Variables
Sci
(
Constraints
:
Graphcaic
C
( 2100
Calc
.
C
1200
4<-170
4280
.
:
Objective Eg
+42200
.
G=#
:
=#
Plc
-
,G)=
2Ct5G
A calculator company produces a scientific calculator and a graphing calculator. Long-term projections indicate an
100 scientific and 80 graphing calculators each day. Because of limitations on production
200 scientific and 170 graphing calculators can be made daily. To satisfy a shipping contract,
expected demand of at least
capacity, no more than
a total of at least
200 calculators much be shipped each day.
If each scientific calculator sold results in a $2 loss, but each graphing calculator produces a
each type should be made daily to maximize net profits?
$5 profit, how many of
:
50
)}FsjYxms
Graphing
0
Points
(
:
4001170)
( 200,170 )
200180
)
so
120180
{
1001100
)
o
fo
if
ifo
(c)
Scientific
1>(100/170)
=
24001+5474=5,1650
-
)+5(ro)=$o
)=s450
)=$
PC 200,170
)=
Pkooiro )=
-
2C
zoo
-
2C
)t5(
no
zoo
-2420
PC 120,80 )=
P( 100,100 )=
2C
-
)t5(
to
109+5400
)=$3oo
-160
MAX
.
Loo
Variables
X
Y
:
#Cab
'
.
Objective Eg
:
#CabX
-
Constraints
10×+209<-140
(
't
V(
6×+89<-72
.
,y)=8x+12y
×
¥*±*
2
You need to buy some filing cabinets. You know that Cabinet X costs $10 per unit, requires six square feet of floor
space, and holds eight cubic feet of files. Cabinet Y costs $20 per unit, requires eight square feet of floor space, and
holds twelve cubic feet of files. You have been given $140 for this purchase, though you don't have to spend that much.
The office has room for no more than 72 square feet of cabinets. How many of which model should you buy, in order to
maximize storage volume?
Points
(
(
0,5
y
:
(
)
8,3 )
from
system
12%
l2°y=84÷
-80¥
it
405-120
' °
•
5
y=3
-
6×+867=72
°
6×=48
a
I
it
•
•
×=8
V(
0,5
)=8( 01+124=605+3
V( 12,0 )= 842 )+12(
o
)=96f+3
8,3=8183+124--1004-3
V(
Max
.
it
×
Variables
Constraints
:
×=oz.o£food×
of Foody
y=Oz
.
×⇐
§f
×+y±5
30
.
8×+13.224
§¥
12×+13.236
2×+1924
8+4
20
In order to ensure optimal health (and thus accurate test results), a lab technician needs to feed the rabbits a daily diet
containing a minimum of 24 grams (g) of fat, 36 g of carbohydrates, and 4 g of protein. But the rabbits should be fed no
more than five ounces of food a day. Rather than order rabbit food that is custom-blended, it is cheaper to order Food X
and Food Y, and blend them for an optimal mix. Food X contains 8 g of fat, 12 g of carbohydrates, and 2 g of protein per
ounce, and costs $0.20 per ounce. Food Y contains 12 g of fat, 12 g of carbohydrates, and 1 g of protein per ounce, at a
cost of $0.30 per ounce. What is the optimal blend.
95
:(
Points
( 0,4 )
( 015 )
(
(
3,0
)
5,0
)
1,2
zoo
:q•
]*
F
q
.
System
)
2xtly=44*12×+14=36
2×-69=24
÷
€1
o
Eg
Objective
C
.2x+
( × ,y)=
40,4 )=
1.2
CC 0,5 )=
1.5
C ( 3,0
)=
C( 5,0
)=
C ( 1,2
)=
.
6
1.0
,8
.
.3y
Min
.
;
;
×
Variables
Constraints
:
f=#of Fifty Pass
R=#ofFor+yPass
'
.
R
1¥
•
#•
f+RE9
5of+4oR
:
F
2400
9
Objective Eg
8
0
:
,R)=8O0F+600R
CLF
A school is preparing a trip for 400 students. The company who is providing the transportation has 10 buses of 50 seats each
and 8 buses of 40 seats, but only has 9 drivers available. The rental cost for a large bus is $800 and $600 for the small bus.
Calculate how many buses of each type should be used for the trip for the least possible cost.
5OFt4OR=4
10
•
Forty ( R )
:
-
points
18,0 )
:
( 4,5 ) System
19,0 )
5
-
.
-
-
5oE5oR=t450
F=RI9
-
|oR= -50
R=5
'
o
F= 4
'
i
'
ji
,
Fifty (F)
((8,05-80018)+60010)=156400
( (9,05800191+6004)=517200
((4,55-80014)+60015)=516200
Min
.
,g