Hart Manufacturing makes three products. Each product requires manufacturing ope
ID: 3131968 • Letter: H
Question
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:
During the next production period, the labor-hours available are 475 in department A, 325 in department B, and 55 in department C. The profit contributions per unit are $23 for product 1, $26 for product 2, and $29 for product 3.
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
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 = $
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, $750 for product 2, and $675 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 = $
Management realized that the optimal product mix, taking setup costs into account, might be different from the one recommended in part (b). Formulate a mixed-integer linear program that takes setup costs into account. Management also stated that we should not consider making more than 180 units of product 1, 170 units of product 2, or 150 units of product 3. Here introduce a 0-1 variable yi that is one if any quantity of product i is produced and zero otherwise. 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)
Solve the mixed-integer linear program formulated in part (d). How much of each product should be produced, and what is the projected total profit contribution? Compare this profit contribution to that obtained in part (c).
P1 =
P2 =
P3 =
Profit = $
The profit is by $ .
Explanation / Answer
(a.) Max 23 P1 + 26 P2 + 29 P3
Subject to:
2.5 P1 + 2.5 P2 + 2.5 P3 475
3.5 P1 + 1 P2 + 2 P3 325
0.25 P1 + 0.25 P2 + 0.5 P3 55
(b.) We can slove this LPP using MS-Excel
P1 = 0
P2 = 160
P3 = 30
Profit = $5030
(c.) Profit in (b) - (400+750+675)
New Profit Contribtuon = 5030-(400+750+675)
= $3205
(d.) We need to add three more contraints
P1 180
P2 170
P3 160
Again solving the LPP:
Even after these constraints our solution remains the same:
(e.) P1 = 0
P2 = 160
P3 = 30
Profit = $5030
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