Linear Programming Worksheet Answer KEY 2011
1) Let x = # of days
in Alaska
Let y = # of days
in Nebraska
February 23, 2011
200
180
160
140
(50, 120)
120
120x + 100y < 18000
x > 50
y > 60
100
80
(100, 60)
Objective Function
P = 3000x + 2800y
(50, 60)
60
(50, 60)
40
20
(50, 120)
200
180
160
140
120
100
80
60
40
(0, 0)
20
(100, 60)
Katie should spend 50 days in Alaska and 120 days in Nebraska to maximize sales.
Sep 13­12:05 PM
1
Linear Programming Worksheet Answer KEY 2011
2) Let x = # of morning ads
Let y = # of evening ads
200x + 50y < 2200
x + y < 20
x > 0
y > 0
Objective Function
P = 90,000x + 30,000y
(0, 20)
50
45
40
35
30
25
20
(0, 20)
15
(8, 12)
10
5
(8, 12)
(11, 0)
February 23, 2011
(11, 0)
(0, 0)
5
10
15
20
25
30
35
40
45
50
You should buy 8 morning ads and 12 evening ads to reach the most listeners.
Sep 13­12:10 PM
2
Linear Programming Worksheet Answer KEY 2011
February 23, 2011
50
3) Let x = # of sweaters 45
Let y = # of dresses 40
x + y < 18
20x + 40y < 600
x > 0
y > 0
Objective Function
P = 55x + 85y
(0, 15)
(6, 12)
35
30
25
20
(0, 15)
15
(6, 12)
10
5
(18, 0)
(18, 0)
(0, 0)
5
10
15
20
25
30
35
40
45
50
Carrie should make 6 sweaters and 12 dresses each day to maximize profit.
Sep 13­12:15 PM
3
Linear Programming Worksheet Answer KEY 2011
February 23, 2011
40
4) Let x = # of standard 36
model tents
32
Let y = # of expedition
28
model tents
x + 2y < 32
3x + 4y < 84
x > 0
0 < y < 12
Objective Function
P = 50x + 80y
20
16
(0, 12)
12
(8, 12)
8
(20, 6)
4
2
40
36
32
(28, 0)
28
24
20
16
8
4
2
(0, 0)
12
(0, 12)
(8, 12)
(20, 6)
(28, 0)
24
The tent company should manufacture 20 standard model tents and 6 expedition
model tents each week to maximize profit.
Sep 13­12:15 PM
4
Linear Programming Worksheet Answer KEY 2011
5) Let x = # of regular tires
Let y = # of snow tires
1/2x + y < 20
2x + y < 60
x + 4y < 60
x > 0
y > 0
Objective Function
P = 10x + 15y
(0, 15)
(20, 10)
(26 2/3, 6 2/3)
(30, 0)
February 23, 2011
50
45
40
35
30
25
20
15
(0, 15)
(20, 10)
10
(26
2/3 ,
5
6 2
/3 )
(30, 0)
(0, 0)
5
10
15
20
25
30
35
40
45
50
The company should make 20 regular tires and 10 snow tires to maximize profit.
They can't make a fraction of a tire so 26.6 and 6.6 is not an option. This situation allows them to make less tires for
the same amount of profit as 26 regular tires and 6 snow tires.
Sep 13­12:15 PM
5
Linear Programming Worksheet Answer KEY 2011
February 23, 2011
Feb 23­12:38 PM
6