_	O
of	_	_	O
sugar	_	_	B-OBJ_NAME
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
packs	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
she	_	_	O
consume	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
her	_	_	O
sugar	_	_	B-OBJ_NAME
intake	_	_	O
?	_	_	O

An	_	_	O
engineering	_	_	O
school	_	_	O
has	_	_	O
a	_	_	O
bridge	_	_	O
building	_	_	O
competition	_	_	O
where	_	_	O
students	_	_	O
must	_	_	O
build	_	_	O
as	_	_	O
many	_	_	O
beam	_	_	B-VAR
bridges	_	_	I-VAR
and	_	_	O
truss	_	_	B-VAR
bridges	_	_	I-VAR
as	_	_	O
they	_	_	O
can	_	_	O
using	_	_	O
Popsicle	_	_	O
sticks	_	_	O
and	_	_	O
glue	_	_	O
.	_	_	O
A	_	_	O
beam	_	_	B-VAR
bridge	_	_	I-VAR
requires	_	_	O
30	_	_	B-PARAM
Popsicle	_	_	O
sticks	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
glue	_	_	O
while	_	_	O
a	_	_	O
truss	_	_	B-VAR
bridge	_	_	I-VAR
requires	_	_	O
50	_	_	B-PARAM
Popsicle	_	_	O
sticks	_	_	O
and	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
glue	_	_	O
.	_	_	O
Each	_	_	O
team	_	_	O
has	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
600	_	_	B-LIMIT
Popsicle	_	_	O
sticks	_	_	O
and	_	_	O
100	_	_	B-LIMIT
units	_	_	O
of	_	_	O
glue	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
each	_	_	O
team	_	_	O
can	_	_	O
build	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
5	_	_	B-LIMIT
truss	_	_	B-VAR
bridges	_	_	I-VAR
and	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
beam	_	_	B-VAR
bridges	_	_	I-VAR
must	_	_	B-CONST_DIR
be	_	_	I-CONST_DIR
larger	_	_	I-CONST_DIR
than	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
truss	_	_	B-VAR
bridges	_	_	I-VAR
.	_	_	O
If	_	_	O
a	_	_	O
beam	_	_	B-VAR
bridge	_	_	I-VAR
can	_	_	O
hold	_	_	O
40	_	_	B-PARAM
grams	_	_	B-OBJ_NAME
and	_	_	O
a	_	_	O
truss	_	_	B-VAR
bridge	_	_	I-VAR
can	_	_	O
hold	_	_	O
60	_	_	B-PARAM
grams	_	_	B-OBJ_NAME
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
bridge	_	_	O
should	_	_	O
a	_	_	O
team	_	_	O
build	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
mass	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
supported	_	_	O
?	_	_	O

A	_	_	O
clinic	_	_	O
administers	_	_	O
two	_	_	O
vaccines	_	_	O
available	_	_	O
for	_	_	O
the	_	_	O
public	_	_	O
to	_	_	O
take	_	_	O
one	_	_	O
at	_	_	O
a	_	_	O
time	_	_	O
.	_	_	O
One	_	_	O
vaccine	_	_	O
is	_	_	O
taken	_	_	O
as	_	_	O
a	_	_	O
pill	_	_	B-VAR
and	_	_	O
another	_	_	O
is	_	_	O
taken	_	_	O
as	_	_	O
a	_	_	O
shot	_	_	B-VAR
.	_	_	O
The	_	_	O
pill	_	_	B-VAR
vaccine	_	_	I-VAR
takes	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
administer	_	_	O
while	_	_	O
the	_	_	O
shot	_	_	B-VAR
takes	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
administer	_	_	O
.	_	_	O
Since	_	_	O
the	_	_	O
shot	_	_	O
has	_	_	O
been	_	_	O
more	_	_	O
thoroughly	_	_	O
studied	_	_	O
,	_	_	O
the	_	_	O
clinic	_	_	O
must	_	_	O
deliver	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
shots	_	_	B-VAR
as	_	_	O
pill	_	_	B-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
the	_	_	O
clinic	_	_	O
must	_	_	O
administer	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
pill	_	_	B-VAR
vaccines	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
clinic	_	_	O
only	_	_	B-CONST_DIR
operates	_	_	O
for	_	_	O
10000	_	_	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
vaccinated	_	_	O
.	_	_	O

A	_	_	O
young	_	_	O
boy	_	_	O
is	_	_	O
trying	_	_	O
to	_	_	O
grow	_	_	O
taller	_	_	O
by	_	_	O
drinking	_	_	O
milk	_	_	B-VAR
and	_	_	O
eating	_	_	O
vegetables	_	_	B-VAR
.	_	_	O
He	_	_	O
wants	_	_	O
to	_	_	O
get	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
100	_	_	B-LIMIT
units	_	_	O
of	_	_	O
calcium	_	_	O
and	_	_	O
50	_	_	B-LIMIT
units	_	_	O
of	_	_	O
iron	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
A	_	_	O
glass	_	_	O
of	_	_	O
milk	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
1	_	_	B-PARAM
and	_	_	O
contains	_	_	O
40	_	_	B-PARAM
units	_	_	O
of	_	_	O
calcium	_	_	O
and	_	_	O
25	_	_	B-PARAM
units	_	_	O
of	_	_	O
iron	_	_	O
.	_	_	O
A	_	_	O
plate	_	_	O
of	_	_	O
vegetables	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
2	_	_	B-PARAM
and	_	_	O
contains	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
calcium	_	_	O
and	_	_	O
30	_	_	B-PARAM
units	_	_	O
of	_	_	O
iron	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
consume	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
cost	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
toy	_	_	O
store	_	_	O
sells	_	_	O
plush	_	_	B-VAR
toys	_	_	I-VAR
and	_	_	O
dolls	_	_	B-VAR
.	_	_	O
Each	_	_	O
plush	_	_	B-VAR
toy	_	_	I-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
3	_	_	B-PARAM
and	_	_	O
each	_	_	O
doll	_	_	B-VAR
costs	_	_	O
the	_	_	O
store	_	_	O
$	_	_	O
2	_	_	B-PARAM
.	_	_	O
The	_	_	O
store	_	_	O
owner	_	_	O
can	_	_	O
spend	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
700	_	_	B-LIMIT
on	_	_	O
inventory	_	_	O
.	_	_	O
Each	_	_	O
plush	_	_	B-VAR
toy	_	_	I-VAR
is	_	_	O
then	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
4	_	_	B-PARAM
while	_	_	O
each	_	_	O
doll	_	_	B-VAR
is	_	_	O
sold	_	_	O
for	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
2	_	_	B-PARAM
.	_	_	O
The	_	_	O
owner	_	_	O
estimates	_	_	O
that	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
90	_	_	B-LIMIT
plush	_	_	B-VAR
toys	_	_	I-VAR
but	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
190	_	_	B-LIMIT
plush	_	_	B-VAR
toys	_	_	I-VAR
are	_	_	O
sold	_	_	O
each	_	_	O
month	_	_	O
.	_	_	O
He	_	_	O
also	_	_	O
estimates	_	_	O
that	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
dolls	_	_	B-VAR
sold	_	_	O
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
twice	_	_	B-PARAM
the	_	_	O
amount	_	_	O
of	_	_	O
plush	_	_	B-VAR
toys	_	_	I-VAR
sold	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
bought	_	_	O
and	_	_	O
sold	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
man	_	_	O
takes	_	_	O
two	_	_	O
supplements	_	_	O
to	_	_	O
get	_	_	O
his	_	_	O
daily	_	_	O
iron	_	_	O
and	_	_	O
calcium	_	_	O
requirements	_	_	O
.	_	_	O
A	_	_	O
pill	_	_	O
of	_	_	O
supplement	_	_	B-VAR
A	_	_	I-VAR
has	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
iron	_	_	O
and	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
calcium	_	_	O
.	_	_	O
A	_	_	O
pill	_	_	O
of	_	_	O
supplement	_	_	B-VAR
B	_	_	I-VAR
contains	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
iron	_	_	O
and	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
calcium	_	_	O
.	_	_	O
The	_	_	O
man	_	_	O
needs	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
40	_	_	B-LIMIT
units	_	_	O
of	_	_	O
iron	_	_	O
and	_	_	O
50	_	_	B-LIMIT
units	_	_	O
of	_	_	O
calcium	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
pill	_	_	O
of	_	_	O
supplement	_	_	B-VAR
A	_	_	I-VAR
is	_	_	O
$	_	_	O
2	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
pill	_	_	O
of	_	_	O
supplement	_	_	B-VAR
B	_	_	I-VAR
is	_	_	O
$	_	_	O
3	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
he	_	_	O
buy	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
costs	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
appliance	_	_	O
company	_	_	O
sells	_	_	O
and	_	_	O
installs	_	_	O
refrigerators	_	_	B-VAR
and	_	_	O
stoves	_	_	B-VAR
.	_	_	O
Each	_	_	O
refrigerator	_	_	B-VAR
takes	_	_	O
60	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
mover	_	_	O
time	_	_	O
and	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
setup	_	_	O
time	_	_	O
.	_	_	O
Each	_	_	O
stove	_	_	B-VAR
takes	_	_	O
45	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
mover	_	_	O
time	_	_	O
and	_	_	O
25	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
setup	_	_	O
time	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
20000	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
mover	_	_	O
time	_	_	O
and	_	_	O
13000	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
setup	_	_	O
time	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
refrigerator	_	_	B-VAR
is	_	_	O
$	_	_	O
400	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
stove	_	_	B-VAR
is	_	_	O
$	_	_	O
260	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
sell	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

An	_	_	O
office	_	_	O
company	_	_	O
makes	_	_	O
desks	_	_	B-VAR
and	_	_	O
drawers	_	_	B-VAR
.	_	_	O
Each	_	_	O
desk	_	_	B-VAR
requires	_	_	O
40	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
assembly	_	_	O
and	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
sanding	_	_	O
.	_	_	O
Each	_	_	O
drawer	_	_	B-VAR
requires	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
assembly	_	_	O
and	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
sanding	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
4000	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
assembly	_	_	O
and	_	_	O
3500	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
sanding	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
desk	_	_	B-VAR
is	_	_	O
$	_	_	O
100	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
drawer	_	_	B-VAR
is	_	_	O
$	_	_	O
90	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
small	_	_	O
bakery	_	_	O
has	_	_	B-CONST_DIR
20000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
batter	_	_	O
and	_	_	O
14000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
milk	_	_	O
to	_	_	O
make	_	_	O
their	_	_	O
crepe	_	_	B-VAR
cakes	_	_	I-VAR
,	_	_	O
sponge	_	_	B-VAR
cakes	_	_	I-VAR
,	_	_	O
and	_	_	O
birthday	_	_	B-VAR
cakes	_	_	I-VAR
.	_	_	O
A	_	_	O
crepe	_	_	B-VAR
cake	_	_	I-VAR
needs	_	_	O
400	_	_	B-PARAM
grams	_	_	O
of	_	_	O
batter	_	_	O
and	_	_	O
200	_	_	B-PARAM
grams	_	_	O
of	_	_	O
milk	_	_	O
.	_	_	O
A	_	_	O
sponge	_	_	B-VAR
cake	_	_	I-VAR
requires	_	_	O
500	_	_	B-PARAM
grams	_	_	O
of	_	_	O
batter	_	_	O
and	_	_	O
300	_	_	B-PARAM
grams	_	_	O
of	_	_	O
milk	_	_	O
.	_	_	O
A	_	_	O
birthday	_	_	B-VAR
cake	_	_	I-VAR
requires	_	_	O
450	_	_	B-PARAM
grams	_	_	O
of	_	_	O
batter	_	_	O
and	_	_	O
350	_	_	B-PARAM
grams	_	_	O
of	_	_	O
milk	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
crepe	_	_	B-VAR
cake	_	_	I-VAR
is	_	_	O
$	_	_	O
12	_	_	B-PARAM
,	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
sponge	_	_	B-VAR
cake	_	_	I-VAR
is	_	_	O
$	_	_	O
10	_	_	B-PARAM
,	_	_	O
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
birthday	_	_	B-VAR
cake	_	_	I-VAR
is	_	_	O
$	_	_	O
15	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
bakery	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
their	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
printing	_	_	O
company	_	_	O
sells	_	_	O
math	_	_	B-VAR
workbooks	_	_	I-VAR
and	_	_	O
English	_	_	B-VAR
workbooks	_	_	I-VAR
.	_	_	O
To	_	_	O
meet	_	_	O
demand	_	_	O
,	_	_	O
they	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
40	_	_	B-LIMIT
math	_	_	B-VAR
workbooks	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
60	_	_	B-LIMIT
English	_	_	B-VAR
workbooks	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
they	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
140	_	_	B-LIMIT
math	_	_	B-VAR
workbooks	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
170	_	_	B-LIMIT
English	_	_	B-VAR
workbooks	_	_	I-VAR
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
a	_	_	O
contract	_	_	O
with	_	_	O
a	_	_	O
school	_	_	O
to	_	_	O
send	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
200	_	_	B-LIMIT
workbooks	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
math	_	_	B-VAR
workbook	_	_	I-VAR
is	_	_	O
$	_	_	O
15	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
English	_	_	B-VAR
workbook	_	_	I-VAR
is	_	_	O
$	_	_	O
17	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
taco	_	_	O
stand	_	_	O
sells	_	_	O
regular	_	_	B-VAR
tacos	_	_	I-VAR
and	_	_	O
deluxe	_	_	B-VAR
tacos	_	_	I-VAR
with	_	_	O
extra	_	_	O
meat	_	_	O
.	_	_	O
The	_	_	O
stand	_	_	O
makes	_	_	O
x1	_	_	O
regular	_	_	B-VAR
tacos	_	_	I-VAR
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
2.50	_	_	B-PARAM
each	_	_	O
and	_	_	O
x2	_	_	O
deluxe	_	_	B-VAR
tacos	_	_	I-VAR
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
3.55	_	_	B-PARAM
each	_	_	O
(	_	_	O
x1	_	_	O
and	_	_	O
x2	_	_	O
are	_	_	O
unknown	_	_	O
variables	_	_	O
both	_	_	O
greater	_	_	O
than	_	_	O
or	_	_	O
equal	_	_	O
to	_	_	O
0	_	_	O
)	_	_	O
.	_	_	O
There	_	_	O
is	_	_	O
a	_	_	O
demand	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
50	_	_	B-LIMIT
regular	_	_	B-VAR
tacos	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
40	_	_	B-LIMIT
deluxe	_	_	B-VAR
tacos	_	_	I-VAR
.	_	_	O
The	_	_	O
stand	_	_	O
only	_	_	O
has	_	_	O
enough	_	_	O
supplies	_	_	O
to	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
70	_	_	B-LIMIT
tacos	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
taco	_	_	O
should	_	_	O
the	_	_	O
stand	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
woman	_	_	O
has	_	_	B-CONST_DIR
$	_	_	O
100000	_	_	B-LIMIT
to	_	_	O
gamble	_	_	O
on	_	_	O
two	_	_	O
sports	_	_	O
bets	_	_	O
:	_	_	O
a	_	_	O
basketball	_	_	B-VAR
tournament	_	_	I-VAR
,	_	_	O
a	_	_	O
horse	_	_	B-VAR
race	_	_	I-VAR
,	_	_	O
and	_	_	O
a	_	_	O
soccer	_	_	B-VAR
game	_	_	I-VAR
.	_	_	O
Based	_	_	O
on	_	_	O
simple	_	_	O
analysis	_	_	O
,	_	_	O
the	_	_	O
woman	_	_	O
determines	_	_	O
her	_	_	O
chance	_	_	O
of	_	_	O
losing	_	_	O
her	_	_	O
money	_	_	O
would	_	_	O
be	_	_	O
50	_	_	B-PARAM
%	_	_	I-PARAM
for	_	_	O
basketball	_	_	B-VAR
tournament	_	_	I-VAR
,	_	_	O
25	_	_	B-PARAM
%	_	_	I-PARAM
for	_	_	O
horse	_	_	B-VAR
race	_	_	I-VAR
,	_	_	O
and	_	_	O
10	_	_	B-PARAM
%	_	_	I-PARAM
for	_	_	O
the	_	_	O
soccer	_	_	B-VAR
game	_	_	I-VAR
.	_	_	O
The	_	_	O
payout	_	_	B-OBJ_NAME
for	_	_	O
each	_	_	O
dollar	_	_	O
put	_	_	O
on	_	_	O
each	_	_	O
bet	_	_	O
will	_	_	O
be	_	_	O
$	_	_	O
1.2	_	_	B-PARAM
for	_	_	O
basketball	_	_	B-VAR
tournament	_	_	I-VAR
,	_	_	O
$	_	_	O
0.5	_	_	B-PARAM
for	_	_	O
horse	_	_	B-VAR
race	_	_	I-VAR
,	_	_	O
and	_	_	O
$	_	_	O
0.1	_	_	B-PARAM
for	_	_	O
the	_	_	O
soccer	_	_	B-VAR
game	_	_	I-VAR
.	_	_	O
Knowing	_	_	O
herself	_	_	O
,	_	_	O
she	_	_	O
limits	_	_	O
her	_	_	O
average	_	_	O
chance	_	_	O
of	_	_	O
losing	_	_	O
her	_	_	O
money	_	_	O
should	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
%	_	_	I-LIMIT
.	_	_	O
Could	_	_	O
you	_	_	O
help	_	_	O
her	_	_	O
determine	_	_	O
how	_	_	O
much	_	_	O
to	_	_	O
money	_	_	O
to	_	_	O
put	_	_	O
on	_	_	O
each	_	_	O
sport	_	_	O
bet	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
her	_	_	O
average	_	_	O
payout	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
fashion	_	_	O
company	_	_	O
sells	_	_	O
regular	_	_	B-VAR
handbags	_	_	I-VAR
and	_	_	O
premium	_	_	B-VAR
handbags	_	_	I-VAR
made	_	_	O
of	_	_	O
higher	_	_	O
quality	_	_	O
material	_	_	O
.	_	_	O
They	_	_	O
can	_	_	O
sell	_	_	O
regular	_	_	B-VAR
handbags	_	_	I-VAR
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
30	_	_	B-PARAM
each	_	_	O
and	_	_	O
premium	_	_	B-VAR
handbags	_	_	I-VAR
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
180	_	_	B-PARAM
each	_	_	O
.	_	_	O
The	_	_	O
total	_	_	O
monthly	_	_	O
cost	_	_	O
of	_	_	O
manufacturing	_	_	O
is	_	_	O
$	_	_	O
200	_	_	B-PARAM
per	_	_	O
regular	_	_	B-VAR
handbag	_	_	I-VAR
and	_	_	O
$	_	_	O
447	_	_	B-PARAM
per	_	_	O
premium	_	_	B-VAR
handbag	_	_	I-VAR
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
a	_	_	O
total	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
250000	_	_	B-LIMIT
and	_	_	O
can	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
475	_	_	B-LIMIT
handbags	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
per	_	_	O
month	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
handbag	_	_	O
should	_	_	O
they	_	_	O
sell	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
its	_	_	O
monthly	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
food	_	_	O
company	_	_	O
would	_	_	O
like	_	_	O
to	_	_	O
run	_	_	O
its	_	_	O
commercials	_	_	O
on	_	_	O
three	_	_	O
streaming	_	_	O
platforms	_	_	O
:	_	_	O
Pi	_	_	B-VAR
TV	_	_	I-VAR
,	_	_	O
Beta	_	_	B-VAR
Video	_	_	I-VAR
and	_	_	O
Gamma	_	_	B-VAR
Live	_	_	I-VAR
.	_	_	O
The	_	_	O
cost	_	_	O
for	_	_	O
a	_	_	O
commercial	_	_	O
as	_	_	O
well	_	_	O
as	_	_	O
the	_	_	O
expected	_	_	O
audience	_	_	B-OBJ_NAME
reach	_	_	O
is	_	_	O
given	_	_	O
.	_	_	O
On	_	_	O
Pi	_	_	B-VAR
TV	_	_	I-VAR
,	_	_	O
a	_	_	O
commercial	_	_	O
costs	_	_	O
$	_	_	O
1200	_	_	B-PARAM
and	_	_	O
attracts	_	_	O
2000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
On	_	_	O
Beta	_	_	B-VAR
Video	_	_	I-VAR
,	_	_	O
a	_	_	O
commercial	_	_	O
costs	_	_	O
$	_	_	O
2000	_	_	B-PARAM
and	_	_	O
attracts	_	_	O
5000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
On	_	_	O
Gamma	_	_	B-VAR
Live	_	_	I-VAR
,	_	_	O
a	_	_	O
commercial	_	_	O
costs	_	_	O
$	_	_	O
4000	_	_	B-PARAM
and	_	_	O
attracts	_	_	O
9000	_	_	B-PARAM
viewers	_	_	B-OBJ_NAME
.	_	_	O
Beta	_	_	B-VAR
Video	_	_	I-VAR
limits	_	_	B-CONST_DIR
the	_	_	I-CONST_DIR
number	_	_	I-CONST_DIR
of	_	_	O
commercials	_	_	O
from	_	_	O
a	_	_	O
single	_	_	O
company	_	_	O
to	_	_	O
8	_	_	B-LIMIT
.	_	_	O
In	_	_	O
order	_	_	O
to	_	_	O
attract	_	_	O
a	_	_	O
wide	_	_	O
range	_	_	O
of	_	_	O
people	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
a	_	_	O
third	_	_	B-LIMIT
of	_	_	O
all	_	_	O
commercials	_	_	O
should	_	_	O
occur	_	_	O
on	_	_	O
Gamma	_	_	B-VAR
Live	_	_	I-VAR
and	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
20	_	_	B-LIMIT
%	_	_	I-LIMIT
should	_	_	O
occur	_	_	O
on	_	_	O
Pi	_	_	B-VAR
TV	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
weekly	_	_	O
budget	_	_	B-CONST_DIR
is	_	_	O
$	_	_	O
20000	_	_	B-LIMIT
,	_	_	O
how	_	_	O
many	_	_	O
commercials	_	_	O
should	_	_	O
be	_	_	O
run	_	_	O
in	_	_	O
each	_	_	O
of	_	_	O
the	_	_	O
three	_	_	O
possible	_	_	O
choices	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
audience	_	_	B-OBJ_NAME
?	_	_	O

Zeta	_	_	O
Bakery	_	_	O
sells	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
cookies	_	_	O
.	_	_	O
They	_	_	O
sell	_	_	O
a	_	_	O
strawberry	_	_	B-VAR
cookie	_	_	I-VAR
and	_	_	O
a	_	_	O
sugar	_	_	B-VAR
cookie	_	_	I-VAR
.	_	_	O
Let	_	_	O
's	_	_	O
say	_	_	O
they	_	_	O
make	_	_	O
x1	_	_	O
strawberry	_	_	B-VAR
cookies	_	_	I-VAR
,	_	_	O
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
5.5	_	_	B-PARAM
each	_	_	O
,	_	_	O
and	_	_	O
x2	_	_	O
sugar	_	_	B-VAR
cookies	_	_	I-VAR
,	_	_	O
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
12	_	_	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
cookies	_	_	O
is	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
strawberry	_	_	B-VAR
cookies	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
80	_	_	B-LIMIT
sugar	_	_	B-VAR
cookies	_	_	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
100	_	_	B-LIMIT
cookies	_	_	O
of	_	_	O
either	_	_	O
type	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
How	_	_	O
much	_	_	O
of	_	_	O
each	_	_	O
cookie	_	_	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
flooring	_	_	O
company	_	_	O
produces	_	_	O
engineered	_	_	O
laminate	_	_	B-VAR
planks	_	_	I-VAR
and	_	_	O
carpets	_	_	B-VAR
.	_	_	O
The	_	_	O
chief	_	_	O
marketer	_	_	O
reports	_	_	O
an	_	_	O
expected	_	_	O
demand	_	_	O
of	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
15,000	_	_	B-LIMIT
square	_	_	O
feet	_	_	O
of	_	_	O
laminate	_	_	B-VAR
planks	_	_	I-VAR
and	_	_	O
5,000	_	_	B-LIMIT
square	_	_	O
feet	_	_	O
of	_	_	O
carpets	_	_	B-VAR
each	_	_	O
week	_	_	O
.	_	_	O
The	_	_	O
shipping	_	_	O
contract	_	_	O
requires	_	_	O
a	_	_	O
total	_	_	B-CONST_DIR
of	_	_	I-CONST_DIR
at	_	_	I-CONST_DIR
least	_	_	I-CONST_DIR
50,000	_	_	B-LIMIT
square	_	_	O
feet	_	_	O
of	_	_	O
products	_	_	O
each	_	_	O
week	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
due	_	_	O
to	_	_	O
a	_	_	O
shortage	_	_	O
of	_	_	O
raw	_	_	O
materials	_	_	O
,	_	_	O
no	_	_	B-CONST_DIR
more	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
40,000	_	_	B-LIMIT
square	_	_	O
feet	_	_	O
of	_	_	O
laminate	_	_	B-VAR
planks	_	_	I-VAR
and	_	_	O
20,000	_	_	B-LIMIT
square	_	_	O
feet	_	_	O
of	_	_	O
carpets	_	_	B-VAR
can	_	_	O
be	_	_	O
produced	_	_	O
weekly	_	_	O
.	_	_	O
If	_	_	O
a	_	_	O
square	_	_	O
foot	_	_	O
of	_	_	O
laminate	_	_	B-VAR
planks	_	_	I-VAR
produces	_	_	O
a	_	_	O
$	_	_	O
2.1	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
and	_	_	O
a	_	_	O
square	_	_	O
foot	_	_	O
of	_	_	O
carpets	_	_	B-VAR
yields	_	_	O
a	_	_	O
$	_	_	O
3.3	_	_	B-PARAM
profit	_	_	B-OBJ_NAME
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
product	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
weekly	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
company	_	_	O
's	_	_	O
profit	_	_	B-OBJ_NAME
?	_	_	O

Bob	_	_	O
wants	_	_	O
to	_	_	O
design	_	_	O
a	_	_	O
diet	_	_	O
consisting	_	_	O
of	_	_	O
protein	_	_	B-VAR
bars	_	_	I-VAR
and	_	_	O
noodles	_	_	B-VAR
.	_	_	O
Assume	_	_	O
that	_	_	O
each	_	_	O
serving	_	_	O
of	_	_	O
noodles	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
5	_	_	B-PARAM
and	_	_	O
contains	_	_	O
600	_	_	B-PARAM
calories	_	_	O
and	_	_	O
1.5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
.	_	_	O
Assume	_	_	O
that	_	_	O
each	_	_	O
serving	_	_	O
of	_	_	O
protein	_	_	B-VAR
bar	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
2.5	_	_	B-PARAM
and	_	_	O
contains	_	_	O
250	_	_	B-PARAM
calories	_	_	O
and	_	_	O
5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
.	_	_	O
He	_	_	O
's	_	_	O
interested	_	_	O
in	_	_	O
spending	_	_	O
as	_	_	O
little	_	_	O
money	_	_	O
as	_	_	O
possible	_	_	O
but	_	_	O
he	_	_	O
wants	_	_	O
to	_	_	O
ensure	_	_	O
that	_	_	O
his	_	_	O
meals	_	_	O
have	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
2000	_	_	B-LIMIT
calories	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
16	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
protein	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
Formulate	_	_	O
a	_	_	O
linear	_	_	O
programming	_	_	O
problem	_	_	O
that	_	_	O
will	_	_	O
help	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
cost	_	_	B-OBJ_NAME
of	_	_	O
the	_	_	O
diet	_	_	O
.	_	_	O

Maple	_	_	O
Oil	_	_	O
processes	_	_	O
three	_	_	O
types	_	_	O
of	_	_	O
crude	_	_	O
oil	_	_	O
:	_	_	O
light	_	_	B-VAR
oil	_	_	I-VAR
,	_	_	O
non	_	_	B-VAR
-	_	_	I-VAR
sticky	_	_	I-VAR
oil	_	_	I-VAR
and	_	_	O
heavy	_	_	B-VAR
oil	_	_	I-VAR
.	_	_	O
Each	_	_	O
tank	_	_	O
of	_	_	O
light	_	_	B-VAR
oil	_	_	I-VAR
produces	_	_	O
a	_	_	O
net	_	_	B-OBJ_NAME
revenue	_	_	I-OBJ_NAME
of	_	_	O
$	_	_	O
550	_	_	B-PARAM
,	_	_	O
each	_	_	O
tank	_	_	O
of	_	_	O
non	_	_	B-VAR
-	_	_	I-VAR
sticky	_	_	I-VAR
oil	_	_	I-VAR
produces	_	_	O
a	_	_	O
net	_	_	B-OBJ_NAME
revenue	_	_	I-OBJ_NAME
of	_	_	O
$	_	_	O
750	_	_	B-PARAM
,	_	_	O
and	_	_	O
each	_	_	O
tank	_	_	O
of	_	_	O
heavy	_	_	B-VAR
oil	_	_	I-VAR
produces	_	_	O
a	_	_	O
net	_	_	B-OBJ_NAME
revenue	_	_	I-OBJ_NAME
of	_	_	O
$	_	_	O
950	_	_	B-PARAM
.	_	_	O
To	_	_	O
process	_	_	O
a	_	_	O
tank	_	_	O
of	_	_	O
light	_	_	B-VAR
oil	_	_	I-VAR
,	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
compound	_	_	O
A	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
compound	_	_	O
B	_	_	O
are	_	_	O
required	_	_	O
.	_	_	O
To	_	_	O
process	_	_	O
a	_	_	O
tank	_	_	O
of	_	_	O
non	_	_	B-VAR
-	_	_	I-VAR
sticky	_	_	I-VAR
oil	_	_	I-VAR
,	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
compound	_	_	O
A	_	_	O
and	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
compound	_	_	O
B	_	_	O
are	_	_	O
required	_	_	O
.	_	_	O
To	_	_	O
process	_	_	O
a	_	_	O
tank	_	_	O
of	_	_	O
heavy	_	_	B-VAR
oil	_	_	I-VAR
,	_	_	O
9	_	_	B-PARAM
units	_	_	O
of	_	_	O
compound	_	_	O
A	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
compound	_	_	O
B	_	_	O
are	_	_	O
required	_	_	O
.	_	_	O
Currently	_	_	O
the	_	_	O
company	_	_	O
has	_	_	B-CONST_DIR
250	_	_	B-LIMIT
units	_	_	O
of	_	_	O
compound	_	_	O
A	_	_	O
and	_	_	O
150	_	_	B-LIMIT
units	_	_	O
of	_	_	O
compound	_	_	O
B	_	_	O
to	_	_	O
process	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
full	_	_	O
or	_	_	O
partial	_	_	O
tanks	_	_	O
of	_	_	O
each	_	_	O
oil	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
process	_	_	O
so	_	_	O
that	_	_	O
net	_	_	B-OBJ_NAME
revenue	_	_	I-OBJ_NAME
is	_	_	O
maximized	_	_	B-OBJ_DIR
?	_	_	O

Forest	_	_	O
Paper	_	_	O
makes	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
products	_	_	O
:	_	_	O
graph	_	_	B-VAR
paper	_	_	I-VAR
and	_	_	O
music	_	_	B-VAR
paper	_	_	I-VAR
.	_	_	O
Each	_	_	O
type	_	_	O
of	_	_	O
paper	_	_	O
requires	_	_	O
the	_	_	O
use	_	_	O
of	_	_	O
two	_	_	O
machines	_	_	O
,	_	_	O
a	_	_	O
printing	_	_	O
machine	_	_	O
and	_	_	O
a	_	_	O
scanning	_	_	O
machine	_	_	O
.	_	_	O
It	_	_	O
takes	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
printing	_	_	O
machine	_	_	O
and	_	_	O
5.5	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
scanning	_	_	O
machine	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
ream	_	_	O
of	_	_	O
graph	_	_	B-VAR
paper	_	_	I-VAR
.	_	_	O
On	_	_	O
the	_	_	O
other	_	_	O
hand	_	_	O
,	_	_	O
it	_	_	O
takes	_	_	O
1.5	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
printing	_	_	O
machine	_	_	O
and	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
on	_	_	O
the	_	_	O
scanning	_	_	O
machine	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
ream	_	_	O
of	_	_	O
music	_	_	B-VAR
paper	_	_	I-VAR
.	_	_	O
Each	_	_	O
machine	_	_	O
is	_	_	O
available	_	_	O
for	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
350	_	_	B-LIMIT
minutes	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
sells	_	_	O
a	_	_	O
package	_	_	O
of	_	_	O
graph	_	_	B-VAR
paper	_	_	I-VAR
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
4	_	_	B-PARAM
and	_	_	O
a	_	_	O
package	_	_	O
of	_	_	O
music	_	_	B-VAR
paper	_	_	I-VAR
at	_	_	O
a	_	_	O
profit	_	_	B-OBJ_NAME
of	_	_	O
$	_	_	O
2.5	_	_	B-PARAM
.	_	_	O
The	_	_	O
company	_	_	O
can	_	_	O
sell	_	_	O
all	_	_	O
the	_	_	O
paper	_	_	O
it	_	_	O
makes	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
reams	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
produce	_	_	O
in	_	_	O
a	_	_	O
day	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O
What	_	_	O
is	_	_	O
that	_	_	O
profit	_	_	O
?	_	_	O

Platinum	_	_	O
Database	_	_	O
sells	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
subscription	_	_	O
software	_	_	O
packages	_	_	O
:	_	_	O
a	_	_	O
personal	_	_	B-VAR
license	_	_	I-VAR
and	_	_	O
a	_	_	O
commercial	_	_	B-VAR
license	_	_	I-VAR
which	_	_	O
will	_	_	O
cost	_	_	O
$	_	_	O
550	_	_	B-PARAM
and	_	_	O
$	_	_	O
2000	_	_	B-PARAM
to	_	_	O
generate	_	_	O
respectively	_	_	O
.	_	_	O
The	_	_	O
marketing	_	_	O
department	_	_	O
estimates	_	_	O
that	_	_	O
they	_	_	O
can	_	_	O
sell	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
300	_	_	B-LIMIT
licenses	_	_	O
for	_	_	O
both	_	_	O
versions	_	_	O
combined	_	_	O
a	_	_	O
month	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
personal	_	_	B-VAR
license	_	_	I-VAR
is	_	_	O
$	_	_	O
450	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
commercial	_	_	B-VAR
version	_	_	I-VAR
is	_	_	O
$	_	_	O
1200	_	_	B-PARAM
.	_	_	O
If	_	_	O
the	_	_	O
company	_	_	O
does	_	_	O
not	_	_	O
want	_	_	O
to	_	_	O
spend	_	_	O
more	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
$	_	_	O
400000	_	_	B-LIMIT
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
software	_	_	O
package	_	_	O
should	_	_	O
they	_	_	O
produce	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
profits	_	_	B-OBJ_NAME
.	_	_	O

Lucy	_	_	O
has	_	_	O
a	_	_	O
dog	_	_	O
and	_	_	O
she	_	_	O
wants	_	_	O
his	_	_	O
food	_	_	O
to	_	_	O
be	_	_	O
mixed	_	_	O
.	_	_	O
In	_	_	O
order	_	_	O
to	_	_	O
keep	_	_	O
the	_	_	O
dog	_	_	O
healthy	_	_	O
but	_	_	O
also	_	_	O
keep	_	_	O
the	_	_	O
food	_	_	O
tasty	_	_	O
,	_	_	O
the	_	_	O
mix	_	_	O
needs	_	_	O
to	_	_	O
have	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
15	_	_	B-LIMIT
units	_	_	O
of	_	_	O
calcium	_	_	O
,	_	_	O
20	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamin	_	_	O
mix	_	_	O
,	_	_	O
and	_	_	O
20	_	_	B-LIMIT
units	_	_	O
of	_	_	O
protein	_	_	O
.	_	_	O
A	_	_	O
regular	_	_	B-VAR
brand	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
20	_	_	B-PARAM
per	_	_	O
bag	_	_	O
and	_	_	O
contains	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
calcium	_	_	O
,	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
mix	_	_	O
,	_	_	O
and	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
.	_	_	O
A	_	_	O
premium	_	_	B-VAR
brand	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
35	_	_	B-PARAM
per	_	_	O
bag	_	_	O
and	_	_	O
contains	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
calcium	_	_	O
,	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
mix	_	_	O
,	_	_	O
and	_	_	O
16	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
bags	_	_	O
of	_	_	O
each	_	_	O
brand	_	_	O
should	_	_	O
Lucy	_	_	O
mix	_	_	O
in	_	_	O
order	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
while	_	_	O
also	_	_	O
meeting	_	_	O
the	_	_	O
taste	_	_	O
and	_	_	O
health	_	_	O
requirements	_	_	O
.	_	_	O

A	_	_	O
car	_	_	O
manufacturing	_	_	O
company	_	_	O
makes	_	_	O
hamburgers	_	_	B-VAR
and	_	_	O
chicken	_	_	B-VAR
wraps	_	_	I-VAR
for	_	_	O
workers	_	_	O
.	_	_	O
They	_	_	O
need	_	_	O
to	_	_	O
ensure	_	_	O
workers	_	_	O
get	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
2200	_	_	B-LIMIT
calories	_	_	O
,	_	_	O
50	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
and	_	_	O
70	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
carbs	_	_	O
.	_	_	O
One	_	_	O
hamburger	_	_	B-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
6.5	_	_	B-PARAM
and	_	_	O
contains	_	_	O
800	_	_	B-PARAM
calories	_	_	O
,	_	_	O
19	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
and	_	_	O
20	_	_	B-PARAM
grams	_	_	O
of	_	_	O
carbs	_	_	O
.	_	_	O
One	_	_	O
chicken	_	_	B-VAR
wrap	_	_	I-VAR
costs	_	_	B-OBJ_NAME
$	_	_	O
4	_	_	B-PARAM
and	_	_	O
contains	_	_	O
450	_	_	B-PARAM
calories	_	_	O
,	_	_	O
12	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
and	_	_	O
10	_	_	B-PARAM
grams	_	_	O
of	_	_	O
carbs	_	_	O
.	_	_	O
What	_	_	O
is	_	_	O
the	_	_	O
minimum	_	_	B-OBJ_DIR
cost	_	_	B-OBJ_NAME
diet	_	_	O
that	_	_	O
the	_	_	O
company	_	_	O
can	_	_	O
provide	_	_	O
for	_	_	O
its	_	_	O
workers	_	_	O
?	_	_	O

A	_	_	O
music	_	_	O
company	_	_	O
produces	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
digital	_	_	O
keyboards	_	_	O
,	_	_	O
one	_	_	O
is	_	_	O
full	_	_	B-VAR
-	_	_	I-VAR
weighted	_	_	I-VAR
and	_	_	O
another	_	_	O
is	_	_	O
semi	_	_	B-VAR
-	_	_	I-VAR
weighted	_	_	I-VAR
.	_	_	O
Both	_	_	O
keyboards	_	_	O
are	_	_	O
sold	_	_	B-OBJ_NAME
for	_	_	O
$	_	_	O
2800	_	_	B-PARAM
and	_	_	O
$	_	_	O
2400	_	_	B-PARAM
respectively	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
about	_	_	O
3500	_	_	B-LIMIT
oscillator	_	_	O
chips	_	_	O
available	_	_	B-CONST_DIR
every	_	_	O
day	_	_	O
from	_	_	O
which	_	_	O
the	_	_	O
full	_	_	B-VAR
-	_	_	I-VAR
weighted	_	_	I-VAR
version	_	_	I-VAR
requires	_	_	O
20	_	_	B-PARAM
chips	_	_	O
while	_	_	O
the	_	_	O
semi	_	_	B-VAR
-	_	_	I-VAR
weighted	_	_	I-VAR
version	_	_	I-VAR
requires	_	_	O
15	_	_	B-PARAM
chips	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
a	_	_	B-CONST_DIR
total	_	_	I-CONST_DIR
of	_	_	I-CONST_DIR
6	_	_	B-LIMIT
working	_	_	O
hours	_	_	O
a	_	_	O
day	_	_	O
.	_	_	O
Both	_	_	O
of	_	_	O
these	_	_	O
keyboards	_	_	O
require	_	_	O
a	_	_	O
production	_	_	O
time	_	_	O
of	_	_	O
1.2	_	_	B-PARAM
hours	_	_	O
.	_	_	O
What	_	_	O
should	_	_	O
be	_	_	O
the	_	_	O
manufacturing	_	_	O
quantity	_	_	O
for	_	_	O
each	_	_	O
of	_	_	O
the	_	_	O
keyboards	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
revenue	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
milk	_	_	O
tea	_	_	O
shop	_	_	O
owner	_	_	O
would	_	_	O
like	_	_	O
to	_	_	O
sell	_	_	O
two	_	_	O
different	_	_	O
milk	_	_	O
teas	_	_	O
:	_	_	O
black	_	_	B-VAR
milk	_	_	I-VAR
tea	_	_	I-VAR
and	_	_	O
matcha	_	_	B-VAR
milk	_	_	I-VAR
tea	_	_	I-VAR
.	_	_	O
Each	_	_	O
contains	_	_	O
both	_	_	O
milk	_	_	O
and	_	_	O
honey	_	_	O
.	_	_	O
A	_	_	O
bottle	_	_	O
of	_	_	O
black	_	_	B-VAR
milk	_	_	I-VAR
tea	_	_	I-VAR
contains	_	_	O
600	_	_	B-PARAM
grams	_	_	O
of	_	_	O
milk	_	_	O
and	_	_	O
10	_	_	B-PARAM
grams	_	_	O
of	_	_	O
honey	_	_	O
,	_	_	O
whereas	_	_	O
a	_	_	O
bottle	_	_	O
of	_	_	O
matcha	_	_	B-VAR
milk	_	_	I-VAR
tea	_	_	I-VAR
contains	_	_	O
525	_	_	B-PARAM
grams	_	_	O
of	_	_	O
milk	_	_	O
and	_	_	O
5	_	_	B-PARAM
grams	_	_	O
of	_	_	O
honey	_	_	O
.	_	_	O
The	_	_	O
profit	_	_	B-OBJ_NAME
from	_	_	O
each	_	_	O
bottle	_	_	O
of	_	_	O
black	_	_	B-VAR
milk	_	_	I-VAR
tea	_	_	I-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
7.5	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
from	_	_	O
each	_	_	O
bottle	_	_	O
of	_	_	O
matcha	_	_	B-VAR
milk	_	_	I-VAR
tea	_	_	I-VAR
sold	_	_	O
is	_	_	O
$	_	_	O
5	_	_	B-PARAM
.	_	_	O
If	_	_	O
his	_	_	O
total	_	_	O
production	_	_	O
must	_	_	O
not	_	_	O
exceed	_	_	O
his	_	_	O
available	_	_	B-CONST_DIR
stock	_	_	O
of	_	_	O
30000	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
milk	_	_	O
and	_	_	O
500	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
honey	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
bottles	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
milk	_	_	O
tea	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profits	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
meat	_	_	O
processing	_	_	O
plant	_	_	O
uses	_	_	O
two	_	_	O
machines	_	_	O
,	_	_	O
a	_	_	O
meat	_	_	O
slicer	_	_	O
and	_	_	O
a	_	_	O
meat	_	_	O
packer	_	_	O
,	_	_	O
to	_	_	O
make	_	_	O
their	_	_	O
hams	_	_	B-VAR
and	_	_	O
pork	_	_	B-VAR
ribs	_	_	I-VAR
.	_	_	O
To	_	_	O
produce	_	_	O
one	_	_	O
batch	_	_	O
of	_	_	O
hams	_	_	B-VAR
requires	_	_	O
4	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
meat	_	_	O
slicer	_	_	O
and	_	_	O
2.5	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
meat	_	_	O
packer	_	_	O
.	_	_	O
To	_	_	O
produce	_	_	O
one	_	_	O
batch	_	_	O
of	_	_	O
pork	_	_	B-VAR
ribs	_	_	I-VAR
requires	_	_	O
2	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
meat	_	_	O
slicer	_	_	O
and	_	_	O
3.5	_	_	B-PARAM
hours	_	_	O
on	_	_	O
the	_	_	O
meat	_	_	O
packer	_	_	O
.	_	_	O
Each	_	_	O
machine	_	_	O
runs	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
4000	_	_	B-LIMIT
hours	_	_	O
per	_	_	O
year	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
batch	_	_	O
of	_	_	O
hams	_	_	B-VAR
is	_	_	O
$	_	_	O
150	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
batch	_	_	O
of	_	_	O
pork	_	_	B-VAR
ribs	_	_	I-VAR
is	_	_	O
$	_	_	O
300	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
batches	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Super	_	_	O
Shop	_	_	O
sells	_	_	O
cat	_	_	O
paw	_	_	O
snacks	_	_	O
and	_	_	O
gold	_	_	O
shark	_	_	O
snacks	_	_	O
in	_	_	O
bulk	_	_	O
.	_	_	O
It	_	_	O
plans	_	_	O
to	_	_	O
sell	_	_	O
them	_	_	O
into	_	_	O
two	_	_	O
snack	_	_	O
mix	_	_	O
products	_	_	O
.	_	_	O
The	_	_	O
first	_	_	B-VAR
mix	_	_	I-VAR
contains	_	_	O
20	_	_	B-PARAM
%	_	_	I-PARAM
cat	_	_	O
paw	_	_	O
snacks	_	_	O
and	_	_	O
80	_	_	B-PARAM
%	_	_	I-PARAM
gold	_	_	O
shark	_	_	O
snacks	_	_	O
.	_	_	O
The	_	_	O
second	_	_	B-VAR
mix	_	_	I-VAR
contains	_	_	O
35	_	_	B-PARAM
%	_	_	I-PARAM
cat	_	_	O
paw	_	_	O
snacks	_	_	O
and	_	_	O
65	_	_	B-PARAM
%	_	_	I-PARAM
gold	_	_	O
shark	_	_	O
snacks	_	_	O
.	_	_	O
The	_	_	O
store	_	_	O
has	_	_	B-CONST_DIR
on	_	_	I-CONST_DIR
hand	_	_	I-CONST_DIR
20	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
cat	_	_	O
paw	_	_	O
snacks	_	_	O
and	_	_	O
50	_	_	B-LIMIT
kg	_	_	O
of	_	_	O
gold	_	_	O
shark	_	_	O
snacks	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
kg	_	_	O
of	_	_	O
the	_	_	O
first	_	_	B-VAR
mix	_	_	I-VAR
is	_	_	O
$	_	_	O
12	_	_	B-PARAM
and	_	_	O
the	_	_	O
profit	_	_	B-OBJ_NAME
per	_	_	O
kg	_	_	O
of	_	_	O
the	_	_	O
second	_	_	B-VAR
mix	_	_	I-VAR
is	_	_	O
$	_	_	O
15	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
kg	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
prepared	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
profit	_	_	B-OBJ_NAME
?	_	_	O

Calcium	_	_	O
and	_	_	O
Magnesium	_	_	O
are	_	_	O
found	_	_	O
in	_	_	O
two	_	_	O
health	_	_	O
supplements	_	_	O
,	_	_	O
health	_	_	B-VAR
supplement	_	_	I-VAR
A	_	_	I-VAR
and	_	_	O
health	_	_	B-VAR
supplement	_	_	I-VAR
B.	_	_	I-VAR
One	_	_	O
serving	_	_	O
of	_	_	O
health	_	_	B-VAR
supplement	_	_	I-VAR
A	_	_	I-VAR
contains	_	_	O
30	_	_	B-PARAM
grams	_	_	O
of	_	_	O
Calcium	_	_	O
and	_	_	O
50	_	_	B-PARAM
grams	_	_	O
of	_	_	O
Magnesium	_	_	O
.	_	_	O
One	_	_	O
serving	_	_	O
of	_	_	O
health	_	_	B-VAR
supplement	_	_	I-VAR
B	_	_	I-VAR
contains	_	_	O
60	_	_	B-PARAM
grams	_	_	O
of	_	_	O
Calcium	_	_	O
and	_	_	O
10	_	_	B-PARAM
grams	_	_	O
of	_	_	O
Magnesium	_	_	O
.	_	_	O
The	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
health	_	_	O
supplement	_	_	O
for	_	_	O
health	_	_	B-VAR
supplement	_	_	I-VAR
A	_	_	I-VAR
is	_	_	O
$	_	_	O
14	_	_	B-PARAM
and	_	_	O
the	_	_	O
cost	_	_	B-OBJ_NAME
per	_	_	O
health	_	_	O
supplement	_	_	O
for	_	_	O
health	_	_	B-VAR
supplement	_	_	I-VAR
B	_	_	I-VAR
is	_	_	O
$	_	_	O
25	_	_	B-PARAM
.	_	_	O
A	_	_	O
patient	_	_	O
must	_	_	O
consume	_	_	O
these	_	_	O
two	_	_	O
health	_	_	O
supplements	_	_	O
every	_	_	O
day	_	_	O
to	_	_	O
get	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
400	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
Calcium	_	_	O
and	_	_	O
50	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
Magnesium	_	_	O
.	_	_	O
Determine	_	_	O
how	_	_	O
much	_	_	O
servings	_	_	O
of	_	_	O
each	_	_	O
supplement	_	_	O
the	_	_	O
patient	_	_	O
needs	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
her	_	_	O
daily	_	_	O
cost	_	_	B-OBJ_NAME
.	_	_	O

A	_	_	O
repairman	_	_	O
fixes	_	_	O
washing	_	_	O
machines	_	_	O
and	_	_	O
freezers	_	_	B-VAR
.	_	_	O
Each	_	_	O
washing	_	_	B-VAR
machine	_	_	I-VAR
takes	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
inspection	_	_	O
and	_	_	O
90	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
fixing	_	_	O
time	_	_	O
.	_	_	O
Each	_	_	O
freezer	_	_	B-VAR
takes	_	_	O
20	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
inspection	_	_	O
and	_	_	O
125	_	_	B-PARAM
minutes	_	_	O
of	_	_	O
fixing	_	_	O
time	_	_	O
.	_	_	O
The	_	_	O
repairman	_	_	O
has	_	_	O
5000	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
for	_	_	O
inspection	_	_	O
and	_	_	O
20000	_	_	B-LIMIT
minutes	_	_	O
available	_	_	B-CONST_DIR
in	_	_	O
his	_	_	O
schedule	_	_	O
.	_	_	O
If	_	_	O
each	_	_	O
washing	_	_	B-VAR
machine	_	_	I-VAR
repaired	_	_	O
earns	_	_	B-OBJ_NAME
him	_	_	O
$	_	_	O
250	_	_	B-PARAM
and	_	_	O
each	_	_	O
freezer	_	_	B-VAR
repaired	_	_	O
earns	_	_	B-OBJ_NAME
his	_	_	O
$	_	_	O
375	_	_	B-PARAM
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
appliance	_	_	O
should	_	_	O
he	_	_	O
fix	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
his	_	_	O
earnings	_	_	B-OBJ_NAME
?	_	_	O

A	_	_	O
clothing	_	_	O
company	_	_	O
can	_	_	O
sell	_	_	O
their	_	_	O
product	_	_	O
in	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
stores	_	_	O
,	_	_	O
a	_	_	O
retail	_	_	B-VAR
store	_	_	I-VAR
and	_	_	O
a	_	_	O
factory	_	_	B-VAR
outlet	_	_	I-VAR
.	_	_	O
A	_	_	O
retail	_	_	B-VAR
store	_	_	I-VAR
brings	_	_	O
in	_	_	O
200	_	_	B-PARAM
customers	_	_	O
every	_	_	O
day	_	_	O
and	_	_	O
requires	_	_	O
6	_	_	B-PARAM
employees	_	_	O
to	_	_	O
operate	_	_	O
.	_	_	O
A	_	_	O
factory	_	_	B-VAR
outlet	_	_	I-VAR
brings	_	_	O
in	_	_	O
80	_	_	B-PARAM
customers	_	_	O
every	_	_	O
day	_	_	O
and	_	_	O
due	_	_	O
to	_	_	O
the	_	_	O
lower	_	_	O
traffic	_	_	O
and	_	_	O
being	_	_	O
in	_	_	O
more	_	_	O
remote	_	_	O
areas	_	_	O
,	_	_	O
requires	_	_	O
4	_	_	B-PARAM
employees	_	_	O
to	_	_	O
run	_	_	O
.	_	_	O
Company	_	_	O
executives	_	_	O
decided	_	_	O
that	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1200	_	_	B-LIMIT
customers	_	_	O
every	_	_	O
day	_	_	O
,	_	_	O
and	_	_	O
can	_	_	O
make	_	_	O
available	_	_	B-CONST_DIR
50	_	_	B-LIMIT
employees	_	_	O
.	_	_	O
How	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
distribute	_	_	O
their	_	_	O
product	_	_	O
to	_	_	O
the	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
store	_	_	O
to	_	_	O
reduce	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
stores	_	_	I-OBJ_NAME
that	_	_	O
must	_	_	O
be	_	_	O
open	_	_	O
?	_	_	O

A	_	_	O
metal	_	_	O
-	_	_	O
working	_	_	O
shop	_	_	O
has	_	_	O
access	_	_	O
to	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
metal	_	_	B-OBJ_NAME
-	_	_	I-OBJ_NAME
working	_	_	I-OBJ_NAME
equipment	_	_	I-OBJ_NAME
,	_	_	O
a	_	_	O
chop	_	_	B-VAR
saw	_	_	I-VAR
and	_	_	O
a	_	_	O
steel	_	_	B-VAR
cutter	_	_	I-VAR
.	_	_	O
A	_	_	O
chop	_	_	B-VAR
saw	_	_	I-VAR
can	_	_	O
work	_	_	O
25	_	_	B-PARAM
pounds	_	_	O
of	_	_	O
steel	_	_	O
and	_	_	O
generates	_	_	O
25	_	_	B-PARAM
units	_	_	O
of	_	_	O
waste	_	_	O
every	_	_	O
day	_	_	O
.	_	_	O
A	_	_	O
steel	_	_	B-VAR
cutter	_	_	I-VAR
can	_	_	O
only	_	_	O
cut	_	_	O
5	_	_	B-PARAM
pounds	_	_	O
of	_	_	O
steel	_	_	O
and	_	_	O
generates	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
waste	_	_	O
every	_	_	O
day	_	_	O
.	_	_	O
The	_	_	O
metal	_	_	O
-	_	_	O
working	_	_	O
shop	_	_	O
is	_	_	O
expecting	_	_	O
an	_	_	O
increase	_	_	O
in	_	_	O
demand	_	_	O
and	_	_	O
must	_	_	B-CONST_DIR
cut	_	_	I-CONST_DIR
520	_	_	B-LIMIT
pounds	_	_	O
of	_	_	O
metal	_	_	O
every	_	_	O
day	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
there	_	_	O
is	_	_	O
a	_	_	O
waste	_	_	O
limitation	_	_	O
due	_	_	O
to	_	_	O
the	_	_	O
fines	_	_	O
that	_	_	O
may	_	_	O
be	_	_	O
in	_	_	O
place	_	_	O
if	_	_	O
too	_	_	O
much	_	_	O
heavy	_	_	O
metal	_	_	O
is	_	_	O
discarded	_	_	O
and	_	_	O
they	_	_	O
may	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
produce	_	_	O
400	_	_	B-LIMIT
units	_	_	O
of	_	_	O
waste	_	_	O
every	_	_	O
day	_	_	O
.	_	_	O
How	_	_	O
should	_	_	O
the	_	_	O
metal	_	_	O
-	_	_	O
working	_	_	O
shop	_	_	O
purchase	_	_	O
their	_	_	O
metal	_	_	B-OBJ_NAME
-	_	_	I-OBJ_NAME
working	_	_	I-OBJ_NAME
equipment	_	_	I-OBJ_NAME
to	_	_	O
decrease	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
metal	_	_	I-OBJ_NAME
-	_	_	I-OBJ_NAME
working	_	_	I-OBJ_NAME
equipment	_	_	I-OBJ_NAME
needed	_	_	O
?	_	_	O

An	_	_	O
oil	_	_	O
and	_	_	O
gas	_	_	O
company	_	_	O
has	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
pipes	_	_	B-OBJ_NAME
,	_	_	O
a	_	_	O
high	_	_	B-VAR
-	_	_	I-VAR
volume	_	_	I-VAR
and	_	_	I-VAR
a	_	_	O
low	_	_	B-VAR
-	_	_	I-VAR
volume	_	_	I-VAR
one	_	_	I-VAR
.	_	_	O
Every	_	_	O
day	_	_	O
,	_	_	O
the	_	_	O
high	_	_	B-VAR
-	_	_	I-VAR
volume	_	_	I-VAR
pipe	_	_	I-VAR
allows	_	_	O
10000	_	_	B-PARAM
US	_	_	O
gallons	_	_	O
and	_	_	O
it	_	_	O
is	_	_	O
recommended	_	_	O
that	_	_	O
12	_	_	B-PARAM
technicians	_	_	O
closely	_	_	O
monitor	_	_	O
the	_	_	O
pipes	_	_	O
to	_	_	O
ensure	_	_	O
that	_	_	O
it	_	_	O
is	_	_	O
functioning	_	_	O
properly	_	_	O
.	_	_	O
Each	_	_	O
day	_	_	O
,	_	_	O
the	_	_	O
low	_	_	B-VAR
-	_	_	I-VAR
volume	_	_	I-VAR
pipe	_	_	I-VAR
allows	_	_	O
5000	_	_	B-PARAM
US	_	_	O
gallons	_	_	O
and	_	_	O
5	_	_	B-PARAM
technicians	_	_	O
should	_	_	O
closely	_	_	O
monitor	_	_	O
for	_	_	O
safety	_	_	O
reasons	_	_	O
.	_	_	O
Every	_	_	O
day	_	_	O
,	_	_	O
the	_	_	O
oil	_	_	O
and	_	_	O
gas	_	_	O
company	_	_	O
needs	_	_	O
to	_	_	O
meet	_	_	O
the	_	_	O
demands	_	_	O
of	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
150000	_	_	B-LIMIT
US	_	_	O
gallons	_	_	O
of	_	_	O
gas	_	_	O
and	_	_	O
they	_	_	O
have	_	_	B-CONST_DIR
160	_	_	B-LIMIT
technicians	_	_	O
that	_	_	O
are	_	_	O
on	_	_	O
their	_	_	O
staff	_	_	O
.	_	_	O
Since	_	_	O
the	_	_	O
high	_	_	B-VAR
-	_	_	I-VAR
volume	_	_	I-VAR
pipe	_	_	I-VAR
has	_	_	O
a	_	_	O
higher	_	_	O
risk	_	_	O
of	_	_	O
environmental	_	_	O
damage	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
35	_	_	B-LIMIT
percent	_	_	I-LIMIT
of	_	_	O
the	_	_	O
pipes	_	_	O
can	_	_	O
be	_	_	O
high	_	_	B-VAR
-	_	_	I-VAR
volume	_	_	I-VAR
ones	_	_	I-VAR
.	_	_	O
Additionally	_	_	O
,	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
a	_	_	O
minimum	_	_	B-CONST_DIR
of	_	_	O
8	_	_	B-LIMIT
low	_	_	B-VAR
-	_	_	I-VAR
volume	_	_	I-VAR
pipes	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
pipe	_	_	O
types	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
reduce	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
pipes	_	_	I-OBJ_NAME
required	_	_	O
?	_	_	O

A	_	_	O
landscaper	_	_	O
has	_	_	B-CONST_DIR
2500	_	_	B-LIMIT
square	_	_	O
feet	_	_	O
of	_	_	O
grass	_	_	O
land	_	_	O
in	_	_	O
a	_	_	O
customer	_	_	O
’s	_	_	O
backyard	_	_	O
where	_	_	O
they	_	_	O
need	_	_	O
to	_	_	O
cut	_	_	O
grass	_	_	O
using	_	_	O
either	_	_	O
a	_	_	O
heavy	_	_	B-VAR
-	_	_	I-VAR
duty	_	_	I-VAR
yard	_	_	I-VAR
machine	_	_	I-VAR
or	_	_	O
a	_	_	O
gas	_	_	B-VAR
lawn	_	_	I-VAR
mower	_	_	I-VAR
.	_	_	O
For	_	_	O
each	_	_	O
square	_	_	O
foot	_	_	O
of	_	_	O
land	_	_	O
,	_	_	O
the	_	_	O
heavy	_	_	B-VAR
-	_	_	I-VAR
duty	_	_	I-VAR
yard	_	_	I-VAR
machine	_	_	I-VAR
requires	_	_	O
2	_	_	B-PARAM
seconds	_	_	B-OBJ_NAME
while	_	_	O
the	_	_	O
gas	_	_	B-VAR
lawn	_	_	I-VAR
mower	_	_	I-VAR
takes	_	_	O
5	_	_	B-PARAM
seconds	_	_	B-OBJ_NAME
.	_	_	O
Per	_	_	O
square	_	_	O
foot	_	_	O
,	_	_	O
the	_	_	O
heavy	_	_	B-VAR
-	_	_	I-VAR
duty	_	_	I-VAR
yard	_	_	I-VAR
machine	_	_	I-VAR
produces	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
pollution	_	_	O
and	_	_	O
requires	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
fuel	_	_	O
.	_	_	O
Conversely	_	_	O
,	_	_	O
the	_	_	O
gas	_	_	B-VAR
lawn	_	_	I-VAR
mower	_	_	I-VAR
generates	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
pollution	_	_	O
for	_	_	O
each	_	_	O
square	_	_	O
foot	_	_	O
and	_	_	O
requires	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
fuel	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
450	_	_	B-LIMIT
units	_	_	O
of	_	_	O
fuel	_	_	O
available	_	_	B-CONST_DIR
and	_	_	O
the	_	_	O
landscaper	_	_	O
can	_	_	O
produce	_	_	O
no	_	_	B-CONST_DIR
more	_	_	I-CONST_DIR
than	_	_	I-CONST_DIR
2000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
pollution	_	_	O
.	_	_	O
For	_	_	O
how	_	_	O
many	_	_	O
square	_	_	O
feet	_	_	O
should	_	_	O
each	_	_	O
machine	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
time	_	_	B-OBJ_NAME
required	_	_	I-OBJ_NAME
to	_	_	O
cut	_	_	O
this	_	_	O
customer	_	_	O
’s	_	_	O
backyard	_	_	O
?	_	_	O

A	_	_	O
neighbourhood	_	_	O
pizza	_	_	O
restaurant	_	_	O
has	_	_	O
opened	_	_	O
and	_	_	O
sells	_	_	O
pizzas	_	_	O
in	_	_	O
two	_	_	O
sizes	_	_	O
;	_	_	O
large	_	_	B-VAR
pizza	_	_	I-VAR
and	_	_	O
medium	_	_	B-VAR
pizza	_	_	I-VAR
.	_	_	O
Large	_	_	B-VAR
pizzas	_	_	I-VAR
require	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
dough	_	_	O
,	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
toppings	_	_	O
.	_	_	O
Medium	_	_	B-VAR
pizzas	_	_	I-VAR
require	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
dough	_	_	O
,	_	_	O
and	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
toppings	_	_	O
.	_	_	O
While	_	_	O
large	_	_	B-VAR
pizzas	_	_	I-VAR
take	_	_	O
12	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
to	_	_	I-OBJ_NAME
bake	_	_	I-OBJ_NAME
,	_	_	O
medium	_	_	B-VAR
pizzas	_	_	I-VAR
require	_	_	O
8	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
to	_	_	I-OBJ_NAME
bake	_	_	I-OBJ_NAME
.	_	_	O
The	_	_	O
neighbourhood	_	_	O
pizza	_	_	O
restaurant	_	_	O
must	_	_	O
use	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
dough	_	_	O
and	_	_	O
4400	_	_	B-LIMIT
units	_	_	O
of	_	_	O
toppings	_	_	O
.	_	_	O
Medium	_	_	B-VAR
pizzas	_	_	I-VAR
are	_	_	O
popular	_	_	O
due	_	_	O
to	_	_	O
a	_	_	O
promotion	_	_	O
,	_	_	O
therefore	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
200	_	_	B-LIMIT
medium	_	_	B-VAR
pizzas	_	_	I-VAR
must	_	_	O
be	_	_	O
made	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
regulars	_	_	O
that	_	_	O
prefer	_	_	O
large	_	_	B-VAR
pizzas	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
two	_	_	B-PARAM
times	_	_	O
as	_	_	O
many	_	_	O
large	_	_	B-VAR
pizzas	_	_	I-VAR
should	_	_	O
be	_	_	O
made	_	_	O
than	_	_	O
medium	_	_	B-VAR
pizzas	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
size	_	_	O
of	_	_	O
pizzas	_	_	O
should	_	_	O
the	_	_	O
neighbourhood	_	_	O
pizza	_	_	O
restaurant	_	_	O
make	_	_	O
to	_	_	O
reduce	_	_	B-OBJ_DIR
time	_	_	B-OBJ_NAME
spent	_	_	I-OBJ_NAME
baking	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
market	_	_	O
owner	_	_	O
wants	_	_	O
to	_	_	O
start	_	_	O
a	_	_	O
jam	_	_	O
business	_	_	O
.	_	_	O
He	_	_	O
can	_	_	O
either	_	_	O
sell	_	_	O
one	_	_	B-OBJ_NAME
unit	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
jam	_	_	I-OBJ_NAME
to	_	_	O
customers	_	_	O
in	_	_	O
a	_	_	O
set	_	_	O
of	_	_	O
small	_	_	B-VAR
packets	_	_	I-VAR
or	_	_	O
jugs	_	_	B-VAR
.	_	_	O
A	_	_	O
set	_	_	O
of	_	_	O
small	_	_	B-VAR
packets	_	_	I-VAR
can	_	_	O
hold	_	_	O
1000	_	_	B-PARAM
ml	_	_	O
of	_	_	O
jam	_	_	O
while	_	_	O
a	_	_	O
jug	_	_	B-VAR
can	_	_	O
hold	_	_	O
1250	_	_	B-PARAM
ml	_	_	O
of	_	_	O
jam	_	_	O
.	_	_	O
Since	_	_	O
a	_	_	O
set	_	_	O
of	_	_	O
small	_	_	B-VAR
packets	_	_	I-VAR
are	_	_	O
more	_	_	O
expensive	_	_	O
to	_	_	O
make	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
many	_	_	O
jugs	_	_	B-VAR
must	_	_	O
be	_	_	O
used	_	_	O
than	_	_	O
sets	_	_	O
of	_	_	O
small	_	_	B-VAR
packets	_	_	I-VAR
.	_	_	O
On	_	_	O
the	_	_	O
other	_	_	O
hand	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
35	_	_	B-LIMIT
sets	_	_	O
of	_	_	O
small	_	_	B-VAR
packets	_	_	I-VAR
should	_	_	O
be	_	_	O
filled	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
market	_	_	O
owner	_	_	O
has	_	_	B-CONST_DIR
65000	_	_	B-LIMIT
ml	_	_	O
of	_	_	O
jam	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
sets	_	_	O
of	_	_	O
small	_	_	O
packets	_	_	O
or	_	_	O
jugs	_	_	B-VAR
should	_	_	O
be	_	_	O
selected	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
units	_	_	I-OBJ_NAME
that	_	_	O
he	_	_	O
can	_	_	O
sell	_	_	O
to	_	_	O
his	_	_	O
customers	_	_	O
?	_	_	O

A	_	_	O
municipality	_	_	O
hires	_	_	O
full	_	_	B-VAR
-	_	_	I-VAR
time	_	_	I-VAR
and	_	_	I-VAR
part	_	_	B-VAR
-	_	_	I-VAR
time	_	_	I-VAR
staff	_	_	I-VAR
to	_	_	O
deliver	_	_	O
mail	_	_	O
.	_	_	O
Part	_	_	B-VAR
-	_	_	I-VAR
time	_	_	I-VAR
staff	_	_	I-VAR
works	_	_	O
15	_	_	B-PARAM
hours	_	_	O
per	_	_	O
week	_	_	O
and	_	_	O
gets	_	_	O
paid	_	_	O
450	_	_	B-PARAM
dollars	_	_	O
whereas	_	_	O
a	_	_	O
full	_	_	B-VAR
-	_	_	I-VAR
time	_	_	I-VAR
staff	_	_	I-VAR
works	_	_	O
40	_	_	B-PARAM
hours	_	_	O
every	_	_	O
week	_	_	O
and	_	_	O
gets	_	_	O
paid	_	_	O
1280	_	_	B-PARAM
dollars	_	_	O
for	_	_	O
that	_	_	O
week	_	_	O
.	_	_	O
Since	_	_	O
it	_	_	O
is	_	_	O
the	_	_	O
week	_	_	O
leading	_	_	O
up	_	_	O
to	_	_	O
a	_	_	O
holiday	_	_	O
,	_	_	O
planning	_	_	O
ahead	_	_	O
,	_	_	O
the	_	_	O
municipality	_	_	O
needs	_	_	B-CONST_DIR
1000	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
mail	_	_	O
staff	_	_	O
labor	_	_	O
.	_	_	O
The	_	_	O
municipality	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
31500	_	_	B-LIMIT
dollars	_	_	O
for	_	_	O
mail	_	_	O
delivery	_	_	O
for	_	_	O
this	_	_	O
season	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
staff	_	_	B-OBJ_NAME
should	_	_	O
the	_	_	O
municipality	_	_	O
hire	_	_	O
to	_	_	O
decrease	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
staff	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
strata	_	_	O
-	_	_	O
management	_	_	O
company	_	_	O
is	_	_	O
looking	_	_	O
into	_	_	O
purchasing	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
air	_	_	B-OBJ_NAME
conditioners	_	_	I-OBJ_NAME
,	_	_	O
a	_	_	O
low	_	_	B-VAR
-	_	_	I-VAR
power	_	_	I-VAR
and	_	_	O
a	_	_	O
high	_	_	B-VAR
-	_	_	I-VAR
power	_	_	I-VAR
model	_	_	I-VAR
.	_	_	O
A	_	_	O
low	_	_	B-VAR
-	_	_	I-VAR
powered	_	_	I-VAR
air	_	_	I-VAR
conditioner	_	_	O
can	_	_	O
cool	_	_	O
down	_	_	O
12	_	_	B-PARAM
housing	_	_	O
units	_	_	O
and	_	_	O
uses	_	_	O
150	_	_	B-PARAM
units	_	_	O
of	_	_	O
electricity	_	_	O
every	_	_	O
day	_	_	O
.	_	_	O
A	_	_	O
high	_	_	B-VAR
-	_	_	I-VAR
power	_	_	I-VAR
model	_	_	I-VAR
can	_	_	O
cool	_	_	O
down	_	_	O
17	_	_	B-PARAM
housing	_	_	O
units	_	_	O
and	_	_	O
uses	_	_	O
250	_	_	B-PARAM
units	_	_	O
of	_	_	O
electricity	_	_	O
every	_	_	O
day	_	_	O
.	_	_	O
Since	_	_	O
the	_	_	O
low	_	_	B-VAR
-	_	_	I-VAR
powered	_	_	I-VAR
model	_	_	I-VAR
is	_	_	O
not	_	_	O
good	_	_	O
for	_	_	O
the	_	_	O
aesthetics	_	_	O
,	_	_	O
the	_	_	O
strata	_	_	O
decided	_	_	O
to	_	_	O
limit	_	_	B-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
low	_	_	B-VAR
-	_	_	I-VAR
powered	_	_	I-VAR
models	_	_	I-VAR
to	_	_	O
only	_	_	O
30	_	_	B-LIMIT
%	_	_	I-LIMIT
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
7	_	_	B-LIMIT
high	_	_	B-VAR
-	_	_	I-VAR
powered	_	_	I-VAR
models	_	_	I-VAR
must	_	_	O
be	_	_	O
used	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
apartment	_	_	O
needs	_	_	O
to	_	_	O
condition	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
250	_	_	B-LIMIT
housing	_	_	O
units	_	_	O
and	_	_	O
has	_	_	O
3400	_	_	B-LIMIT
units	_	_	O
of	_	_	O
electricity	_	_	O
available	_	_	B-CONST_DIR
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
air	_	_	B-OBJ_NAME
conditioner	_	_	I-OBJ_NAME
should	_	_	O
the	_	_	O
strata	_	_	O
company	_	_	O
buy	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	B-OBJ_NAME
total	_	_	I-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
air	_	_	I-OBJ_NAME
conditioners	_	_	I-OBJ_NAME
?	_	_	O

An	_	_	O
extremely	_	_	O
large	_	_	O
ski	_	_	O
resort	_	_	O
is	_	_	O
looking	_	_	O
into	_	_	O
purchasing	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
ski	_	_	B-OBJ_NAME
lifts	_	_	I-OBJ_NAME
,	_	_	O
a	_	_	O
densely	_	_	B-VAR
-	_	_	I-VAR
seated	_	_	I-VAR
one	_	_	I-VAR
and	_	_	O
a	_	_	O
loosely	_	_	B-VAR
-	_	_	I-VAR
seated	_	_	I-VAR
one	_	_	I-VAR
.	_	_	O
The	_	_	O
densely	_	_	B-VAR
-	_	_	I-VAR
seated	_	_	I-VAR
ski	_	_	I-VAR
lift	_	_	I-VAR
is	_	_	O
able	_	_	O
to	_	_	O
bring	_	_	O
45	_	_	B-PARAM
guests	_	_	O
up	_	_	O
the	_	_	O
slopes	_	_	O
every	_	_	O
minute	_	_	O
whereas	_	_	O
the	_	_	O
loosely	_	_	B-VAR
-	_	_	I-VAR
seated	_	_	I-VAR
ski	_	_	I-VAR
lift	_	_	O
can	_	_	O
transport	_	_	O
20	_	_	B-PARAM
guests	_	_	O
every	_	_	O
minute	_	_	O
.	_	_	O
The	_	_	O
densely	_	_	B-VAR
-	_	_	I-VAR
seated	_	_	I-VAR
ski	_	_	I-VAR
lift	_	_	O
uses	_	_	O
30	_	_	B-PARAM
units	_	_	O
of	_	_	O
electricity	_	_	O
and	_	_	O
the	_	_	O
loosely	_	_	B-VAR
-	_	_	I-VAR
seated	_	_	I-VAR
lift	_	_	I-VAR
uses	_	_	O
22	_	_	B-PARAM
units	_	_	O
of	_	_	O
electricity	_	_	O
.	_	_	O
There	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
five	_	_	B-LIMIT
loosely	_	_	B-VAR
-	_	_	I-VAR
seated	_	_	I-VAR
ski	_	_	I-VAR
lifts	_	_	O
because	_	_	O
they	_	_	O
move	_	_	O
slower	_	_	O
and	_	_	O
are	_	_	O
friendlier	_	_	O
for	_	_	O
beginners	_	_	O
.	_	_	O
The	_	_	O
ski	_	_	O
resort	_	_	O
needs	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1000	_	_	B-LIMIT
guests	_	_	O
every	_	_	O
minute	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
profit	_	_	O
and	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
940	_	_	B-LIMIT
units	_	_	O
of	_	_	O
electricity	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
ski	_	_	B-OBJ_NAME
lifts	_	_	I-OBJ_NAME
should	_	_	O
they	_	_	O
plan	_	_	O
to	_	_	O
install	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	B-OBJ_NAME
total	_	_	I-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
ski	_	_	I-OBJ_NAME
lifts	_	_	I-OBJ_NAME
needed	_	_	O
?	_	_	O

A	_	_	O
restaurant	_	_	O
has	_	_	O
two	_	_	O
combos	_	_	O
available	_	_	O
to	_	_	O
their	_	_	O
customers	_	_	O
,	_	_	O
an	_	_	O
original	_	_	B-VAR
and	_	_	O
an	_	_	O
experimental	_	_	B-VAR
meal	_	_	I-VAR
.	_	_	O
The	_	_	O
original	_	_	B-VAR
meal	_	_	I-VAR
typically	_	_	O
generates	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
food	_	_	O
waste	_	_	O
and	_	_	O
45	_	_	B-PARAM
units	_	_	O
of	_	_	O
wrapping	_	_	O
waste	_	_	O
and	_	_	O
takes	_	_	O
10	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
to	_	_	I-OBJ_NAME
cook	_	_	I-OBJ_NAME
.	_	_	O
In	_	_	O
comparison	_	_	O
,	_	_	O
the	_	_	O
experimental	_	_	B-VAR
meal	_	_	I-VAR
generates	_	_	O
25	_	_	B-PARAM
units	_	_	O
of	_	_	O
food	_	_	O
waste	_	_	O
and	_	_	O
35	_	_	B-PARAM
units	_	_	O
of	_	_	O
wrapping	_	_	O
waste	_	_	O
and	_	_	O
takes	_	_	O
15	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
to	_	_	I-OBJ_NAME
cook	_	_	I-OBJ_NAME
.	_	_	O
The	_	_	O
restaurant	_	_	O
can	_	_	O
have	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
900	_	_	B-LIMIT
units	_	_	O
of	_	_	O
wrapping	_	_	O
waste	_	_	O
and	_	_	O
can	_	_	O
have	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
800	_	_	B-LIMIT
units	_	_	O
of	_	_	O
food	_	_	O
waste	_	_	O
as	_	_	O
regulated	_	_	O
by	_	_	O
the	_	_	O
government	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
combo	_	_	O
should	_	_	O
be	_	_	O
pushed	_	_	O
for	_	_	O
by	_	_	O
the	_	_	O
waiting	_	_	O
staff	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
cooking	_	_	B-OBJ_NAME
time	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
smoothie	_	_	O
shop	_	_	O
has	_	_	O
a	_	_	O
promotion	_	_	O
for	_	_	O
their	_	_	O
two	_	_	O
smoothies	_	_	O
;	_	_	O
an	_	_	O
acai	_	_	B-VAR
berry	_	_	I-VAR
smoothie	_	_	I-VAR
and	_	_	O
a	_	_	O
banana	_	_	B-VAR
chocolate	_	_	I-VAR
smoothie	_	_	I-VAR
.	_	_	O
It	_	_	O
takes	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
acai	_	_	O
berries	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	B-OBJ_NAME
to	_	_	O
make	_	_	O
the	_	_	O
acai	_	_	B-VAR
berry	_	_	I-VAR
smoothie	_	_	I-VAR
.	_	_	O
It	_	_	O
takes	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
banana	_	_	O
chocolate	_	_	O
and	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	B-OBJ_NAME
to	_	_	O
make	_	_	O
the	_	_	O
banana	_	_	B-VAR
chocolate	_	_	I-VAR
smoothie	_	_	I-VAR
.	_	_	O
Banana	_	_	B-VAR
chocolate	_	_	I-VAR
smoothies	_	_	I-VAR
are	_	_	O
more	_	_	O
popular	_	_	O
and	_	_	O
thus	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
banana	_	_	B-VAR
chocolate	_	_	I-VAR
smoothies	_	_	O
made	_	_	O
must	_	_	O
be	_	_	O
more	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
acai	_	_	B-VAR
berry	_	_	I-VAR
smoothies	_	_	I-VAR
made	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
the	_	_	O
acai	_	_	B-VAR
berry	_	_	I-VAR
smoothies	_	_	I-VAR
have	_	_	O
a	_	_	O
loyal	_	_	O
customer	_	_	O
base	_	_	O
,	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
35	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
smoothies	_	_	O
made	_	_	O
must	_	_	O
be	_	_	O
acai	_	_	B-VAR
berry	_	_	I-VAR
smoothies	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
smoothie	_	_	O
shop	_	_	O
has	_	_	B-CONST_DIR
3500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
acai	_	_	O
berries	_	_	O
and	_	_	O
3200	_	_	B-LIMIT
units	_	_	O
of	_	_	O
banana	_	_	O
chocolate	_	_	O
,	_	_	O
to	_	_	O
reduce	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
water	_	_	I-OBJ_NAME
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
smoothie	_	_	O
type	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
?	_	_	O

A	_	_	O
hospital	_	_	O
hires	_	_	O
ultrasound	_	_	B-VAR
technicians	_	_	I-VAR
and	_	_	O
graduate	_	_	B-VAR
researchers	_	_	I-VAR
to	_	_	O
image	_	_	O
patients	_	_	O
.	_	_	O
An	_	_	O
ultrasound	_	_	B-VAR
technician	_	_	I-VAR
works	_	_	O
8	_	_	B-PARAM
hours	_	_	O
per	_	_	O
shift	_	_	O
while	_	_	O
a	_	_	O
graduate	_	_	B-VAR
researcher	_	_	I-VAR
works	_	_	O
5	_	_	B-PARAM
hours	_	_	O
per	_	_	O
shift	_	_	O
.	_	_	O
Ultrasound	_	_	B-VAR
technicians	_	_	I-VAR
are	_	_	O
paid	_	_	O
$	_	_	O
300	_	_	B-PARAM
per	_	_	O
shift	_	_	O
while	_	_	O
graduate	_	_	B-VAR
researchers	_	_	I-VAR
are	_	_	O
paid	_	_	O
$	_	_	O
100	_	_	B-PARAM
per	_	_	O
shift	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
due	_	_	O
to	_	_	O
regulations	_	_	O
,	_	_	O
there	_	_	O
must	_	_	B-CONST_DIR
be	_	_	I-CONST_DIR
twice	_	_	B-PARAM
as	_	_	O
many	_	_	O
ultrasound	_	_	B-VAR
technician	_	_	I-VAR
shifts	_	_	O
than	_	_	O
graduate	_	_	B-VAR
researcher	_	_	I-VAR
shifts	_	_	O
.	_	_	O
Currently	_	_	O
,	_	_	O
the	_	_	O
hospital	_	_	O
needs	_	_	B-CONST_DIR
500	_	_	B-LIMIT
hours	_	_	O
of	_	_	O
ultrasound	_	_	O
services	_	_	O
to	_	_	O
meet	_	_	O
needs	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
hospital	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
14000	_	_	B-LIMIT
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
worker	_	_	B-OBJ_NAME
certified	_	_	O
to	_	_	O
use	_	_	O
the	_	_	O
ultrasound	_	_	O
should	_	_	O
be	_	_	O
scheduled	_	_	O
to	_	_	O
reduce	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
workers	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
tourism	_	_	O
company	_	_	O
can	_	_	O
buy	_	_	O
sedans	_	_	B-VAR
or	_	_	O
buses	_	_	B-VAR
to	_	_	O
add	_	_	O
to	_	_	O
their	_	_	O
fleet	_	_	O
of	_	_	O
vehicles	_	_	B-OBJ_NAME
to	_	_	O
increase	_	_	O
their	_	_	O
capacity	_	_	O
for	_	_	O
more	_	_	O
tourists	_	_	O
.	_	_	O
A	_	_	O
sedan	_	_	B-VAR
can	_	_	O
seat	_	_	O
50	_	_	B-PARAM
tourists	_	_	O
per	_	_	O
day	_	_	O
but	_	_	O
results	_	_	O
in	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
pollution	_	_	O
.	_	_	O
A	_	_	O
bus	_	_	B-VAR
can	_	_	O
seat	_	_	O
250	_	_	B-PARAM
tourists	_	_	O
per	_	_	O
day	_	_	O
but	_	_	O
results	_	_	O
in	_	_	O
40	_	_	B-PARAM
units	_	_	O
of	_	_	O
pollution	_	_	O
.	_	_	O
The	_	_	O
city	_	_	O
has	_	_	O
limited	_	_	O
this	_	_	O
tourism	_	_	O
company	_	_	O
to	_	_	O
producing	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
800	_	_	B-LIMIT
units	_	_	O
of	_	_	O
pollutants	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
To	_	_	O
make	_	_	O
a	_	_	O
profit	_	_	O
,	_	_	O
this	_	_	O
tourism	_	_	O
company	_	_	O
must	_	_	O
take	_	_	O
care	_	_	O
of	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
4600	_	_	B-LIMIT
customers	_	_	O
per	_	_	O
day	_	_	O
.	_	_	O
Planning	_	_	O
to	_	_	O
make	_	_	O
a	_	_	O
profit	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
sedans	_	_	B-VAR
and	_	_	O
how	_	_	O
many	_	_	O
buses	_	_	B-VAR
should	_	_	O
this	_	_	O
tourism	_	_	O
company	_	_	O
purchase	_	_	O
to	_	_	O
decrease	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
vehicles	_	_	I-OBJ_NAME
needed	_	_	O
?	_	_	O

Platinum	_	_	O
in	_	_	O
combination	_	_	O
with	_	_	O
palladium	_	_	O
has	_	_	O
been	_	_	O
used	_	_	O
as	_	_	O
a	_	_	O
catalyst	_	_	O
in	_	_	O
cars	_	_	O
and	_	_	O
it	_	_	O
changes	_	_	O
carbon	_	_	O
monoxide	_	_	O
,	_	_	O
which	_	_	O
is	_	_	O
toxic	_	_	O
,	_	_	O
into	_	_	O
carbon	_	_	B-OBJ_NAME
dioxide	_	_	I-OBJ_NAME
.	_	_	O
An	_	_	O
automotive	_	_	O
company	_	_	O
is	_	_	O
comparing	_	_	O
two	_	_	O
different	_	_	O
catalysts	_	_	O
,	_	_	O
a	_	_	O
palladium	_	_	B-VAR
-	_	_	I-VAR
heavy	_	_	I-VAR
catalyst	_	_	I-VAR
and	_	_	O
a	_	_	O
platinum	_	_	B-VAR
-	_	_	I-VAR
heavy	_	_	I-VAR
catalyst	_	_	I-VAR
.	_	_	O
The	_	_	O
process	_	_	O
with	_	_	O
a	_	_	O
palladium	_	_	B-VAR
-	_	_	I-VAR
heavy	_	_	I-VAR
catalyst	_	_	I-VAR
requires	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
platinum	_	_	O
and	_	_	O
25	_	_	B-PARAM
units	_	_	O
of	_	_	O
palladium	_	_	O
and	_	_	O
can	_	_	O
perform	_	_	O
the	_	_	O
conversion	_	_	O
to	_	_	O
carbon	_	_	O
dioxide	_	_	O
at	_	_	O
a	_	_	O
rate	_	_	O
of	_	_	O
5	_	_	B-PARAM
units	_	_	B-OBJ_NAME
per	_	_	I-OBJ_NAME
second	_	_	I-OBJ_NAME
.	_	_	O
A	_	_	O
platinum	_	_	B-VAR
-	_	_	I-VAR
heavy	_	_	I-VAR
catalyst	_	_	I-VAR
requires	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
platinum	_	_	O
and	_	_	O
14	_	_	B-PARAM
units	_	_	O
of	_	_	O
palladium	_	_	O
and	_	_	O
converts	_	_	O
to	_	_	O
carbon	_	_	O
dioxide	_	_	O
at	_	_	O
a	_	_	O
rate	_	_	O
of	_	_	O
4	_	_	B-PARAM
units	_	_	B-OBJ_NAME
per	_	_	I-OBJ_NAME
second	_	_	I-OBJ_NAME
.	_	_	O
There	_	_	O
are	_	_	O
450	_	_	B-LIMIT
units	_	_	O
of	_	_	O
platinum	_	_	O
and	_	_	O
390	_	_	B-LIMIT
units	_	_	O
of	_	_	O
palladium	_	_	O
available	_	_	B-CONST_DIR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
catalyst	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
converted	_	_	I-OBJ_NAME
into	_	_	I-OBJ_NAME
carbon	_	_	I-OBJ_NAME
dioxide	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
dessert	_	_	O
shop	_	_	O
is	_	_	O
popular	_	_	O
for	_	_	O
their	_	_	O
only	_	_	O
two	_	_	O
desserts	_	_	O
-	_	_	O
matcha	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
and	_	_	O
orange	_	_	B-VAR
sorbet	_	_	I-VAR
.	_	_	O
Two	_	_	B-PARAM
units	_	_	O
of	_	_	O
flavouring	_	_	B-OBJ_NAME
and	_	_	O
four	_	_	B-PARAM
units	_	_	O
of	_	_	O
ice	_	_	O
cream	_	_	O
is	_	_	O
required	_	_	O
to	_	_	O
make	_	_	O
one	_	_	O
order	_	_	O
of	_	_	O
matcha	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
.	_	_	O
Four	_	_	B-PARAM
units	_	_	O
of	_	_	O
flavouring	_	_	B-OBJ_NAME
and	_	_	O
three	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	O
is	_	_	O
required	_	_	O
to	_	_	O
make	_	_	O
an	_	_	O
order	_	_	O
of	_	_	O
orange	_	_	B-VAR
sorbet	_	_	I-VAR
.	_	_	O
The	_	_	O
dessert	_	_	O
shop	_	_	O
has	_	_	O
recently	_	_	O
been	_	_	O
getting	_	_	O
more	_	_	O
orders	_	_	O
online	_	_	O
for	_	_	O
orange	_	_	B-VAR
sorbet	_	_	I-VAR
and	_	_	O
therefore	_	_	O
,	_	_	O
there	_	_	O
should	_	_	O
be	_	_	O
more	_	_	B-CONST_DIR
orange	_	_	B-VAR
sorbet	_	_	I-VAR
made	_	_	O
than	_	_	O
matcha	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
fifteen	_	_	B-LIMIT
percent	_	_	I-LIMIT
of	_	_	O
desserts	_	_	O
made	_	_	O
must	_	_	O
be	_	_	O
matcha	_	_	B-VAR
ice	_	_	I-VAR
cream	_	_	I-VAR
.	_	_	O
The	_	_	O
dessert	_	_	O
shop	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
600	_	_	B-LIMIT
units	_	_	O
of	_	_	O
ice	_	_	O
cream	_	_	O
and	_	_	O
550	_	_	B-LIMIT
units	_	_	O
of	_	_	O
water	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
dessert	_	_	O
should	_	_	O
the	_	_	O
shop	_	_	O
make	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
amount	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
flavouring	_	_	I-OBJ_NAME
needed	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
lighting	_	_	O
company	_	_	O
has	_	_	O
access	_	_	O
to	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
lights	_	_	O
to	_	_	O
provide	_	_	O
their	_	_	O
customers	_	_	O
,	_	_	O
an	_	_	O
LED	_	_	B-VAR
fixture	_	_	I-VAR
,	_	_	O
and	_	_	O
a	_	_	O
fluorescence	_	_	B-VAR
lamp	_	_	I-VAR
.	_	_	O
The	_	_	O
LED	_	_	B-VAR
light	_	_	I-VAR
uses	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
electricity	_	_	O
per	_	_	O
hour	_	_	O
and	_	_	O
needs	_	_	O
to	_	_	O
be	_	_	O
changed	_	_	O
3	_	_	B-PARAM
times	_	_	B-OBJ_NAME
a	_	_	O
decade	_	_	O
.	_	_	O
Conversely	_	_	O
,	_	_	O
the	_	_	O
fluorescence	_	_	B-VAR
lamp	_	_	I-VAR
uses	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
electricity	_	_	O
per	_	_	O
hour	_	_	O
and	_	_	O
needs	_	_	O
to	_	_	O
be	_	_	O
changed	_	_	O
4	_	_	B-PARAM
times	_	_	B-OBJ_NAME
a	_	_	O
decade	_	_	O
.	_	_	O
Due	_	_	O
to	_	_	O
previous	_	_	O
installations	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
%	_	_	I-LIMIT
implemented	_	_	O
lights	_	_	O
must	_	_	O
be	_	_	O
fluorescence	_	_	B-VAR
lamps	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
customer	_	_	O
requires	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
300	_	_	B-LIMIT
light	_	_	O
fixtures	_	_	O
and	_	_	O
can	_	_	O
use	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
2000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
electricity	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
light	_	_	O
should	_	_	O
be	_	_	O
installed	_	_	O
to	_	_	O
reduce	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
light	_	_	I-OBJ_NAME
changes	_	_	I-OBJ_NAME
?	_	_	O

An	_	_	O
autobody	_	_	O
shop	_	_	O
needs	_	_	O
to	_	_	O
purchase	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
car	_	_	O
jacks	_	_	O
,	_	_	O
an	_	_	O
automatic	_	_	B-VAR
electric	_	_	I-VAR
one	_	_	I-VAR
,	_	_	O
or	_	_	O
a	_	_	O
gas	_	_	B-VAR
-	_	_	I-VAR
powered	_	_	I-VAR
one	_	_	I-VAR
.	_	_	O
The	_	_	O
automatic	_	_	B-VAR
electric	_	_	I-VAR
one	_	_	I-VAR
can	_	_	O
process	_	_	O
5	_	_	B-PARAM
cars	_	_	B-OBJ_NAME
every	_	_	I-OBJ_NAME
hour	_	_	I-OBJ_NAME
and	_	_	O
uses	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
electricity	_	_	O
whereas	_	_	O
the	_	_	O
gas	_	_	B-VAR
-	_	_	I-VAR
powered	_	_	I-VAR
one	_	_	I-VAR
can	_	_	O
process	_	_	O
4	_	_	B-PARAM
cars	_	_	B-OBJ_NAME
each	_	_	I-OBJ_NAME
hour	_	_	I-OBJ_NAME
using	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
gas	_	_	O
.	_	_	O
Since	_	_	O
there	_	_	O
is	_	_	O
a	_	_	O
limit	_	_	O
to	_	_	O
how	_	_	O
many	_	_	O
automatic	_	_	B-VAR
electric	_	_	I-VAR
ones	_	_	I-VAR
there	_	_	O
can	_	_	O
be	_	_	O
due	_	_	O
to	_	_	O
the	_	_	O
limited	_	_	O
number	_	_	O
of	_	_	O
power	_	_	O
outlets	_	_	O
,	_	_	O
the	_	_	O
shop	_	_	O
must	_	_	O
use	_	_	O
less	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
15	_	_	B-LIMIT
automatic	_	_	B-VAR
electric	_	_	I-VAR
ones	_	_	I-VAR
.	_	_	O
The	_	_	O
shop	_	_	O
can	_	_	O
use	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
50	_	_	B-LIMIT
units	_	_	O
of	_	_	O
electricity	_	_	O
and	_	_	O
80	_	_	B-LIMIT
units	_	_	O
of	_	_	O
gas	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
jack	_	_	O
should	_	_	O
the	_	_	O
shop	_	_	O
purchase	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
cars	_	_	I-OBJ_NAME
processed	_	_	I-OBJ_NAME
every	_	_	I-OBJ_NAME
hour	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
keyboard	_	_	O
manufacturer	_	_	O
makes	_	_	O
mechanical	_	_	B-VAR
and	_	_	O
standard	_	_	B-VAR
keyboards	_	_	I-VAR
.	_	_	O
Mechanical	_	_	B-VAR
keyboards	_	_	I-VAR
are	_	_	O
becoming	_	_	O
more	_	_	O
popular	_	_	O
and	_	_	O
thus	_	_	O
the	_	_	O
manufacturer	_	_	O
aims	_	_	B-CONST_DIR
to	_	_	I-CONST_DIR
have	_	_	I-CONST_DIR
five	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
many	_	_	O
mechanical	_	_	B-VAR
than	_	_	O
standard	_	_	B-VAR
keyboards	_	_	I-VAR
.	_	_	O
A	_	_	O
mechanical	_	_	B-VAR
keyboard	_	_	I-VAR
costs	_	_	O
five	_	_	B-PARAM
units	_	_	O
of	_	_	O
plastic	_	_	O
and	_	_	O
two	_	_	B-PARAM
units	_	_	O
of	_	_	O
solder	_	_	O
whereas	_	_	O
a	_	_	O
standard	_	_	B-VAR
keyboard	_	_	I-VAR
costs	_	_	O
two	_	_	B-PARAM
units	_	_	O
of	_	_	O
plastic	_	_	O
and	_	_	O
one	_	_	B-PARAM
unit	_	_	O
of	_	_	O
solder	_	_	O
.	_	_	O
There	_	_	O
are	_	_	O
still	_	_	O
customers	_	_	O
that	_	_	O
prefer	_	_	O
a	_	_	O
less	_	_	O
noisy	_	_	O
alternative	_	_	O
.	_	_	O
Therefore	_	_	O
,	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
standard	_	_	B-VAR
keyboards	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
1000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
plastic	_	_	O
and	_	_	O
250	_	_	B-LIMIT
units	_	_	O
of	_	_	O
solder	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
be	_	_	O
manufactured	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
keyboards	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
singer	_	_	O
has	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
concerts	_	_	O
he	_	_	O
can	_	_	O
hold	_	_	O
,	_	_	O
pop	_	_	B-VAR
and	_	_	O
R&B.	_	_	B-VAR
Each	_	_	O
pop	_	_	B-VAR
concert	_	_	I-VAR
will	_	_	O
bring	_	_	O
in	_	_	O
100	_	_	B-PARAM
audience	_	_	O
members	_	_	O
and	_	_	O
take	_	_	O
2	_	_	B-PARAM
days	_	_	O
of	_	_	O
practice	_	_	O
.	_	_	O
Every	_	_	O
R&B	_	_	B-VAR
concert	_	_	I-VAR
brings	_	_	O
in	_	_	O
240	_	_	B-PARAM
audience	_	_	O
members	_	_	O
and	_	_	O
takes	_	_	O
4	_	_	B-PARAM
days	_	_	O
of	_	_	O
practice	_	_	O
.	_	_	O
The	_	_	O
singer	_	_	O
must	_	_	O
bring	_	_	O
in	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10000	_	_	B-LIMIT
audience	_	_	O
members	_	_	O
and	_	_	O
only	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
180	_	_	B-LIMIT
days	_	_	O
for	_	_	O
practice	_	_	O
.	_	_	O
If	_	_	O
he	_	_	O
can	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
perform	_	_	O
40	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
his	_	_	O
concerts	_	_	O
as	_	_	O
R&B	_	_	B-VAR
because	_	_	O
he	_	_	O
likes	_	_	O
pop	_	_	B-VAR
songs	_	_	O
more	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
concert	_	_	O
should	_	_	O
be	_	_	O
created	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
concerts	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
food	_	_	O
delivery	_	_	O
person	_	_	O
can	_	_	O
either	_	_	O
have	_	_	O
shifts	_	_	O
on	_	_	O
bikes	_	_	B-VAR
or	_	_	O
scooters	_	_	B-VAR
.	_	_	O
A	_	_	O
shift	_	_	O
on	_	_	O
a	_	_	O
bike	_	_	B-VAR
can	_	_	O
deliver	_	_	O
10	_	_	B-PARAM
orders	_	_	O
,	_	_	O
takes	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
energy	_	_	O
,	_	_	O
and	_	_	O
brings	_	_	O
in	_	_	O
$	_	_	O
50	_	_	B-PARAM
on	_	_	O
tips	_	_	B-OBJ_NAME
because	_	_	O
it	_	_	O
is	_	_	O
faster	_	_	O
.	_	_	O
A	_	_	O
shift	_	_	O
on	_	_	O
a	_	_	O
scooter	_	_	B-VAR
can	_	_	O
deliver	_	_	O
7	_	_	B-PARAM
orders	_	_	O
,	_	_	O
takes	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
energy	_	_	O
,	_	_	O
and	_	_	O
brings	_	_	O
in	_	_	O
$	_	_	O
43	_	_	B-PARAM
on	_	_	O
tips	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
delivery	_	_	O
person	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
40	_	_	B-LIMIT
shifts	_	_	O
a	_	_	O
month	_	_	O
and	_	_	O
has	_	_	B-CONST_DIR
230	_	_	B-LIMIT
units	_	_	O
of	_	_	O
energy	_	_	O
and	_	_	O
must	_	_	O
bring	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
320	_	_	B-LIMIT
orders	_	_	O
.	_	_	O
He	_	_	O
must	_	_	O
have	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
shifts	_	_	O
on	_	_	O
a	_	_	O
scooter	_	_	B-VAR
because	_	_	O
bikes	_	_	B-VAR
are	_	_	O
harder	_	_	O
to	_	_	O
get	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
shifts	_	_	O
on	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
transportation	_	_	O
should	_	_	O
the	_	_	O
delivery	_	_	O
person	_	_	O
schedule	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
tips	_	_	B-OBJ_NAME
received	_	_	I-OBJ_NAME
?	_	_	O

There	_	_	O
are	_	_	O
two	_	_	O
ways	_	_	O
to	_	_	O
extract	_	_	O
a	_	_	O
metal	_	_	O
from	_	_	O
mined	_	_	O
ores	_	_	O
.	_	_	O
The	_	_	O
first	_	_	O
way	_	_	O
is	_	_	O
to	_	_	O
use	_	_	O
process	_	_	B-VAR
J	_	_	I-VAR
and	_	_	O
the	_	_	O
second	_	_	O
is	_	_	O
process	_	_	B-VAR
P.	_	_	I-VAR
Process	_	_	B-VAR
J	_	_	I-VAR
can	_	_	O
extract	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
metal	_	_	B-OBJ_NAME
using	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	O
and	_	_	O
produces	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
pollution	_	_	O
.	_	_	O
Process	_	_	B-VAR
P	_	_	I-VAR
can	_	_	O
extract	_	_	O
9	_	_	B-PARAM
units	_	_	O
of	_	_	O
metal	_	_	B-OBJ_NAME
using	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	O
and	_	_	O
produces	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
pollution	_	_	O
.	_	_	O
There	_	_	O
can	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
1500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
water	_	_	O
1350	_	_	B-LIMIT
units	_	_	O
of	_	_	O
pollution	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
processes	_	_	O
should	_	_	O
be	_	_	O
performed	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
metal	_	_	I-OBJ_NAME
extracted	_	_	O
?	_	_	O

A	_	_	O
handmade	_	_	O
sports	_	_	O
equipment	_	_	O
manufacturing	_	_	O
company	_	_	O
makes	_	_	O
basketballs	_	_	B-VAR
and	_	_	O
footballs	_	_	B-VAR
.	_	_	O
Basketballs	_	_	B-VAR
require	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
materials	_	_	O
and	_	_	O
1	_	_	B-PARAM
hour	_	_	O
to	_	_	O
make	_	_	O
whereas	_	_	O
footballs	_	_	B-VAR
require	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
materials	_	_	O
and	_	_	O
2	_	_	B-PARAM
hours	_	_	O
to	_	_	O
make	_	_	O
.	_	_	O
The	_	_	O
manufacturing	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
1500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
materials	_	_	O
and	_	_	O
their	_	_	O
workers	_	_	O
working	_	_	O
at	_	_	O
max	_	_	O
capacity	_	_	O
can	_	_	O
work	_	_	O
for	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
750	_	_	B-LIMIT
hours	_	_	O
.	_	_	O
Since	_	_	O
basketballs	_	_	B-VAR
sell	_	_	O
better	_	_	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
basketballs	_	_	B-VAR
as	_	_	O
footballs	_	_	B-VAR
but	_	_	O
the	_	_	O
manufacturing	_	_	O
company	_	_	O
would	_	_	O
like	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
footballs	_	_	B-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
manufacturing	_	_	O
company	_	_	O
make	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
sports	_	_	I-OBJ_NAME
equipment	_	_	I-OBJ_NAME
produced	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
researcher	_	_	O
is	_	_	O
outsourcing	_	_	O
annotations	_	_	O
and	_	_	O
has	_	_	O
two	_	_	O
options	_	_	O
:	_	_	O
a	_	_	O
specialized	_	_	B-VAR
third	_	_	I-VAR
-	_	_	I-VAR
party	_	_	I-VAR
or	_	_	O
a	_	_	O
common	_	_	B-VAR
third	_	_	I-VAR
-	_	_	I-VAR
party	_	_	I-VAR
annotation	_	_	I-VAR
company	_	_	I-VAR
.	_	_	O
The	_	_	O
specialized	_	_	B-VAR
company	_	_	I-VAR
can	_	_	O
annotate	_	_	O
at	_	_	O
a	_	_	O
rate	_	_	O
of	_	_	O
60	_	_	B-PARAM
images	_	_	O
per	_	_	O
hour	_	_	O
whereas	_	_	O
the	_	_	O
common	_	_	B-VAR
company	_	_	I-VAR
can	_	_	O
annotate	_	_	O
at	_	_	O
a	_	_	O
rate	_	_	O
of	_	_	O
40	_	_	B-PARAM
images	_	_	O
per	_	_	O
hour	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
the	_	_	O
specialized	_	_	B-VAR
company	_	_	I-VAR
charges	_	_	O
$	_	_	O
100	_	_	B-PARAM
per	_	_	B-OBJ_NAME
hour	_	_	I-OBJ_NAME
and	_	_	O
the	_	_	O
common	_	_	B-VAR
company	_	_	I-VAR
charges	_	_	O
$	_	_	O
72	_	_	B-PARAM
per	_	_	B-OBJ_NAME
hour	_	_	I-OBJ_NAME
.	_	_	O
The	_	_	O
researcher	_	_	O
has	_	_	O
deadlines	_	_	O
to	_	_	O
meet	_	_	O
and	_	_	O
must	_	_	O
complete	_	_	O
a	_	_	O
dataset	_	_	O
of	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10,000	_	_	B-LIMIT
images	_	_	O
.	_	_	O
They	_	_	O
also	_	_	O
have	_	_	O
some	_	_	O
special	_	_	O
images	_	_	O
that	_	_	O
only	_	_	O
the	_	_	O
specialized	_	_	B-VAR
company	_	_	I-VAR
can	_	_	O
annotate	_	_	O
.	_	_	O
Therefore	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
a	_	_	O
third	_	_	B-LIMIT
of	_	_	O
work	_	_	O
must	_	_	O
be	_	_	O
allocated	_	_	O
to	_	_	O
the	_	_	O
specialized	_	_	B-VAR
company	_	_	I-VAR
.	_	_	O
How	_	_	O
should	_	_	O
the	_	_	O
researcher	_	_	O
distribute	_	_	O
the	_	_	O
annotations	_	_	O
to	_	_	O
the	_	_	O
two	_	_	O
companies	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
cost	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
annotating	_	_	I-OBJ_NAME
the	_	_	I-OBJ_NAME
whole	_	_	I-OBJ_NAME
dataset	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
soda	_	_	O
company	_	_	O
sells	_	_	O
soda	_	_	O
in	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
containers	_	_	O
:	_	_	O
cans	_	_	B-VAR
and	_	_	O
glass	_	_	B-VAR
bottles	_	_	I-VAR
.	_	_	O
A	_	_	O
can	_	_	B-VAR
holds	_	_	O
250	_	_	B-PARAM
ml	_	_	O
of	_	_	O
soda	_	_	O
whereas	_	_	O
a	_	_	O
bottle	_	_	B-VAR
holds	_	_	O
1000	_	_	B-PARAM
ml	_	_	O
of	_	_	O
soda	_	_	O
.	_	_	O
The	_	_	O
soda	_	_	O
company	_	_	O
needs	_	_	O
to	_	_	O
bottle	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1000000	_	_	B-LIMIT
ml	_	_	O
of	_	_	O
soda	_	_	O
every	_	_	O
day	_	_	O
and	_	_	O
due	_	_	O
to	_	_	O
the	_	_	O
ability	_	_	O
to	_	_	O
sell	_	_	O
soda	_	_	B-VAR
cans	_	_	I-VAR
as	_	_	O
packs	_	_	O
,	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	I-PARAM
more	_	_	O
cans	_	_	B-VAR
than	_	_	O
glass	_	_	B-VAR
bottles	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
because	_	_	O
of	_	_	O
previous	_	_	O
contracts	_	_	O
with	_	_	O
gas	_	_	O
stations	_	_	O
,	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
glass	_	_	B-VAR
bottles	_	_	I-VAR
made	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
units	_	_	I-OBJ_NAME
produced	_	_	O
?	_	_	O

A	_	_	O
brewery	_	_	O
can	_	_	O
ferment	_	_	O
their	_	_	O
product	_	_	O
into	_	_	O
either	_	_	O
wine	_	_	B-VAR
or	_	_	O
kombucha	_	_	B-VAR
.	_	_	O
Each	_	_	O
unit	_	_	O
of	_	_	O
wine	_	_	B-VAR
requires	_	_	O
3	_	_	B-PARAM
units	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
fruit	_	_	I-OBJ_NAME
and	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	O
.	_	_	O
Each	_	_	O
unit	_	_	O
of	_	_	O
kombucha	_	_	B-VAR
requires	_	_	O
5	_	_	B-PARAM
units	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
fruit	_	_	I-OBJ_NAME
and	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
tea	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
7000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
water	_	_	O
and	_	_	O
9000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
tea	_	_	O
.	_	_	O
Wine	_	_	B-VAR
sells	_	_	O
for	_	_	O
more	_	_	O
,	_	_	O
therefore	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
wine	_	_	B-VAR
must	_	_	O
be	_	_	O
larger	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
kombucha	_	_	B-VAR
.	_	_	O
Additionally	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
their	_	_	O
products	_	_	O
made	_	_	O
must	_	_	O
be	_	_	O
kombucha	_	_	B-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
brewery	_	_	O
make	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
units	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
fruit	_	_	I-OBJ_NAME
required	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
dentist	_	_	O
has	_	_	B-CONST_DIR
3000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
resin	_	_	O
to	_	_	O
fill	_	_	O
cavities	_	_	O
in	_	_	O
both	_	_	O
molars	_	_	B-VAR
and	_	_	O
canines	_	_	B-VAR
.	_	_	O
Molars	_	_	B-VAR
require	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
resin	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
pain	_	_	B-OBJ_NAME
killer	_	_	I-OBJ_NAME
.	_	_	O
Canines	_	_	B-VAR
require	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
resin	_	_	O
and	_	_	O
2.3	_	_	B-PARAM
units	_	_	O
of	_	_	O
pain	_	_	B-OBJ_NAME
killer	_	_	I-OBJ_NAME
.	_	_	O
Since	_	_	O
this	_	_	O
dentist	_	_	O
sees	_	_	O
more	_	_	O
cavities	_	_	O
in	_	_	O
canines	_	_	B-VAR
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
60	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
cavities	_	_	O
filled	_	_	O
must	_	_	O
be	_	_	O
in	_	_	O
canines	_	_	B-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
the	_	_	O
dentist	_	_	O
must	_	_	O
reserve	_	_	O
materials	_	_	O
to	_	_	O
fill	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
45	_	_	B-LIMIT
molars	_	_	B-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
teeth	_	_	O
should	_	_	O
the	_	_	O
dentist	_	_	O
schedule	_	_	O
to	_	_	O
fill	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
pain	_	_	I-OBJ_NAME
killer	_	_	I-OBJ_NAME
needed	_	_	O
?	_	_	O

A	_	_	O
chemical	_	_	O
company	_	_	O
uses	_	_	O
two	_	_	O
tests	_	_	O
,	_	_	O
a	_	_	O
salinity	_	_	B-VAR
test	_	_	I-VAR
and	_	_	O
a	_	_	O
pH	_	_	B-VAR
test	_	_	I-VAR
.	_	_	O
Each	_	_	O
unit	_	_	O
of	_	_	O
the	_	_	O
salinity	_	_	B-VAR
test	_	_	I-VAR
requires	_	_	O
three	_	_	B-PARAM
probes	_	_	B-OBJ_NAME
.	_	_	O
Whereas	_	_	O
each	_	_	O
unit	_	_	O
of	_	_	O
the	_	_	O
pH	_	_	B-VAR
test	_	_	I-VAR
requires	_	_	O
two	_	_	B-PARAM
probes	_	_	B-OBJ_NAME
.	_	_	O
The	_	_	O
chemical	_	_	O
company	_	_	O
must	_	_	O
perform	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
250	_	_	B-LIMIT
pH	_	_	B-VAR
tests	_	_	I-VAR
.	_	_	O
In	_	_	O
total	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
400	_	_	B-LIMIT
tests	_	_	O
must	_	_	O
be	_	_	O
performed	_	_	O
.	_	_	O
Further	_	_	O
,	_	_	O
because	_	_	O
of	_	_	O
the	_	_	O
importance	_	_	O
of	_	_	O
the	_	_	O
salinity	_	_	B-VAR
test	_	_	I-VAR
,	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
1.5	_	_	B-PARAM
times	_	_	I-PARAM
more	_	_	O
pH	_	_	B-VAR
tests	_	_	I-VAR
than	_	_	O
salinity	_	_	B-VAR
tests	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
times	_	_	O
should	_	_	O
each	_	_	O
test	_	_	O
be	_	_	O
performed	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
probes	_	_	I-OBJ_NAME
used	_	_	O
?	_	_	O

A	_	_	O
navy	_	_	O
ship	_	_	O
is	_	_	O
stocking	_	_	O
food	_	_	O
onto	_	_	O
their	_	_	O
submarine	_	_	O
and	_	_	O
their	_	_	O
staff	_	_	O
can	_	_	O
eat	_	_	O
either	_	_	O
a	_	_	O
salad	_	_	B-VAR
or	_	_	O
fruit	_	_	B-VAR
bowl	_	_	I-VAR
for	_	_	O
their	_	_	O
fibre	_	_	O
and	_	_	O
vitamin	_	_	O
intake	_	_	O
.	_	_	O
The	_	_	O
nutritionist	_	_	O
in	_	_	O
charge	_	_	O
of	_	_	O
this	_	_	O
voyage	_	_	O
needs	_	_	O
to	_	_	O
ensure	_	_	O
that	_	_	O
their	_	_	O
staff	_	_	O
gets	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
90	_	_	B-LIMIT
units	_	_	O
of	_	_	O
vitamin	_	_	O
and	_	_	O
110	_	_	B-LIMIT
units	_	_	O
of	_	_	O
fibre	_	_	O
each	_	_	O
.	_	_	O
Each	_	_	O
salad	_	_	B-VAR
contains	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamins	_	_	O
and	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
fibre	_	_	O
.	_	_	O
Each	_	_	O
fruit	_	_	B-VAR
bowl	_	_	I-VAR
contains	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
vitamin	_	_	O
and	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
fibre	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
since	_	_	O
fruit	_	_	B-VAR
bowls	_	_	I-VAR
take	_	_	O
longer	_	_	O
to	_	_	O
prepare	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
their	_	_	O
meals	_	_	O
should	_	_	O
be	_	_	O
fruit	_	_	B-VAR
bowls	_	_	I-VAR
.	_	_	O
If	_	_	O
each	_	_	O
salad	_	_	B-VAR
contains	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
potassium	_	_	B-OBJ_NAME
and	_	_	O
each	_	_	O
fruit	_	_	B-VAR
bowl	_	_	I-VAR
contains	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
potassium	_	_	B-OBJ_NAME
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
they	_	_	O
prepare	_	_	O
for	_	_	O
each	_	_	O
staff	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
their	_	_	O
potassium	_	_	B-OBJ_NAME
intake	_	_	I-OBJ_NAME
?	_	_	O

An	_	_	O
incandescent	_	_	O
bulb	_	_	O
manufacturing	_	_	O
company	_	_	O
uses	_	_	O
either	_	_	O
an	_	_	O
argon	_	_	B-VAR
gas	_	_	I-VAR
approach	_	_	I-VAR
or	_	_	O
halogen	_	_	B-VAR
gas	_	_	I-VAR
approach	_	_	I-VAR
to	_	_	O
fill	_	_	O
their	_	_	O
light	_	_	B-OBJ_NAME
bulbs	_	_	I-OBJ_NAME
.	_	_	O
The	_	_	O
argon	_	_	B-VAR
gas	_	_	I-VAR
approach	_	_	I-VAR
uses	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
gas	_	_	O
and	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
glass	_	_	O
to	_	_	O
make	_	_	O
2	_	_	B-PARAM
light	_	_	B-OBJ_NAME
bulbs	_	_	I-OBJ_NAME
.	_	_	O
The	_	_	O
halogen	_	_	B-VAR
gas	_	_	I-VAR
approach	_	_	I-VAR
uses	_	_	O
12	_	_	B-PARAM
units	_	_	O
of	_	_	O
gas	_	_	O
and	_	_	O
8	_	_	B-PARAM
units	_	_	O
of	_	_	O
glass	_	_	O
to	_	_	O
make	_	_	O
3	_	_	B-PARAM
light	_	_	B-OBJ_NAME
bulbs	_	_	I-OBJ_NAME
.	_	_	O
Additionally	_	_	O
,	_	_	O
the	_	_	O
argon	_	_	B-VAR
gas	_	_	I-VAR
approach	_	_	I-VAR
generates	_	_	O
3	_	_	B-PARAM
units	_	_	O
of	_	_	O
heat	_	_	O
while	_	_	O
the	_	_	O
halogen	_	_	B-VAR
gas	_	_	I-VAR
approach	_	_	I-VAR
creates	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
heat	_	_	O
.	_	_	O
The	_	_	O
manufacturing	_	_	O
company	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
150	_	_	B-LIMIT
units	_	_	O
of	_	_	O
gas	_	_	O
and	_	_	O
120	_	_	B-LIMIT
units	_	_	O
of	_	_	O
glass	_	_	O
.	_	_	O
If	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
28	_	_	B-LIMIT
units	_	_	O
of	_	_	O
heat	_	_	O
can	_	_	O
be	_	_	O
generated	_	_	O
during	_	_	O
the	_	_	O
manufacturing	_	_	O
process	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
method	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
light	_	_	I-OBJ_NAME
bulbs	_	_	I-OBJ_NAME
produced	_	_	O
?	_	_	O

A	_	_	O
biotechnology	_	_	O
company	_	_	O
has	_	_	O
35,000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
antibiotics	_	_	O
available	_	_	B-CONST_DIR
which	_	_	O
is	_	_	O
important	_	_	O
to	_	_	O
the	_	_	O
process	_	_	O
of	_	_	O
making	_	_	O
a	_	_	O
first	_	_	B-VAR
-	_	_	I-VAR
dose	_	_	I-VAR
and	_	_	O
second	_	_	B-VAR
-	_	_	I-VAR
dose	_	_	I-VAR
of	_	_	O
vaccines	_	_	O
.	_	_	O
The	_	_	O
first	_	_	B-VAR
-	_	_	I-VAR
dose	_	_	I-VAR
vaccine	_	_	I-VAR
requires	_	_	O
30	_	_	B-PARAM
units	_	_	O
of	_	_	O
antibiotics	_	_	O
and	_	_	O
20	_	_	B-PARAM
mg	_	_	O
of	_	_	O
gelatine	_	_	B-OBJ_NAME
whereas	_	_	O
the	_	_	O
second	_	_	B-VAR
-	_	_	I-VAR
dose	_	_	I-VAR
vaccine	_	_	I-VAR
requires	_	_	O
65	_	_	B-PARAM
units	_	_	O
of	_	_	O
antibiotics	_	_	O
and	_	_	O
60	_	_	B-PARAM
mg	_	_	O
of	_	_	O
gelatine	_	_	B-OBJ_NAME
.	_	_	O
Since	_	_	O
the	_	_	O
first	_	_	B-VAR
-	_	_	I-VAR
dose	_	_	I-VAR
vaccine	_	_	I-VAR
is	_	_	O
required	_	_	O
before	_	_	O
the	_	_	O
second	_	_	B-VAR
-	_	_	I-VAR
dose	_	_	I-VAR
vaccine	_	_	I-VAR
,	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
more	_	_	B-CONST_DIR
first	_	_	B-VAR
-	_	_	I-VAR
dose	_	_	I-VAR
than	_	_	O
second	_	_	B-VAR
-	_	_	I-VAR
dose	_	_	I-VAR
vaccines	_	_	I-VAR
manufactured	_	_	O
.	_	_	O
However	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
40	_	_	B-LIMIT
second	_	_	B-VAR
-	_	_	I-VAR
dose	_	_	I-VAR
vaccines	_	_	I-VAR
must	_	_	O
be	_	_	O
made	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
vaccine	_	_	O
should	_	_	O
be	_	_	O
made	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
gelatine	_	_	I-OBJ_NAME
used	_	_	O
?	_	_	O

Both	_	_	O
subsoil	_	_	B-VAR
and	_	_	O
topsoil	_	_	B-VAR
need	_	_	O
to	_	_	O
be	_	_	O
added	_	_	O
to	_	_	O
a	_	_	O
garden	_	_	O
bed	_	_	O
.	_	_	O
One	_	_	O
bag	_	_	O
of	_	_	O
subsoil	_	_	B-VAR
requires	_	_	O
10	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	B-OBJ_NAME
to	_	_	O
hydrate	_	_	O
while	_	_	O
one	_	_	O
bag	_	_	O
of	_	_	O
topsoil	_	_	B-VAR
requires	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	B-OBJ_NAME
to	_	_	O
hydrate	_	_	O
every	_	_	O
day	_	_	O
.	_	_	O
The	_	_	O
truck	_	_	O
used	_	_	O
to	_	_	O
transport	_	_	O
the	_	_	O
dirt	_	_	O
has	_	_	O
limited	_	_	O
capacity	_	_	O
and	_	_	O
therefore	_	_	O
,	_	_	O
the	_	_	O
farmer	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
150	_	_	B-LIMIT
bags	_	_	O
of	_	_	O
topsoil	_	_	B-VAR
and	_	_	O
subsoil	_	_	B-VAR
combined	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
10	_	_	B-LIMIT
bags	_	_	O
of	_	_	O
topsoil	_	_	B-VAR
must	_	_	O
be	_	_	O
used	_	_	O
.	_	_	O
Since	_	_	O
the	_	_	O
topsoil	_	_	B-VAR
is	_	_	O
more	_	_	O
expensive	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
30	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
all	_	_	O
bags	_	_	O
of	_	_	O
soil	_	_	O
can	_	_	O
be	_	_	O
topsoil	_	_	B-VAR
.	_	_	O
How	_	_	O
many	_	_	O
bags	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
bought	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
water	_	_	I-OBJ_NAME
required	_	_	O
to	_	_	O
hydrate	_	_	O
the	_	_	O
garden	_	_	O
bed	_	_	O
?	_	_	O

A	_	_	O
clinical	_	_	O
firm	_	_	O
has	_	_	O
two	_	_	O
factories	_	_	O
,	_	_	O
a	_	_	O
northern	_	_	B-VAR
factory	_	_	I-VAR
and	_	_	O
a	_	_	O
western	_	_	B-VAR
factory	_	_	I-VAR
,	_	_	O
where	_	_	O
they	_	_	O
make	_	_	O
expensive	_	_	O
anti	_	_	O
-	_	_	O
itch	_	_	O
injections	_	_	O
and	_	_	O
topical	_	_	O
cream	_	_	O
.	_	_	O
Every	_	_	O
hour	_	_	B-OBJ_NAME
,	_	_	O
the	_	_	O
northern	_	_	B-VAR
factory	_	_	I-VAR
makes	_	_	O
800	_	_	B-PARAM
g	_	_	O
of	_	_	O
anti	_	_	O
-	_	_	O
itch	_	_	O
injections	_	_	O
and	_	_	O
700	_	_	B-PARAM
g	_	_	O
of	_	_	O
topical	_	_	O
cream	_	_	O
.	_	_	O
Every	_	_	O
hour	_	_	B-OBJ_NAME
,	_	_	O
the	_	_	O
western	_	_	B-VAR
factory	_	_	I-VAR
makes	_	_	O
650	_	_	B-PARAM
g	_	_	O
of	_	_	O
anti	_	_	O
-	_	_	O
itch	_	_	O
injections	_	_	O
and	_	_	O
750	_	_	B-PARAM
g	_	_	O
of	_	_	O
topical	_	_	O
cream	_	_	O
.	_	_	O
The	_	_	O
northern	_	_	B-VAR
factory	_	_	I-VAR
requires	_	_	O
40	_	_	B-PARAM
units	_	_	O
of	_	_	O
plastic	_	_	O
per	_	_	O
hour	_	_	B-OBJ_NAME
while	_	_	O
the	_	_	O
western	_	_	B-VAR
factory	_	_	I-VAR
requires	_	_	O
35	_	_	B-PARAM
units	_	_	O
of	_	_	O
plastic	_	_	O
to	_	_	O
manufacture	_	_	O
the	_	_	O
packaging	_	_	O
.	_	_	O
The	_	_	O
clinical	_	_	O
firm	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
60,000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
plastic	_	_	O
.	_	_	O
Further	_	_	O
,	_	_	O
they	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
800,000	_	_	B-LIMIT
g	_	_	O
of	_	_	O
anti	_	_	O
-	_	_	O
itch	_	_	O
injections	_	_	O
and	_	_	O
700,000	_	_	B-LIMIT
g	_	_	O
of	_	_	O
topical	_	_	O
cream	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
hours	_	_	B-OBJ_NAME
should	_	_	O
each	_	_	O
factory	_	_	O
be	_	_	O
run	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
time	_	_	I-OBJ_NAME
needed	_	_	O
?	_	_	O

A	_	_	O
hospital	_	_	O
prepares	_	_	O
batches	_	_	O
of	_	_	O
medication	_	_	B-VAR
patches	_	_	I-VAR
and	_	_	O
anti	_	_	B-VAR
-	_	_	I-VAR
biotic	_	_	I-VAR
creams	_	_	I-VAR
.	_	_	O
Each	_	_	O
medication	_	_	B-VAR
patch	_	_	I-VAR
requires	_	_	O
3	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
prepare	_	_	O
and	_	_	O
5	_	_	B-PARAM
units	_	_	O
of	_	_	O
materials	_	_	O
.	_	_	O
Each	_	_	O
anti	_	_	B-VAR
-	_	_	I-VAR
biotic	_	_	I-VAR
cream	_	_	I-VAR
requires	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
prepare	_	_	O
and	_	_	O
6	_	_	B-PARAM
units	_	_	O
of	_	_	O
materials	_	_	O
.	_	_	O
Since	_	_	O
anti	_	_	B-VAR
-	_	_	I-VAR
biotic	_	_	I-VAR
creams	_	_	I-VAR
are	_	_	O
used	_	_	O
more	_	_	O
often	_	_	O
,	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-PARAM
as	_	_	O
many	_	_	O
anti	_	_	B-VAR
-	_	_	I-VAR
biotic	_	_	I-VAR
creams	_	_	I-VAR
as	_	_	O
medication	_	_	B-VAR
patches	_	_	I-VAR
.	_	_	O
Due	_	_	O
to	_	_	O
storage	_	_	O
reasons	_	_	O
,	_	_	O
the	_	_	O
hospital	_	_	O
can	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
100	_	_	B-LIMIT
batches	_	_	O
of	_	_	O
medication	_	_	B-VAR
patches	_	_	I-VAR
and	_	_	O
anti	_	_	B-VAR
-	_	_	I-VAR
biotic	_	_	I-VAR
creams	_	_	I-VAR
in	_	_	O
total	_	_	O
.	_	_	O
The	_	_	O
hospital	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
400	_	_	B-LIMIT
minutes	_	_	O
of	_	_	O
staff	_	_	O
to	_	_	O
spare	_	_	O
and	_	_	O
530	_	_	B-LIMIT
units	_	_	O
of	_	_	O
materials	_	_	O
.	_	_	O
If	_	_	O
each	_	_	O
batch	_	_	O
of	_	_	O
medication	_	_	B-VAR
patches	_	_	I-VAR
can	_	_	O
treat	_	_	O
3	_	_	B-PARAM
people	_	_	B-OBJ_NAME
and	_	_	O
each	_	_	O
batch	_	_	O
of	_	_	O
anti	_	_	B-VAR
-	_	_	I-VAR
biotic	_	_	I-VAR
cream	_	_	I-VAR
can	_	_	O
treat	_	_	O
2	_	_	B-PARAM
people	_	_	B-OBJ_NAME
,	_	_	O
how	_	_	O
many	_	_	O
batches	_	_	O
of	_	_	O
each	_	_	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
macro	_	_	O
-	_	_	O
counting	_	_	O
fitness	_	_	O
guru	_	_	O
only	_	_	O
eats	_	_	O
salmon	_	_	B-VAR
and	_	_	O
eggs	_	_	B-VAR
.	_	_	O
Each	_	_	O
bowl	_	_	O
of	_	_	O
salmon	_	_	B-VAR
contains	_	_	O
300	_	_	B-PARAM
calories	_	_	O
,	_	_	O
15	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
and	_	_	O
80	_	_	B-PARAM
mg	_	_	O
of	_	_	O
sodium	_	_	B-OBJ_NAME
.	_	_	O
Each	_	_	O
bowl	_	_	O
of	_	_	O
eggs	_	_	B-VAR
contains	_	_	O
200	_	_	B-PARAM
calories	_	_	O
,	_	_	O
8	_	_	B-PARAM
grams	_	_	O
of	_	_	O
protein	_	_	O
,	_	_	O
and	_	_	O
20	_	_	B-PARAM
mg	_	_	O
of	_	_	O
sodium	_	_	B-OBJ_NAME
.	_	_	O
Since	_	_	O
the	_	_	O
fitness	_	_	O
guru	_	_	O
has	_	_	O
a	_	_	O
limit	_	_	O
to	_	_	O
how	_	_	O
many	_	_	O
eggs	_	_	B-VAR
he	_	_	O
would	_	_	O
like	_	_	O
to	_	_	O
eat	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
40	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
his	_	_	O
meals	_	_	O
can	_	_	O
be	_	_	O
eggs	_	_	B-VAR
.	_	_	O
The	_	_	O
fitness	_	_	O
guru	_	_	O
needs	_	_	O
to	_	_	O
eat	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
2000	_	_	B-LIMIT
calories	_	_	O
and	_	_	O
90	_	_	B-LIMIT
grams	_	_	O
of	_	_	O
protein	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
meal	_	_	O
should	_	_	O
he	_	_	O
eat	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
his	_	_	O
sodium	_	_	B-OBJ_NAME
intake	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
woman	_	_	O
on	_	_	O
a	_	_	O
diet	_	_	O
needs	_	_	O
to	_	_	O
eat	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
meal	_	_	O
preps	_	_	O
,	_	_	O
a	_	_	O
smoothie	_	_	B-VAR
and	_	_	O
a	_	_	O
protein	_	_	B-VAR
bar	_	_	I-VAR
.	_	_	O
Each	_	_	O
smoothie	_	_	B-VAR
contains	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	B-OBJ_NAME
and	_	_	O
300	_	_	B-PARAM
calories	_	_	O
.	_	_	O
Each	_	_	O
protein	_	_	B-VAR
bar	_	_	I-VAR
contains	_	_	O
7	_	_	B-PARAM
units	_	_	O
of	_	_	O
protein	_	_	B-OBJ_NAME
and	_	_	O
250	_	_	B-PARAM
calories	_	_	O
.	_	_	O
The	_	_	O
woman	_	_	O
must	_	_	O
eat	_	_	O
2	_	_	B-PARAM
times	_	_	I-PARAM
more	_	_	B-CONST_DIR
protein	_	_	B-VAR
bars	_	_	I-VAR
than	_	_	O
smoothies	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
woman	_	_	O
can	_	_	O
consume	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
2000	_	_	B-LIMIT
calories	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
she	_	_	O
eat	_	_	O
or	_	_	O
drink	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
her	_	_	O
protein	_	_	B-OBJ_NAME
intake	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
student	_	_	O
takes	_	_	O
calcium	_	_	B-VAR
pills	_	_	I-VAR
and	_	_	O
vitamin	_	_	B-VAR
D	_	_	I-VAR
pills	_	_	I-VAR
one	_	_	O
after	_	_	O
the	_	_	O
other	_	_	O
.	_	_	O
Each	_	_	O
calcium	_	_	B-VAR
pill	_	_	I-VAR
takes	_	_	O
5	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
to	_	_	O
be	_	_	O
effective	_	_	O
while	_	_	O
each	_	_	O
vitamin	_	_	B-VAR
D	_	_	I-VAR
pill	_	_	I-VAR
takes	_	_	O
6	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
to	_	_	O
be	_	_	O
effective	_	_	O
.	_	_	O
Over	_	_	O
a	_	_	O
month	_	_	O
,	_	_	O
the	_	_	O
student	_	_	O
must	_	_	O
take	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
130	_	_	B-LIMIT
pills	_	_	O
of	_	_	O
medication	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
40	_	_	B-LIMIT
should	_	_	O
be	_	_	O
vitamin	_	_	B-VAR
D	_	_	I-VAR
pills	_	_	I-VAR
because	_	_	O
they	_	_	O
enhance	_	_	O
the	_	_	O
absorption	_	_	O
of	_	_	O
calcium	_	_	O
in	_	_	O
the	_	_	O
body	_	_	O
.	_	_	O
Since	_	_	O
vitamin	_	_	B-VAR
D	_	_	I-VAR
is	_	_	O
complimentary	_	_	O
to	_	_	O
calcium	_	_	O
,	_	_	O
the	_	_	O
student	_	_	O
must	_	_	O
take	_	_	O
more	_	_	B-CONST_DIR
calcium	_	_	B-VAR
pills	_	_	I-VAR
than	_	_	O
vitamin	_	_	B-VAR
D	_	_	I-VAR
pills	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
pills	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
student	_	_	O
take	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
time	_	_	I-OBJ_NAME
it	_	_	O
takes	_	_	O
for	_	_	O
the	_	_	O
medication	_	_	O
to	_	_	O
be	_	_	O
effective	_	_	O
?	_	_	O

A	_	_	O
senior	_	_	O
home	_	_	O
has	_	_	O
snacks	_	_	O
of	_	_	O
spinach	_	_	B-VAR
and	_	_	O
soybeans	_	_	B-VAR
to	_	_	O
increase	_	_	O
their	_	_	O
intake	_	_	O
of	_	_	O
iron	_	_	O
.	_	_	O
A	_	_	O
cup	_	_	O
of	_	_	O
spinach	_	_	B-VAR
contains	_	_	O
100	_	_	B-PARAM
units	_	_	O
of	_	_	O
fibre	_	_	O
and	_	_	O
5	_	_	B-PARAM
mg	_	_	O
of	_	_	O
iron	_	_	O
.	_	_	O
A	_	_	O
cup	_	_	O
of	_	_	O
soybeans	_	_	B-VAR
contains	_	_	O
80	_	_	B-PARAM
units	_	_	O
of	_	_	O
fibre	_	_	O
and	_	_	O
12	_	_	B-PARAM
mg	_	_	O
of	_	_	O
iron	_	_	O
.	_	_	O
Due	_	_	O
to	_	_	O
other	_	_	O
nutritional	_	_	O
requirements	_	_	O
,	_	_	O
the	_	_	O
nurses	_	_	O
decided	_	_	O
that	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
cups	_	_	O
of	_	_	O
spinach	_	_	B-VAR
must	_	_	B-CONST_DIR
exceed	_	_	I-CONST_DIR
the	_	_	O
number	_	_	O
of	_	_	O
cups	_	_	O
of	_	_	O
soybeans	_	_	B-VAR
.	_	_	O
Furthermore	_	_	O
,	_	_	O
a	_	_	O
cup	_	_	O
of	_	_	O
spinach	_	_	B-VAR
contains	_	_	O
30	_	_	B-PARAM
calories	_	_	B-OBJ_NAME
while	_	_	O
a	_	_	O
cup	_	_	O
of	_	_	O
soybeans	_	_	B-VAR
contains	_	_	O
100	_	_	B-PARAM
calories	_	_	B-OBJ_NAME
.	_	_	O
If	_	_	O
they	_	_	O
schedule	_	_	O
that	_	_	O
the	_	_	O
elderly	_	_	O
need	_	_	O
in	_	_	O
total	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
12000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
fibre	_	_	O
and	_	_	O
300	_	_	B-LIMIT
mg	_	_	O
of	_	_	O
iron	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
cups	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
the	_	_	O
nurses	_	_	O
schedule	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
seniors	_	_	O
’	_	_	O
total	_	_	O
caloric	_	_	B-OBJ_NAME
intake	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
disease	_	_	O
testing	_	_	O
station	_	_	O
is	_	_	O
conducting	_	_	O
a	_	_	O
temperature	_	_	B-VAR
check	_	_	I-VAR
and/or	_	_	O
a	_	_	O
blood	_	_	B-VAR
test	_	_	I-VAR
on	_	_	O
each	_	_	O
patient	_	_	O
.	_	_	O
A	_	_	O
temperature	_	_	B-VAR
check	_	_	I-VAR
takes	_	_	O
2	_	_	B-PARAM
minutes	_	_	O
while	_	_	O
a	_	_	O
blood	_	_	B-VAR
test	_	_	I-VAR
takes	_	_	O
10	_	_	B-PARAM
minutes	_	_	O
.	_	_	O
The	_	_	O
disease	_	_	O
testing	_	_	O
station	_	_	O
must	_	_	O
conduct	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
45	_	_	B-LIMIT
blood	_	_	B-VAR
tests	_	_	I-VAR
.	_	_	O
Since	_	_	O
the	_	_	O
temperature	_	_	B-VAR
check	_	_	I-VAR
is	_	_	O
recommended	_	_	O
to	_	_	O
be	_	_	O
performed	_	_	O
on	_	_	O
most	_	_	O
people	_	_	O
,	_	_	O
the	_	_	O
testing	_	_	O
station	_	_	O
requires	_	_	O
that	_	_	O
the	_	_	O
temperature	_	_	B-VAR
check	_	_	I-VAR
is	_	_	O
performed	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
many	_	_	O
as	_	_	O
the	_	_	O
blood	_	_	B-VAR
test	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
disease	_	_	O
testing	_	_	O
station	_	_	O
only	_	_	B-CONST_DIR
has	_	_	O
a	_	_	O
total	_	_	O
of	_	_	O
22000	_	_	B-LIMIT
staff	_	_	O
minutes	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
test	_	_	B-VAR
or	_	_	O
check	_	_	B-VAR
should	_	_	O
be	_	_	O
done	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
patients	_	_	I-OBJ_NAME
seen	_	_	O
?	_	_	O

In	_	_	O
a	_	_	O
science	_	_	O
fair	_	_	O
,	_	_	O
there	_	_	O
are	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
tables	_	_	O
that	_	_	O
can	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
display	_	_	O
the	_	_	O
children	_	_	O
’s	_	_	O
science	_	_	O
experiments	_	_	O
.	_	_	O
At	_	_	O
the	_	_	O
circular	_	_	B-VAR
tables	_	_	I-VAR
,	_	_	O
4	_	_	B-PARAM
poster	_	_	O
boards	_	_	O
and	_	_	O
5	_	_	B-PARAM
participants	_	_	O
can	_	_	O
fit	_	_	O
around	_	_	O
the	_	_	O
table	_	_	O
to	_	_	O
cater	_	_	O
to	_	_	O
8	_	_	B-PARAM
guests	_	_	B-OBJ_NAME
.	_	_	O
At	_	_	O
the	_	_	O
rectangular	_	_	B-VAR
tables	_	_	I-VAR
,	_	_	O
4	_	_	B-PARAM
poster	_	_	O
boards	_	_	O
and	_	_	O
4	_	_	B-PARAM
participants	_	_	O
can	_	_	O
fit	_	_	O
around	_	_	O
the	_	_	O
table	_	_	O
to	_	_	O
cater	_	_	O
to	_	_	O
12	_	_	B-PARAM
guests	_	_	B-OBJ_NAME
.	_	_	O
However	_	_	O
,	_	_	O
each	_	_	O
circular	_	_	B-VAR
table	_	_	I-VAR
takes	_	_	O
up	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
space	_	_	O
while	_	_	O
each	_	_	O
rectangular	_	_	B-VAR
table	_	_	I-VAR
takes	_	_	O
up	_	_	O
20	_	_	B-PARAM
units	_	_	O
of	_	_	O
space	_	_	O
.	_	_	O
The	_	_	O
science	_	_	O
fair	_	_	O
has	_	_	O
must	_	_	O
be	_	_	O
able	_	_	O
to	_	_	O
fit	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
500	_	_	B-LIMIT
participants	_	_	O
and	_	_	O
300	_	_	B-LIMIT
poster	_	_	O
boards	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
science	_	_	O
fair	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
1900	_	_	B-LIMIT
units	_	_	O
of	_	_	O
space	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
table	_	_	O
should	_	_	O
be	_	_	O
set	_	_	O
up	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
catered	_	_	I-OBJ_NAME
guests	_	_	I-OBJ_NAME
?	_	_	O

Both	_	_	O
coconut	_	_	B-VAR
oil	_	_	I-VAR
and	_	_	O
lavender	_	_	B-VAR
need	_	_	O
to	_	_	O
be	_	_	O
added	_	_	O
to	_	_	O
a	_	_	O
body	_	_	O
wash	_	_	O
.	_	_	O
One	_	_	O
unit	_	_	O
of	_	_	O
coconut	_	_	B-VAR
oil	_	_	I-VAR
takes	_	_	O
0.7	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
to	_	_	O
be	_	_	O
effective	_	_	O
while	_	_	O
one	_	_	O
unit	_	_	O
of	_	_	O
lavender	_	_	B-VAR
takes	_	_	O
0.9	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
to	_	_	O
be	_	_	O
effective	_	_	O
.	_	_	O
The	_	_	O
body	_	_	O
wash	_	_	O
must	_	_	O
contain	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
300	_	_	B-LIMIT
units	_	_	O
of	_	_	O
coconut	_	_	B-VAR
oil	_	_	I-VAR
and	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
550	_	_	B-LIMIT
units	_	_	O
of	_	_	O
both	_	_	O
ingredients	_	_	O
.	_	_	O
Since	_	_	O
too	_	_	O
much	_	_	O
coconut	_	_	B-VAR
oil	_	_	I-VAR
can	_	_	O
make	_	_	O
the	_	_	O
body	_	_	O
wash	_	_	O
too	_	_	O
oily	_	_	O
,	_	_	O
there	_	_	O
can	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
thrice	_	_	B-PARAM
the	_	_	O
amount	_	_	O
of	_	_	O
coconut	_	_	B-VAR
oil	_	_	I-VAR
as	_	_	O
lavenders	_	_	B-VAR
in	_	_	O
the	_	_	O
body	_	_	O
wash	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
units	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
added	_	_	O
to	_	_	O
the	_	_	O
body	_	_	O
wash	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
amount	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
time	_	_	I-OBJ_NAME
it	_	_	O
takes	_	_	O
for	_	_	O
the	_	_	O
mixture	_	_	O
to	_	_	O
be	_	_	O
effective	_	_	O
?	_	_	O
(	_	_	O
Note	_	_	O
:	_	_	O
one	_	_	O
must	_	_	O
be	_	_	O
added	_	_	O
before	_	_	O
the	_	_	O
other	_	_	O
)	_	_	O

A	_	_	O
drop	_	_	O
-	_	_	O
in	_	_	O
clinic	_	_	O
is	_	_	O
performing	_	_	O
a	_	_	O
test	_	_	B-OBJ_NAME
either	_	_	O
through	_	_	O
the	_	_	O
ear	_	_	B-VAR
or	_	_	O
blood	_	_	B-VAR
.	_	_	O
A	_	_	O
blood	_	_	B-VAR
test	_	_	I-VAR
takes	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
perform	_	_	O
while	_	_	O
an	_	_	O
ear	_	_	B-VAR
test	_	_	I-VAR
takes	_	_	O
5	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
perform	_	_	O
.	_	_	O
Since	_	_	O
the	_	_	O
blood	_	_	B-VAR
test	_	_	I-VAR
is	_	_	O
more	_	_	O
accurate	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
three	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
many	_	_	O
blood	_	_	B-VAR
tests	_	_	I-VAR
should	_	_	O
be	_	_	O
performed	_	_	O
as	_	_	O
ear	_	_	B-VAR
tests	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
12	_	_	B-LIMIT
ear	_	_	B-VAR
tests	_	_	I-VAR
must	_	_	O
be	_	_	O
administered	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
drop	_	_	O
-	_	_	O
in	_	_	O
clinic	_	_	O
operates	_	_	B-CONST_DIR
for	_	_	O
7525	_	_	B-LIMIT
minutes	_	_	O
,	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
tests	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
performed	_	_	O
.	_	_	O

A	_	_	O
researcher	_	_	O
must	_	_	O
perform	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
experiments	_	_	O
,	_	_	O
in	_	_	B-VAR
-	_	_	I-VAR
vivo	_	_	I-VAR
and	_	_	O
ex	_	_	B-VAR
-	_	_	I-VAR
vivo	_	_	I-VAR
.	_	_	O
In	_	_	B-VAR
-	_	_	I-VAR
vivo	_	_	I-VAR
experiments	_	_	I-VAR
requires	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
prepare	_	_	O
and	_	_	O
60	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
execute	_	_	O
.	_	_	O
Ex	_	_	B-VAR
-	_	_	I-VAR
vivo	_	_	I-VAR
experiments	_	_	I-VAR
require	_	_	O
45	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
prepare	_	_	O
and	_	_	O
30	_	_	B-PARAM
minutes	_	_	O
to	_	_	O
execute	_	_	O
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
in	_	_	B-VAR
-	_	_	I-VAR
vivo	_	_	I-VAR
experiments	_	_	I-VAR
gives	_	_	O
the	_	_	O
researcher	_	_	O
2	_	_	B-PARAM
units	_	_	O
of	_	_	O
radiation	_	_	B-OBJ_NAME
while	_	_	O
ex	_	_	B-VAR
-	_	_	I-VAR
vivo	_	_	I-VAR
experiments	_	_	I-VAR
give	_	_	O
the	_	_	O
researcher	_	_	O
3	_	_	B-PARAM
unites	_	_	O
of	_	_	O
radiation	_	_	B-OBJ_NAME
.	_	_	O
At	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
400	_	_	B-LIMIT
minutes	_	_	O
can	_	_	O
be	_	_	O
used	_	_	O
for	_	_	O
preparation	_	_	O
and	_	_	O
500	_	_	B-LIMIT
minutes	_	_	O
for	_	_	O
execution	_	_	O
of	_	_	O
the	_	_	O
experiment	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
experiment	_	_	O
should	_	_	O
be	_	_	O
scheduled	_	_	O
by	_	_	O
the	_	_	O
researcher	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
radiation	_	_	I-OBJ_NAME
received	_	_	O
by	_	_	O
the	_	_	O
researcher	_	_	O
?	_	_	O

Both	_	_	O
chemical	_	_	B-VAR
A	_	_	I-VAR
and	_	_	O
chemical	_	_	B-VAR
B	_	_	I-VAR
need	_	_	O
to	_	_	O
be	_	_	O
added	_	_	O
to	_	_	O
a	_	_	O
mixer	_	_	O
for	_	_	O
making	_	_	O
bread	_	_	O
.	_	_	O
One	_	_	O
unit	_	_	O
of	_	_	O
chemical	_	_	B-VAR
A	_	_	I-VAR
takes	_	_	O
30	_	_	B-PARAM
seconds	_	_	B-OBJ_NAME
to	_	_	O
be	_	_	O
effective	_	_	O
while	_	_	O
one	_	_	O
unit	_	_	O
of	_	_	O
chemical	_	_	B-VAR
B	_	_	I-VAR
takes	_	_	O
45	_	_	B-PARAM
seconds	_	_	B-OBJ_NAME
to	_	_	O
be	_	_	O
effective	_	_	O
.	_	_	O
Because	_	_	O
chemical	_	_	B-VAR
A	_	_	I-VAR
can	_	_	O
be	_	_	O
dangerous	_	_	O
,	_	_	O
there	_	_	O
has	_	_	O
to	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
a	_	_	O
third	_	_	B-PARAM
as	_	_	O
much	_	_	O
chemical	_	_	B-VAR
A	_	_	I-VAR
as	_	_	O
chemical	_	_	B-VAR
B	_	_	I-VAR
in	_	_	O
the	_	_	O
mixer	_	_	O
.	_	_	O
If	_	_	O
there	_	_	O
has	_	_	O
to	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
300	_	_	B-LIMIT
units	_	_	O
of	_	_	O
chemical	_	_	B-VAR
A	_	_	I-VAR
in	_	_	O
the	_	_	O
mixer	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
total	_	_	O
chemicals	_	_	O
in	_	_	O
the	_	_	O
mixer	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
units	_	_	O
of	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
added	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
time	_	_	I-OBJ_NAME
it	_	_	O
takes	_	_	O
for	_	_	O
the	_	_	O
mixed	_	_	O
bread	_	_	O
to	_	_	O
be	_	_	O
ready	_	_	O
?	_	_	O

A	_	_	O
research	_	_	O
group	_	_	O
is	_	_	O
making	_	_	O
fabric	_	_	O
and	_	_	O
plastic	_	_	O
using	_	_	O
two	_	_	O
methods	_	_	O
,	_	_	O
method	_	_	B-VAR
A	_	_	I-VAR
and	_	_	O
method	_	_	B-VAR
B.	_	_	I-VAR
Method	_	_	B-VAR
A	_	_	I-VAR
produces	_	_	O
25	_	_	B-PARAM
units	_	_	O
of	_	_	O
fabric	_	_	O
and	_	_	O
14	_	_	B-PARAM
units	_	_	O
of	_	_	O
plastic	_	_	O
per	_	_	O
hour	_	_	B-OBJ_NAME
.	_	_	O
Method	_	_	B-VAR
B	_	_	I-VAR
produces	_	_	O
45	_	_	B-PARAM
units	_	_	O
of	_	_	O
fabric	_	_	O
and	_	_	O
25	_	_	B-PARAM
units	_	_	O
of	_	_	O
plastic	_	_	O
per	_	_	O
hour	_	_	B-OBJ_NAME
.	_	_	O
Method	_	_	B-VAR
A	_	_	I-VAR
requires	_	_	O
60	_	_	B-PARAM
units	_	_	O
of	_	_	O
a	_	_	O
special	_	_	O
element	_	_	O
while	_	_	O
method	_	_	B-VAR
B	_	_	I-VAR
requires	_	_	O
65	_	_	B-PARAM
units	_	_	O
of	_	_	O
the	_	_	O
same	_	_	O
special	_	_	O
element	_	_	O
.	_	_	O
The	_	_	O
research	_	_	O
group	_	_	O
has	_	_	O
available	_	_	B-CONST_DIR
3500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
the	_	_	O
special	_	_	O
element	_	_	O
and	_	_	O
must	_	_	O
make	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1400	_	_	B-LIMIT
units	_	_	O
of	_	_	O
fabric	_	_	O
and	_	_	O
1000	_	_	B-LIMIT
units	_	_	O
of	_	_	O
plastic	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
method	_	_	O
should	_	_	O
be	_	_	O
executed	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
time	_	_	B-OBJ_NAME
needed	_	_	O
?	_	_	O

A	_	_	O
hospital	_	_	O
purchases	_	_	O
two	_	_	O
pills	_	_	O
available	_	_	O
for	_	_	O
the	_	_	O
patients	_	_	O
to	_	_	O
take	_	_	O
one	_	_	O
at	_	_	O
a	_	_	O
time	_	_	O
.	_	_	O
One	_	_	O
pill	_	_	O
is	_	_	O
taken	_	_	O
as	_	_	O
a	_	_	O
prevention	_	_	B-VAR
and	_	_	O
another	_	_	O
is	_	_	O
taken	_	_	O
for	_	_	O
treatment	_	_	B-VAR
.	_	_	O
The	_	_	O
prevention	_	_	B-VAR
pill	_	_	I-VAR
takes	_	_	O
15	_	_	B-PARAM
dollars	_	_	O
to	_	_	O
make	_	_	O
while	_	_	O
the	_	_	O
treatment	_	_	B-VAR
pill	_	_	I-VAR
takes	_	_	O
25	_	_	B-PARAM
dollars	_	_	O
to	_	_	O
make	_	_	O
.	_	_	O
Since	_	_	O
the	_	_	O
prevention	_	_	B-VAR
pill	_	_	I-VAR
is	_	_	O
in	_	_	O
higher	_	_	O
demand	_	_	O
,	_	_	O
the	_	_	O
hospital	_	_	O
must	_	_	O
purchase	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
two	_	_	B-PARAM
times	_	_	I-PARAM
as	_	_	O
many	_	_	O
prevention	_	_	B-VAR
pills	_	_	I-VAR
as	_	_	O
treatment	_	_	B-VAR
pills	_	_	I-VAR
.	_	_	O
In	_	_	O
addition	_	_	O
,	_	_	O
the	_	_	O
hospital	_	_	O
must	_	_	O
purchase	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
50	_	_	B-LIMIT
treatment	_	_	B-VAR
pills	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
clinic	_	_	O
only	_	_	O
has	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
10000	_	_	B-LIMIT
dollars	_	_	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
treated	_	_	O
.	_	_	O

A	_	_	O
candle	_	_	O
-	_	_	O
making	_	_	O
company	_	_	O
can	_	_	O
move	_	_	O
their	_	_	O
inventory	_	_	O
of	_	_	O
candles	_	_	O
using	_	_	O
freight	_	_	B-VAR
and	_	_	O
air	_	_	B-VAR
.	_	_	O
Freight	_	_	B-VAR
can	_	_	O
transport	_	_	O
5	_	_	B-PARAM
tons	_	_	O
per	_	_	O
trip	_	_	O
while	_	_	O
using	_	_	O
air	_	_	B-VAR
can	_	_	O
transport	_	_	O
3	_	_	B-PARAM
tons	_	_	O
per	_	_	O
trip	_	_	O
.	_	_	O
Since	_	_	O
freight	_	_	B-VAR
take	_	_	O
longer	_	_	O
,	_	_	O
the	_	_	O
cost	_	_	O
for	_	_	O
each	_	_	O
freight	_	_	B-VAR
trip	_	_	I-VAR
is	_	_	O
$	_	_	O
300	_	_	B-PARAM
while	_	_	O
the	_	_	O
cost	_	_	O
over	_	_	O
air	_	_	B-VAR
for	_	_	O
each	_	_	O
trip	_	_	O
is	_	_	O
$	_	_	O
550	_	_	B-PARAM
.	_	_	O
The	_	_	O
company	_	_	O
needs	_	_	O
to	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
200	_	_	B-LIMIT
tons	_	_	O
of	_	_	O
candles	_	_	O
and	_	_	O
they	_	_	O
have	_	_	O
a	_	_	O
budget	_	_	B-CONST_DIR
of	_	_	O
$	_	_	O
20000	_	_	B-LIMIT
.	_	_	O
Additionally	_	_	O
,	_	_	O
due	_	_	O
to	_	_	O
some	_	_	O
urgent	_	_	O
orders	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
30	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
tons	_	_	O
of	_	_	O
candles	_	_	O
must	_	_	O
be	_	_	O
transported	_	_	O
through	_	_	O
air	_	_	B-VAR
.	_	_	O
There	_	_	O
must	_	_	O
also	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
trips	_	_	O
through	_	_	O
freight	_	_	B-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
trip	_	_	O
by	_	_	O
each	_	_	O
should	_	_	O
be	_	_	O
scheduled	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
trips	_	_	I-OBJ_NAME
?	_	_	O

Due	_	_	O
to	_	_	O
an	_	_	O
accident	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
550	_	_	B-LIMIT
locals	_	_	O
must	_	_	O
be	_	_	O
moved	_	_	O
across	_	_	O
a	_	_	O
lake	_	_	O
.	_	_	O
They	_	_	O
can	_	_	O
either	_	_	O
be	_	_	O
transported	_	_	O
over	_	_	O
the	_	_	O
lake	_	_	O
by	_	_	O
a	_	_	O
kayak	_	_	B-VAR
or	_	_	O
a	_	_	O
motorboat	_	_	B-VAR
.	_	_	O
Kayaks	_	_	B-VAR
can	_	_	O
transport	_	_	O
4	_	_	B-PARAM
people	_	_	O
every	_	_	O
trip	_	_	O
and	_	_	O
motorboats	_	_	B-VAR
can	_	_	O
transport	_	_	O
5	_	_	B-PARAM
people	_	_	O
every	_	_	O
trip	_	_	O
.	_	_	O
Kayaks	_	_	B-VAR
take	_	_	O
5	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
per	_	_	I-OBJ_NAME
trip	_	_	I-OBJ_NAME
whereas	_	_	O
motorboats	_	_	B-VAR
take	_	_	O
3	_	_	B-PARAM
minutes	_	_	B-OBJ_NAME
per	_	_	I-OBJ_NAME
trip	_	_	I-OBJ_NAME
.	_	_	O
Due	_	_	O
to	_	_	O
the	_	_	O
limited	_	_	O
number	_	_	O
of	_	_	O
motorboats	_	_	B-VAR
available	_	_	O
to	_	_	O
the	_	_	O
locals	_	_	O
,	_	_	O
there	_	_	O
can	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
25	_	_	B-LIMIT
motorboat	_	_	B-VAR
trips	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
75	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
trips	_	_	O
should	_	_	O
be	_	_	O
by	_	_	O
kayak	_	_	B-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
transportation	_	_	O
method	_	_	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
time	_	_	I-OBJ_NAME
needed	_	_	O
to	_	_	O
transport	_	_	O
all	_	_	O
the	_	_	O
locals	_	_	O
?	_	_	O

An	_	_	O
airport	_	_	O
can	_	_	O
either	_	_	O
install	_	_	O
escalators	_	_	B-VAR
or	_	_	O
elevators	_	_	B-VAR
.	_	_	O
Escalators	_	_	B-VAR
can	_	_	O
transport	_	_	O
20	_	_	B-PARAM
people	_	_	O
every	_	_	O
minute	_	_	O
whereas	_	_	O
elevators	_	_	B-VAR
can	_	_	O
transport	_	_	O
8	_	_	B-PARAM
people	_	_	O
every	_	_	O
minute	_	_	O
.	_	_	O
Escalators	_	_	B-VAR
take	_	_	O
up	_	_	O
5	_	_	B-PARAM
units	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
space	_	_	I-OBJ_NAME
while	_	_	O
elevators	_	_	B-VAR
take	_	_	O
2	_	_	B-PARAM
units	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
space	_	_	I-OBJ_NAME
.	_	_	O
The	_	_	O
airport	_	_	O
needs	_	_	O
to	_	_	O
have	_	_	O
enough	_	_	O
capacity	_	_	O
to	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
400	_	_	B-LIMIT
people	_	_	O
every	_	_	O
minute	_	_	O
.	_	_	O
Additionally	_	_	O
,	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
three	_	_	B-LIMIT
times	_	_	O
more	_	_	O
escalators	_	_	B-VAR
than	_	_	O
elevators	_	_	B-VAR
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
2	_	_	B-LIMIT
elevators	_	_	B-VAR
must	_	_	O
be	_	_	O
used	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
should	_	_	O
the	_	_	O
airport	_	_	O
install	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
units	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
space	_	_	I-OBJ_NAME
taken	_	_	I-OBJ_NAME
?	_	_	O

An	_	_	O
amusement	_	_	O
park	_	_	O
has	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
games	_	_	O
:	_	_	O
throwing	_	_	B-VAR
and	_	_	O
climbing	_	_	B-VAR
games	_	_	I-VAR
.	_	_	O
Throwing	_	_	B-VAR
games	_	_	I-VAR
attract	_	_	O
15	_	_	B-PARAM
customers	_	_	B-OBJ_NAME
every	_	_	I-OBJ_NAME
hour	_	_	I-OBJ_NAME
and	_	_	O
climbing	_	_	B-VAR
games	_	_	I-VAR
attract	_	_	O
8	_	_	B-PARAM
customers	_	_	B-OBJ_NAME
every	_	_	I-OBJ_NAME
hour	_	_	I-OBJ_NAME
.	_	_	O
Throwing	_	_	B-VAR
games	_	_	I-VAR
costs	_	_	O
the	_	_	O
amusement	_	_	O
park	_	_	O
$	_	_	O
2	_	_	B-PARAM
in	_	_	O
prizes	_	_	O
per	_	_	O
hour	_	_	O
whereas	_	_	O
climbing	_	_	B-VAR
games	_	_	I-VAR
cost	_	_	O
$	_	_	O
3	_	_	B-PARAM
in	_	_	O
prizes	_	_	O
per	_	_	O
hour	_	_	O
.	_	_	O
Since	_	_	O
throwing	_	_	B-VAR
games	_	_	I-VAR
yield	_	_	O
the	_	_	O
most	_	_	O
profit	_	_	O
,	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-PARAM
as	_	_	O
many	_	_	O
throwing	_	_	B-VAR
games	_	_	I-VAR
as	_	_	O
climbing	_	_	B-VAR
games	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
games	_	_	O
must	_	_	O
be	_	_	O
climbing	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
amusement	_	_	O
park	_	_	O
can	_	_	O
have	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
$	_	_	O
100	_	_	B-LIMIT
in	_	_	O
prizes	_	_	O
every	_	_	O
hour	_	_	O
,	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
customers	_	_	I-OBJ_NAME
attracted	_	_	I-OBJ_NAME
every	_	_	I-OBJ_NAME
hour	_	_	I-OBJ_NAME
.	_	_	O

The	_	_	O
government	_	_	O
is	_	_	O
reworking	_	_	O
the	_	_	O
pipes	_	_	O
to	_	_	O
transport	_	_	O
water	_	_	O
to	_	_	O
houses	_	_	O
in	_	_	O
the	_	_	O
area	_	_	O
.	_	_	O
The	_	_	O
water	_	_	O
can	_	_	O
be	_	_	O
transported	_	_	O
through	_	_	O
wide	_	_	B-VAR
pipes	_	_	I-VAR
or	_	_	O
narrow	_	_	B-VAR
pipes	_	_	I-VAR
.	_	_	O
Wide	_	_	B-VAR
pipes	_	_	I-VAR
can	_	_	O
transport	_	_	O
25	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	O
per	_	_	O
minute	_	_	O
and	_	_	O
narrow	_	_	B-VAR
pipes	_	_	I-VAR
can	_	_	O
transport	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
water	_	_	O
per	_	_	O
minute	_	_	O
.	_	_	O
Due	_	_	O
to	_	_	O
logistics	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
wide	_	_	B-VAR
pipes	_	_	I-VAR
can	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
a	_	_	B-PARAM
third	_	_	I-PARAM
the	_	_	O
number	_	_	O
of	_	_	O
narrow	_	_	B-VAR
pipes	_	_	I-VAR
.	_	_	O
If	_	_	O
there	_	_	O
needs	_	_	O
to	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
900	_	_	B-LIMIT
units	_	_	O
of	_	_	O
water	_	_	O
transported	_	_	O
every	_	_	O
minute	_	_	O
,	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
wide	_	_	B-VAR
pipes	_	_	I-VAR
must	_	_	O
be	_	_	O
used	_	_	O
,	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
pipes	_	_	I-OBJ_NAME
required	_	_	O
.	_	_	O

A	_	_	O
daycare	_	_	O
center	_	_	O
has	_	_	O
children	_	_	O
they	_	_	O
must	_	_	O
pick	_	_	O
up	_	_	O
and	_	_	O
can	_	_	O
use	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
vehicles	_	_	O
:	_	_	O
bus	_	_	B-VAR
or	_	_	O
a	_	_	O
personal	_	_	B-VAR
car	_	_	I-VAR
.	_	_	O
A	_	_	O
bus	_	_	B-VAR
can	_	_	O
carry	_	_	O
9	_	_	B-PARAM
children	_	_	O
while	_	_	O
a	_	_	O
personal	_	_	B-VAR
car	_	_	I-VAR
can	_	_	O
carry	_	_	O
4	_	_	B-PARAM
children	_	_	O
.	_	_	O
The	_	_	O
daycare	_	_	O
has	_	_	O
to	_	_	O
pick	_	_	O
up	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
100	_	_	B-LIMIT
children	_	_	O
.	_	_	O
Additionally	_	_	O
,	_	_	O
due	_	_	O
to	_	_	O
limitations	_	_	O
of	_	_	O
pollution	_	_	O
,	_	_	O
there	_	_	O
must	_	_	B-CONST_DIR
be	_	_	I-CONST_DIR
more	_	_	I-CONST_DIR
buses	_	_	B-VAR
than	_	_	O
personal	_	_	B-VAR
cars	_	_	I-VAR
.	_	_	O
But	_	_	O
some	_	_	O
children	_	_	O
require	_	_	O
extra	_	_	O
attention	_	_	O
.	_	_	O
Therefore	_	_	O
,	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
personal	_	_	B-VAR
cars	_	_	I-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
form	_	_	O
of	_	_	O
transportation	_	_	O
should	_	_	O
the	_	_	O
daycare	_	_	O
center	_	_	O
schedule	_	_	O
for	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
vehicles	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
hospital	_	_	O
can	_	_	O
transport	_	_	O
their	_	_	O
patients	_	_	O
either	_	_	O
using	_	_	O
a	_	_	O
type	_	_	B-VAR
II	_	_	I-VAR
ambulance	_	_	I-VAR
or	_	_	O
hospital	_	_	B-VAR
van	_	_	I-VAR
.	_	_	O
The	_	_	O
hospital	_	_	O
needs	_	_	B-CONST_DIR
to	_	_	I-CONST_DIR
transport	_	_	I-CONST_DIR
320	_	_	B-LIMIT
patients	_	_	O
every	_	_	O
day	_	_	O
.	_	_	O
A	_	_	O
type	_	_	B-VAR
II	_	_	I-VAR
ambulance	_	_	I-VAR
is	_	_	O
mounted	_	_	O
on	_	_	O
a	_	_	O
truck	_	_	O
-	_	_	O
style	_	_	O
chassis	_	_	O
and	_	_	O
can	_	_	O
move	_	_	O
20	_	_	B-PARAM
patients	_	_	O
every	_	_	O
shift	_	_	O
and	_	_	O
costs	_	_	B-OBJ_NAME
the	_	_	O
hospital	_	_	O
(	_	_	O
including	_	_	O
gas	_	_	O
and	_	_	O
salary	_	_	O
)	_	_	O
$	_	_	O
820	_	_	B-PARAM
.	_	_	O
A	_	_	O
hospital	_	_	B-VAR
van	_	_	I-VAR
can	_	_	O
move	_	_	O
15	_	_	B-PARAM
patients	_	_	O
and	_	_	O
costs	_	_	B-OBJ_NAME
the	_	_	O
hospital	_	_	O
$	_	_	O
550	_	_	B-PARAM
every	_	_	O
shift	_	_	O
.	_	_	O
The	_	_	O
hospital	_	_	O
can	_	_	O
have	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
60	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
shifts	_	_	O
be	_	_	O
hospital	_	_	B-VAR
vans	_	_	I-VAR
due	_	_	O
to	_	_	O
union	_	_	O
limitations	_	_	O
of	_	_	O
the	_	_	O
type	_	_	B-VAR
II	_	_	I-VAR
ambulance	_	_	I-VAR
drivers	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
shift	_	_	O
using	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
vehicle	_	_	O
should	_	_	O
be	_	_	O
scheduled	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
cost	_	_	I-OBJ_NAME
to	_	_	O
the	_	_	O
hospital	_	_	O
?	_	_	O

A	_	_	O
production	_	_	O
company	_	_	O
needs	_	_	O
to	_	_	O
transport	_	_	O
their	_	_	O
equipment	_	_	O
and	_	_	O
staff	_	_	O
for	_	_	O
a	_	_	O
movie	_	_	O
they	_	_	O
are	_	_	O
shooting	_	_	O
using	_	_	O
large	_	_	B-VAR
mobile	_	_	I-VAR
production	_	_	I-VAR
units	_	_	I-VAR
or	_	_	O
small	_	_	B-VAR
mobile	_	_	I-VAR
production	_	_	I-VAR
units	_	_	I-VAR
.	_	_	O
Large	_	_	B-VAR
mobile	_	_	I-VAR
production	_	_	I-VAR
units	_	_	I-VAR
can	_	_	O
hold	_	_	O
6	_	_	B-PARAM
people	_	_	O
and	_	_	O
takes	_	_	O
up	_	_	O
2	_	_	B-PARAM
parking	_	_	B-OBJ_NAME
spots	_	_	I-OBJ_NAME
whereas	_	_	O
small	_	_	B-VAR
mobile	_	_	I-VAR
production	_	_	I-VAR
units	_	_	I-VAR
can	_	_	O
hold	_	_	O
only	_	_	O
2	_	_	B-PARAM
people	_	_	O
and	_	_	O
takes	_	_	O
up	_	_	O
1	_	_	B-PARAM
parking	_	_	B-OBJ_NAME
spot	_	_	I-OBJ_NAME
.	_	_	O
Movie	_	_	O
stars	_	_	O
prefer	_	_	O
to	_	_	O
have	_	_	O
their	_	_	O
small	_	_	B-VAR
mobile	_	_	I-VAR
production	_	_	I-VAR
unit	_	_	I-VAR
to	_	_	O
share	_	_	O
with	_	_	O
a	_	_	O
close	_	_	O
staff	_	_	O
,	_	_	O
therefore	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
units	_	_	O
must	_	_	O
be	_	_	O
small	_	_	B-VAR
mobile	_	_	I-VAR
units	_	_	I-VAR
.	_	_	O
However	_	_	O
,	_	_	O
due	_	_	O
to	_	_	O
logistic	_	_	O
limitations	_	_	O
,	_	_	O
large	_	_	B-VAR
mobile	_	_	I-VAR
production	_	_	I-VAR
units	_	_	I-VAR
are	_	_	O
more	_	_	O
space	_	_	O
efficient	_	_	O
per	_	_	O
spot	_	_	O
,	_	_	O
they	_	_	O
must	_	_	O
make	_	_	O
up	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
75	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
all	_	_	O
vehicles	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
movie	_	_	O
needs	_	_	B-CONST_DIR
to	_	_	I-CONST_DIR
transport	_	_	I-CONST_DIR
80	_	_	B-LIMIT
people	_	_	O
,	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
parking	_	_	I-OBJ_NAME
spots	_	_	I-OBJ_NAME
required	_	_	O
by	_	_	O
this	_	_	O
production	_	_	O
.	_	_	O

A	_	_	O
taxi	_	_	O
company	_	_	O
will	_	_	O
purchase	_	_	O
vehicles	_	_	O
to	_	_	O
rent	_	_	O
to	_	_	O
their	_	_	O
drivers	_	_	O
.	_	_	O
They	_	_	O
are	_	_	O
interested	_	_	O
in	_	_	O
purchasing	_	_	O
either	_	_	O
motorcycles	_	_	B-VAR
or	_	_	O
sedans	_	_	B-VAR
.	_	_	O
A	_	_	O
motorcycle	_	_	B-VAR
can	_	_	O
transport	_	_	O
30	_	_	B-PARAM
people	_	_	O
,	_	_	O
produces	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
pollution	_	_	O
,	_	_	O
and	_	_	O
earns	_	_	B-OBJ_NAME
the	_	_	O
taxi	_	_	O
company	_	_	O
$	_	_	O
100	_	_	B-PARAM
per	_	_	O
shift	_	_	O
.	_	_	O
A	_	_	O
sedan	_	_	B-VAR
can	_	_	O
transport	_	_	O
70	_	_	B-PARAM
people	_	_	O
,	_	_	O
produces	_	_	O
15	_	_	B-PARAM
units	_	_	O
of	_	_	O
pollution	_	_	O
and	_	_	O
earns	_	_	B-OBJ_NAME
the	_	_	O
company	_	_	O
$	_	_	O
225	_	_	B-PARAM
per	_	_	O
shift	_	_	O
.	_	_	O
Because	_	_	O
not	_	_	O
every	_	_	O
customer	_	_	O
is	_	_	O
comfortable	_	_	O
with	_	_	O
a	_	_	O
motorcycle	_	_	B-VAR
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
25	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
vehicles	_	_	O
can	_	_	O
be	_	_	O
motorcycles	_	_	B-VAR
.	_	_	O
Additionally	_	_	O
,	_	_	O
the	_	_	O
company	_	_	O
has	_	_	O
committed	_	_	O
to	_	_	O
producing	_	_	O
less	_	_	B-CONST_DIR
than	_	_	I-CONST_DIR
200	_	_	B-LIMIT
units	_	_	O
of	_	_	O
pollution	_	_	O
.	_	_	O
The	_	_	O
company	_	_	O
needs	_	_	O
to	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
1200	_	_	B-LIMIT
people	_	_	O
every	_	_	O
shift	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
vehicle	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
earnings	_	_	I-OBJ_NAME
for	_	_	O
the	_	_	O
taxi	_	_	O
company	_	_	O
per	_	_	O
shift	_	_	O
?	_	_	O

A	_	_	O
mask	_	_	O
making	_	_	O
company	_	_	O
ships	_	_	O
masks	_	_	O
to	_	_	O
their	_	_	O
retail	_	_	O
stores	_	_	O
using	_	_	O
small	_	_	B-VAR
boxes	_	_	I-VAR
and	_	_	O
large	_	_	B-VAR
boxes	_	_	I-VAR
.	_	_	O
A	_	_	O
small	_	_	B-VAR
box	_	_	I-VAR
holds	_	_	O
25	_	_	B-PARAM
masks	_	_	O
whereas	_	_	O
a	_	_	O
large	_	_	B-VAR
box	_	_	I-VAR
holds	_	_	O
45	_	_	B-PARAM
masks	_	_	O
.	_	_	O
Since	_	_	O
small	_	_	B-VAR
boxes	_	_	I-VAR
are	_	_	O
easier	_	_	O
to	_	_	O
stack	_	_	O
and	_	_	O
will	_	_	O
be	_	_	O
used	_	_	O
first	_	_	O
to	_	_	O
stock	_	_	O
stores	_	_	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
small	_	_	B-VAR
boxes	_	_	I-VAR
as	_	_	O
large	_	_	B-VAR
boxes	_	_	I-VAR
.	_	_	O
Additionally	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
5	_	_	B-LIMIT
large	_	_	B-VAR
boxes	_	_	I-VAR
must	_	_	O
be	_	_	O
used	_	_	O
.	_	_	O
If	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
750	_	_	B-LIMIT
masks	_	_	O
are	_	_	O
required	_	_	O
to	_	_	O
be	_	_	O
distributed	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
size	_	_	O
of	_	_	O
box	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
boxes	_	_	I-OBJ_NAME
needed	_	_	O
?	_	_	O

A	_	_	O
company	_	_	O
in	_	_	O
the	_	_	O
desert	_	_	O
can	_	_	O
transport	_	_	O
goods	_	_	O
to	_	_	O
rural	_	_	O
cities	_	_	O
either	_	_	O
by	_	_	O
camel	_	_	B-VAR
caravans	_	_	I-VAR
or	_	_	O
desert	_	_	B-VAR
trucks	_	_	I-VAR
.	_	_	O
A	_	_	O
camel	_	_	B-VAR
caravan	_	_	I-VAR
can	_	_	O
deliver	_	_	O
50	_	_	B-PARAM
units	_	_	O
of	_	_	O
goods	_	_	O
per	_	_	O
trip	_	_	O
and	_	_	O
takes	_	_	O
12	_	_	B-PARAM
hours	_	_	B-OBJ_NAME
.	_	_	O
A	_	_	O
desert	_	_	B-VAR
truck	_	_	I-VAR
can	_	_	O
deliver	_	_	O
150	_	_	B-PARAM
units	_	_	O
of	_	_	O
goods	_	_	O
per	_	_	O
trip	_	_	O
and	_	_	O
takes	_	_	O
5	_	_	B-PARAM
hours	_	_	B-OBJ_NAME
.	_	_	O
However	_	_	O
,	_	_	O
due	_	_	O
to	_	_	O
the	_	_	O
cost	_	_	O
of	_	_	O
fuel	_	_	O
,	_	_	O
the	_	_	O
company	_	_	O
prefers	_	_	O
to	_	_	O
have	_	_	O
more	_	_	B-CONST_DIR
camel	_	_	B-VAR
caravans	_	_	I-VAR
than	_	_	O
desert	_	_	B-VAR
trucks	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
company	_	_	O
needs	_	_	B-CONST_DIR
to	_	_	I-CONST_DIR
deliver	_	_	I-CONST_DIR
1500	_	_	B-LIMIT
units	_	_	O
of	_	_	O
goods	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
method	_	_	O
of	_	_	O
transportation	_	_	O
should	_	_	O
the	_	_	O
company	_	_	O
organize	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
hours	_	_	I-OBJ_NAME
required	_	_	O
?	_	_	O

A	_	_	O
dim	_	_	O
sum	_	_	O
restaurant	_	_	O
can	_	_	O
deliver	_	_	O
their	_	_	O
food	_	_	O
by	_	_	O
cart	_	_	B-VAR
or	_	_	O
by	_	_	O
hand	_	_	B-VAR
.	_	_	O
Servers	_	_	O
can	_	_	O
deliver	_	_	O
by	_	_	O
cart	_	_	B-VAR
and	_	_	O
have	_	_	O
70	_	_	B-PARAM
customer	_	_	O
interactions	_	_	O
and	_	_	O
will	_	_	O
have	_	_	O
to	_	_	O
refill	_	_	O
food	_	_	O
five	_	_	B-PARAM
times	_	_	B-OBJ_NAME
an	_	_	I-OBJ_NAME
hour	_	_	I-OBJ_NAME
.	_	_	O
They	_	_	O
can	_	_	O
also	_	_	O
deliver	_	_	O
more	_	_	O
food	_	_	O
by	_	_	O
hand	_	_	B-VAR
,	_	_	O
due	_	_	O
to	_	_	O
the	_	_	O
increased	_	_	O
mobility	_	_	O
,	_	_	O
and	_	_	O
have	_	_	O
85	_	_	B-PARAM
customer	_	_	O
interactions	_	_	O
while	_	_	O
refilling	_	_	O
food	_	_	O
twenty	_	_	B-PARAM
times	_	_	B-OBJ_NAME
an	_	_	I-OBJ_NAME
hour	_	_	I-OBJ_NAME
.	_	_	O
However	_	_	O
,	_	_	O
the	_	_	O
customers	_	_	O
get	_	_	O
more	_	_	O
options	_	_	O
when	_	_	O
delivering	_	_	O
by	_	_	O
cart	_	_	O
,	_	_	O
therefore	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
70	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
delivery	_	_	O
shifts	_	_	O
must	_	_	O
be	_	_	O
by	_	_	O
cart	_	_	B-VAR
.	_	_	O
There	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
3	_	_	B-LIMIT
servers	_	_	O
delivering	_	_	O
by	_	_	O
hand	_	_	B-VAR
for	_	_	O
their	_	_	O
direct	_	_	O
customer	_	_	O
service	_	_	O
.	_	_	O
If	_	_	O
the	_	_	O
restaurant	_	_	O
wants	_	_	O
to	_	_	O
have	_	_	B-CONST_DIR
4000	_	_	B-LIMIT
customer	_	_	O
interactions	_	_	O
per	_	_	O
hour	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
form	_	_	O
of	_	_	O
delivery	_	_	O
should	_	_	O
the	_	_	O
dim	_	_	O
sum	_	_	O
restaurant	_	_	O
schedule	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
refills	_	_	I-OBJ_NAME
per	_	_	I-OBJ_NAME
hour	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
concert	_	_	O
organizer	_	_	O
has	_	_	O
to	_	_	O
transport	_	_	O
equipment	_	_	O
using	_	_	O
carts	_	_	B-VAR
or	_	_	O
trolleys	_	_	B-VAR
.	_	_	O
Carts	_	_	B-VAR
can	_	_	O
transport	_	_	O
5	_	_	B-PARAM
kg	_	_	O
/	_	_	O
min	_	_	O
of	_	_	O
equipment	_	_	O
and	_	_	O
requires	_	_	O
2	_	_	B-PARAM
workers	_	_	B-OBJ_NAME
.	_	_	O
Trolleys	_	_	B-VAR
can	_	_	O
transport	_	_	O
7	_	_	B-PARAM
kg	_	_	O
/	_	_	O
min	_	_	O
of	_	_	O
equipment	_	_	O
and	_	_	O
requires	_	_	O
4	_	_	B-PARAM
workers	_	_	B-OBJ_NAME
.	_	_	O
There	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
12	_	_	B-LIMIT
trolleys	_	_	B-VAR
to	_	_	O
be	_	_	O
used	_	_	O
.	_	_	O
Additionally	_	_	O
,	_	_	O
only	_	_	O
a	_	_	O
maximum	_	_	B-CONST_DIR
of	_	_	O
40	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
transportation	_	_	O
can	_	_	O
be	_	_	O
using	_	_	O
trolleys	_	_	B-VAR
.	_	_	O
The	_	_	O
organizer	_	_	O
has	_	_	B-CONST_DIR
to	_	_	I-CONST_DIR
deliver	_	_	I-CONST_DIR
at	_	_	O
a	_	_	O
rate	_	_	O
of	_	_	O
100	_	_	B-LIMIT
kg	_	_	O
/	_	_	O
min	_	_	O
of	_	_	O
equipment	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
transportation	_	_	O
method	_	_	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
workers	_	_	I-OBJ_NAME
?	_	_	O

A	_	_	O
golf	_	_	O
course	_	_	O
is	_	_	O
hosting	_	_	O
an	_	_	O
event	_	_	O
and	_	_	O
can	_	_	O
transport	_	_	O
guests	_	_	O
using	_	_	O
either	_	_	O
golf	_	_	B-VAR
carts	_	_	I-VAR
or	_	_	O
pull	_	_	B-VAR
carts	_	_	I-VAR
.	_	_	O
A	_	_	O
golf	_	_	B-VAR
cart	_	_	I-VAR
can	_	_	O
take	_	_	O
4	_	_	B-PARAM
guests	_	_	O
while	_	_	O
a	_	_	O
pull	_	_	B-VAR
cart	_	_	I-VAR
can	_	_	O
take	_	_	O
1	_	_	B-PARAM
guest	_	_	O
.	_	_	O
Since	_	_	O
golf	_	_	B-VAR
carts	_	_	I-VAR
take	_	_	O
up	_	_	O
a	_	_	O
lot	_	_	O
of	_	_	O
space	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
60	_	_	B-LIMIT
%	_	_	O
of	_	_	O
carts	_	_	O
can	_	_	O
be	_	_	O
golf	_	_	B-VAR
carts	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
golf	_	_	O
course	_	_	O
needs	_	_	O
to	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
80	_	_	B-LIMIT
guests	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
cart	_	_	O
should	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
number	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
carts	_	_	I-OBJ_NAME
needed	_	_	O
?	_	_	O

A	_	_	O
cruise	_	_	O
company	_	_	O
can	_	_	O
either	_	_	O
have	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
trips	_	_	O
,	_	_	O
a	_	_	O
large	_	_	B-VAR
cruise	_	_	I-VAR
ship	_	_	I-VAR
or	_	_	O
a	_	_	O
small	_	_	B-VAR
cruise	_	_	I-VAR
ship	_	_	I-VAR
.	_	_	O
A	_	_	O
large	_	_	B-VAR
cruise	_	_	I-VAR
ship	_	_	I-VAR
trip	_	_	O
can	_	_	O
carry	_	_	O
2000	_	_	B-PARAM
customers	_	_	O
and	_	_	O
produces	_	_	O
20	_	_	B-PARAM
units	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
pollution	_	_	I-OBJ_NAME
.	_	_	O
A	_	_	O
small	_	_	B-VAR
cruise	_	_	I-VAR
ship	_	_	I-VAR
trip	_	_	O
can	_	_	O
carry	_	_	O
800	_	_	B-PARAM
customers	_	_	O
and	_	_	O
produces	_	_	O
15	_	_	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
most	_	_	I-CONST_DIR
7	_	_	B-LIMIT
large	_	_	B-VAR
cruise	_	_	I-VAR
ship	_	_	I-VAR
trips	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
40	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
total	_	_	O
trips	_	_	O
must	_	_	O
be	_	_	O
made	_	_	O
by	_	_	O
small	_	_	B-VAR
cruise	_	_	I-VAR
ships	_	_	I-VAR
.	_	_	O
If	_	_	O
the	_	_	O
cruise	_	_	O
company	_	_	O
aims	_	_	O
to	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20000	_	_	B-LIMIT
customers	_	_	O
,	_	_	O
how	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
size	_	_	O
of	_	_	O
cruise	_	_	O
ships	_	_	O
should	_	_	O
the	_	_	O
company	_	_	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
park	_	_	O
is	_	_	O
designing	_	_	O
their	_	_	O
trails	_	_	O
and	_	_	O
can	_	_	O
either	_	_	O
create	_	_	O
a	_	_	O
wide	_	_	B-VAR
trail	_	_	I-VAR
or	_	_	O
a	_	_	O
narrow	_	_	B-VAR
trail	_	_	I-VAR
.	_	_	O
A	_	_	O
wide	_	_	B-VAR
trail	_	_	I-VAR
can	_	_	O
take	_	_	O
50	_	_	B-PARAM
visitors	_	_	O
every	_	_	O
day	_	_	O
while	_	_	O
the	_	_	O
narrow	_	_	B-VAR
trail	_	_	I-VAR
expects	_	_	O
20	_	_	B-PARAM
visitors	_	_	O
every	_	_	O
day	_	_	O
.	_	_	O
The	_	_	O
wide	_	_	B-VAR
trail	_	_	I-VAR
will	_	_	O
introduce	_	_	O
6	_	_	B-PARAM
units	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
garbage	_	_	I-OBJ_NAME
and	_	_	O
the	_	_	O
narrow	_	_	B-VAR
trail	_	_	I-VAR
will	_	_	O
introduce	_	_	O
3	_	_	B-PARAM
units	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
garbage	_	_	I-OBJ_NAME
.	_	_	O
There	_	_	O
can	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
3	_	_	B-LIMIT
wide	_	_	B-VAR
trails	_	_	I-VAR
and	_	_	O
the	_	_	O
park	_	_	O
hopes	_	_	O
to	_	_	O
have	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
225	_	_	B-LIMIT
visitors	_	_	O
every	_	_	O
day	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
trail	_	_	O
should	_	_	O
the	_	_	O
park	_	_	O
construct	_	_	O
to	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
amount	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
garbage	_	_	I-OBJ_NAME
produced	_	_	O
.	_	_	O

Grain	_	_	O
is	_	_	O
transported	_	_	O
from	_	_	O
a	_	_	O
farm	_	_	O
to	_	_	O
local	_	_	O
grocery	_	_	O
stores	_	_	O
in	_	_	O
either	_	_	O
large	_	_	B-VAR
bags	_	_	I-VAR
or	_	_	O
tiny	_	_	B-VAR
bags	_	_	I-VAR
.	_	_	O
Large	_	_	B-VAR
bags	_	_	I-VAR
can	_	_	O
hold	_	_	O
25	_	_	B-PARAM
kg	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
grain	_	_	I-OBJ_NAME
and	_	_	O
requires	_	_	O
4	_	_	B-PARAM
units	_	_	O
of	_	_	O
energy	_	_	O
to	_	_	O
transport	_	_	O
.	_	_	O
Tiny	_	_	B-VAR
bags	_	_	I-VAR
can	_	_	O
hold	_	_	O
6	_	_	B-PARAM
kg	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
grain	_	_	I-OBJ_NAME
and	_	_	O
requires	_	_	O
1.5	_	_	B-PARAM
units	_	_	O
of	_	_	O
energy	_	_	O
to	_	_	O
transport	_	_	O
.	_	_	O
The	_	_	O
distribution	_	_	O
process	_	_	O
has	_	_	O
access	_	_	B-CONST_DIR
to	_	_	I-CONST_DIR
110	_	_	B-LIMIT
units	_	_	O
of	_	_	O
energy	_	_	O
.	_	_	O
Because	_	_	O
of	_	_	O
popularity	_	_	O
of	_	_	O
buying	_	_	O
in	_	_	O
bulk	_	_	O
,	_	_	O
there	_	_	O
must	_	_	B-CONST_DIR
be	_	_	I-CONST_DIR
twice	_	_	B-PARAM
as	_	_	O
many	_	_	O
large	_	_	B-VAR
bags	_	_	I-VAR
as	_	_	O
tiny	_	_	B-VAR
bags	_	_	I-VAR
of	_	_	O
rice	_	_	O
.	_	_	O
Additionally	_	_	O
,	_	_	O
there	_	_	O
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
20	_	_	B-LIMIT
tiny	_	_	B-VAR
bags	_	_	I-VAR
of	_	_	O
rice	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
size	_	_	O
of	_	_	O
rice	_	_	O
bags	_	_	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
grain	_	_	I-OBJ_NAME
in	_	_	O
weight	_	_	O
?	_	_	O

A	_	_	O
railway	_	_	O
company	_	_	O
is	_	_	O
planning	_	_	O
the	_	_	O
infrastructure	_	_	O
for	_	_	O
the	_	_	O
city	_	_	O
and	_	_	O
is	_	_	O
considering	_	_	O
two	_	_	O
types	_	_	O
of	_	_	O
transportation	_	_	O
,	_	_	O
trains	_	_	B-VAR
and	_	_	O
trams	_	_	B-VAR
.	_	_	O
Each	_	_	O
train	_	_	B-VAR
can	_	_	O
transport	_	_	O
120	_	_	B-PARAM
people	_	_	O
per	_	_	O
hour	_	_	O
comfortably	_	_	O
and	_	_	O
each	_	_	O
tram	_	_	B-VAR
can	_	_	O
transport	_	_	O
30	_	_	B-PARAM
people	_	_	O
per	_	_	O
hour	_	_	O
comfortably	_	_	O
.	_	_	O
Since	_	_	O
trains	_	_	B-VAR
take	_	_	O
longer	_	_	O
to	_	_	O
build	_	_	O
,	_	_	O
the	_	_	O
number	_	_	O
of	_	_	O
trams	_	_	B-VAR
must	_	_	O
be	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
twice	_	_	B-PARAM
the	_	_	O
number	_	_	O
of	_	_	O
trains	_	_	B-VAR
.	_	_	O
If	_	_	O
the	_	_	O
railway	_	_	O
company	_	_	O
wants	_	_	O
to	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
600	_	_	B-LIMIT
people	_	_	O
per	_	_	O
hour	_	_	O
,	_	_	O
minimize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	B-OBJ_NAME
number	_	_	I-OBJ_NAME
of	_	_	I-OBJ_NAME
transportation	_	_	I-OBJ_NAME
units	_	_	I-OBJ_NAME
required	_	_	O
.	_	_	O

A	_	_	O
village	_	_	O
delivers	_	_	O
mail	_	_	O
to	_	_	O
nearby	_	_	O
villages	_	_	O
either	_	_	O
by	_	_	O
runners	_	_	B-VAR
or	_	_	O
canoers	_	_	B-VAR
.	_	_	O
Runners	_	_	B-VAR
can	_	_	O
carry	_	_	O
three	_	_	B-PARAM
bags	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
mail	_	_	I-OBJ_NAME
each	_	_	O
time	_	_	O
and	_	_	O
takes	_	_	O
4	_	_	B-PARAM
hours	_	_	O
.	_	_	O
Canoers	_	_	B-VAR
can	_	_	O
carry	_	_	O
ten	_	_	B-PARAM
bags	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
mail	_	_	I-OBJ_NAME
each	_	_	O
time	_	_	O
and	_	_	O
takes	_	_	O
2	_	_	B-PARAM
hours	_	_	O
.	_	_	O
At	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
33	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
deliveries	_	_	O
can	_	_	O
be	_	_	O
by	_	_	O
canoe	_	_	B-VAR
.	_	_	O
Additionally	_	_	O
,	_	_	O
the	_	_	O
village	_	_	O
can	_	_	O
spare	_	_	O
at	_	_	B-CONST_DIR
most	_	_	I-CONST_DIR
200	_	_	B-LIMIT
total	_	_	O
hours	_	_	O
and	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
4	_	_	B-LIMIT
runners	_	_	B-VAR
must	_	_	O
be	_	_	O
used	_	_	O
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
way	_	_	O
to	_	_	O
deliver	_	_	O
must	_	_	O
be	_	_	O
used	_	_	O
to	_	_	O
maximize	_	_	B-OBJ_DIR
the	_	_	O
total	_	_	O
amount	_	_	B-OBJ_NAME
of	_	_	I-OBJ_NAME
mail	_	_	I-OBJ_NAME
that	_	_	O
can	_	_	O
be	_	_	O
delivered	_	_	O
?	_	_	O

A	_	_	O
party	_	_	O
organizer	_	_	O
needs	_	_	O
to	_	_	O
transport	_	_	O
party	_	_	O
goers	_	_	O
either	_	_	O
by	_	_	O
limousine	_	_	B-VAR
or	_	_	O
bus	_	_	B-VAR
.	_	_	O
Limousines	_	_	B-VAR
can	_	_	O
carry	_	_	O
12	_	_	B-PARAM
people	_	_	O
and	_	_	O
buses	_	_	B-VAR
can	_	_	O
carry	_	_	O
18	_	_	B-PARAM
people	_	_	O
.	_	_	O
They	_	_	O
need	_	_	O
to	_	_	O
transport	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
400	_	_	B-LIMIT
people	_	_	O
.	_	_	O
Because	_	_	O
limousines	_	_	B-VAR
are	_	_	O
more	_	_	O
attractive	_	_	O
,	_	_	O
at	_	_	B-CONST_DIR
least	_	_	I-CONST_DIR
70	_	_	B-LIMIT
%	_	_	I-LIMIT
of	_	_	O
the	_	_	O
vehicles	_	_	O
must	_	_	O
be	_	_	O
limousines	_	_	B-VAR
.	_	_	O
How	_	_	O
many	_	_	O
of	_	_	O
each	_	_	O
type	_	_	O
of	_	_	O
vehicle	_	_	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
limousines	_	_	I-OBJ_NAME
and	_	_	I-OBJ_NAME
buses	_	_	I-OBJ_NAME
used	_	_	I-OBJ_NAME
?	_	_	O
