Problem 31

Problem 31(Algorithmic)

Hart Manufacturing makes three products. Each product requires manufacturing operations in three departments: A, B, and C. The labor-hour requirements, by department, are as follows:

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Department Product 1 Product 2 Product 3

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A 1.5 3 2

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B 2 1 2.5

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C 0.25 0.25 0.25

During the next production period, the labor-hours available are 450 in department A, 350 in department B, and 50 in department C. The profit contributions per unit are $25 for product 1, $28 for product 2, and $30 for product 3.

(a) Formulate a linear programming model for maximizing total profit contribution.

If required, round your answers to two decimal places. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300)

Let Pi = units of product i produced

Max P1 + P2 + P3

s.t.

P1 + P2 + 2P3 ≤

2P1 + P2 + P3 ≤

P1 + 0.25P2 + P3 ≤

P1, P2, P3 ≥ 0

(b) Solve the linear program formulated in part (a). How much of each product should be produced, and what is the projected total profit contribution?

P1 =

P2 =

P3 =

Profit = $

(c) After evaluating the solution obtained in part (b), one of the production supervisors noted that production setup costs had not been taken into account. She noted that setup costs are $400 for product 1, $550 for product 2, and $600 for product 3. If the solution developed in part (b) is to be used, what is the total profit contribution after taking into account the setup costs?

Profit = $

(d) Management realized that the optimal product mix, taking setup costs into account, might be different from the one recommended in part (b)....