linear programming answer key 1) Let x = # of days
in Alaska
Let y = # of days
in Nebraska
October 15, 2008
200
180
160
140
(50, 120)
120
120x + 100y < 18000
y < ­1.2x + 180
x > 50
y > 60
100
80
(100, 60)
60
Final Constraint
3000x + 2800y
(50, 60)
40
20
200
180
160
140
120
100
80
60
40
20
Katie should spend 50 days in Alaska and 120 days in Nebraska to maximize sales.
Sep 13­12:05 PM
1
linear programming answer key 2) Let x = # of morning ads
Let y = # of evening ads
200x + 50y < 2200
y < ­4x + 44
x + y < 20
y < ­x + 20
x > 0
y > 0
October 15, 2008
50
45
40
35
30
25
20
(0, 20)
15
(8, 12)
10
Final Constraint
90,000x + 30,000y
5
(11, 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 answer key 3) Let x = # of sweaters
Let y = # of dresses
x + y < 18
y < ­x + 18
20x + 40y < 600
y < ­1/2x + 15
x > 0
y > 0
Final Constraint
55x + 85y
October 15, 2008
50
45
40
35
30
25
20
(0, 15)
15
(6, 12)
10
5
(18, 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 answer key October 15, 2008
40
4) Let x = # of standard 36
model tents
32
Let y = # of expedition
28
model tents
24
x + 2y < 32
y < ­1/2x + 16
3x + 4y < 84
y < ­3/4x + 21
x > 0
0 < y < 12
Final Constraint
50x + 80y
20
16
(0, 12)
12
(8, 12)
8
(20, 6)
4
2
40
36
32
28
24
20
16
12
8
4
2
(28, 0)
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 answer key 5) Let x = # of regular tires
Let y = # of snow tires
1/2x + y < 20
y < ­1/2x + 20
2x + y < 60
y < ­2x + 60
x + 4y < 60
y < ­1/4x + 15
x > 0
y > 0
Final Constraint
10x + 15y
October 15, 2008
50
45
40
35
30
25
20
15
(0, 15)
(20, 10)
10
(26 2/
3 , 6 2
5
/3)
(30, 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