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Question

: Calibri (Body) AaBbCcDd AaBbCcDd AaBbC Paste Clip board Font Paragraph Styles onun 7-33 on page 281. The computer output given below is for Problem 7-31. Use this to answer the following questions. (a) What is the optimal solution? (b) Change the right-hand side of constraint 1 to 11 (instead of 10) and resolve the problem. How much did the profit increase as a result of this? (c) Change the right-hand side of constraint 1 to 6 (instead of 10) and resolve the problem. How much did the profit decrease as a result of this? Looking at the graph, what would happen if the right-hand- side value were to go below 6?. (d) Change the right-hand-side value of constraint 1 to 5 (instead of 10) and resolve the problem. How much did the profit decrease from the original profit as a result of this? (e) Using the computer output on this page, what is the dual price of constraint 1? What is the lower bound on this? (f) What conclusions can you draw from this regarding the bounds of the right-hand-side values and the dual price?

Explanation / Answer

I am solving the first four sub-parts as per Chegg guidelines, post multiple question to get the remaining answers

a)

The optimal solution is (x1=6,x2=4)

Profit (Maximization ) = 8x1 + 5x2 = 8(6) + 5(4) = 68$

b)

Maximize Z=8x1 + 5x2

New constraints are

x1 + x2 <= 11

x1 <= 6

Solving the equation, we get x1=6 and x2=5

Profit = 8(6) + 5(5) = 73$

c)

Maximize Z=8x1 + 5x2

New constraints are

x1 + x2 <= 6

x1 <= 6

Solving the equation, we get x1=6 and x2=0

Profit = 8(6) + 5(0) = 48$

The profit will decrease by 20$, decreasing it less than 6 will further decrease the profit

d)

Maximize Z=8x1 + 5x2

New constraints are

x1 + x2 <= 5

x1 <= 6

Solving the equation, we get x1=5 and x2=0

Profit = 8(5) + 5(0) = 40$

There is a loss of 28$ as compared to the original profit

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