Consider the following linear programming problem: Max Z = $15x + $20y Subject to: 8x + 5y ≤ 40 0.4x + y ≥ 4 x, y ≥ 0 Determine the values for x and y that will maximize revenue. Given this optimal revenue, what is the amount of slack associated with the first constraint?

Question

Mathematics

Wesley Barker

7 July, 05:31

Consider the following linear programming problem: Max Z = $15x + $20y Subject to: 8x + 5y ≤ 40 0.4x + y ≥ 4 x, y ≥ 0 Determine the values for x and y that will maximize revenue. Given this optimal revenue, what is the amount of slack associated with the first constraint?

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Answers (1)

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Logan Vaughan · Answer 1

x=0, y=8

slack is zero

surplus is 4

Step-by-step explanation:

See graph for optimal region

if x=0, y=8

15 (0) + 20 (8) = 160

if x = 0, y=4

15 (0) + 20 (4) = 80

if x=10/3, y=8/3

15 (10/3) + 20 (8/3) = 310/3

Slack

8 (0) + 5 (8) ≤ 40

40≤40

slack is zero

0.4 (0) + 8 ≥ 4

8 ≥ 4