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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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hafsaabdulhai

Answer:

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

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