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Problem 11

A company manufactures two products, \(\mathrm{A}\) and \(\mathrm{B}\), on machines \(\mathrm{I}\) and \(\mathrm{II}\). The company will realize a profit of \(\$ 3 /\) unit of product \(A\) and a profit of \(\$ 4 /\) unit of product \(B\). Manufacturing 1 unit of product A requires 6 min on machine I and 5 min on machine II. Manufacturing 1 unit of product \(\mathrm{B}\) requires 9 min on machine I and 4 min on machine II. There are 5 hr of time available on machine I and \(3 \mathrm{hr}\) of time available on machine II in each work shift. a. How many units of each product should be produced in each shift to maximize the company's profit? b. Find the range of values that the contribution to the profit of 1 unit of product A can assume without changing the optimal solution. c. Find the range of values that the resource associated with the time constraint on machine I can assume. d. Find the shadow price for the resource associated with the time constraint on machine \(\mathrm{I}\),

Expert verified

In summary, to maximize profit, the company should produce 20 units of product A and 20 units of product B per shift, with a maximum profit of $ 140. The range of values for product A's profit is \([4, +\infty)\), and the range for the resource constraint of machine I is \([180, 360]\). The shadow price for machine I's time constraint is $5.

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Chapter 3

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Chapter 3

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Chapter 3

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Chapter 3

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Chapter 3

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