# Linear Programming: Hart Manufacturing

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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#### Solution Preview

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.