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Linear Programming: Hart Manufacturing

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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:

Department Product 1 Product 2 Product 3
A 1.5 3 2
B 2 1 2.5
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.

Formulate a linear programming model for maximizing total profit contribution. Answer the questions in the attached case.

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https://brainmass.com/math/linear-programming/linear-programming-hart-manufacturing-517145

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a) Let pi = units of product i produced:
Max 25p1 + 28p2 + 30p3
s.t.
1.5p1 + 3p2 + 2p3 < 450
2p1 + 1p2 + 2.5p3 < 350
.25p1 + .25p2 + .25p3 < 50
p1, p2, p3 > 0

b) The optimal solution is:
p1 = 60; p2 = 80; p3 = 60; Value = 5540
The solution provides a profit of $5540.

c) Since the solution in part (b) calls for producing all three products, the total setup cost is
$1550 = $400 + $550 + $600.
Subtracting the total ...

Solution Summary

The expert examines linear programming for Hart Manufacturing.

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Linear programming model problem

LAYOUT OF TABLE below is shown better in attached file... thank you

Hart Manufacturing makes three products. Each product requires manufacturing operations in three departments: A, B and C. The labor-hour requirements, by department, are:
2
Department
Product 1
Product 2
Product 2
A
1.50
3.00
2.00
B
2.00
1.00
2.50
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. Provide the formulation.
b- ) Solve the linear program formulated in part (a) by using Excel. Include the computer output. How much of each product should be produced and what is the projected total profit contribution?
c- ) After evaluating the solution obtained in part (a), 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 after taking into account the setup costs?
d- 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 cost into account. Management has also stated that we should not consider making more than 175 units of product 1, 150 of product 2, or 140 units of product 3. Provide the formulation.
e- Solve the mixed integer linear program formulated in part (d) by using Excel. Include the computer output. How much of each product should be produced and what is the projected profit? Compare this profit to that obtained in part (c).

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