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 3A 1.50 3.00 2.00B 2.00 1.00 2.50C 0.25 0.25 0.25During 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. 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

Missing Part of the Question

The management also stated that we should not consider making more than 175 units for product 1, 150units of product 2, or 140 units of product 3.

Answer and Explanation:

Given

Department Product 1 Product 2 Product 3

A 1.50 3.00 2.00

B 2.00 1.00 2.50

C 0.25 0.25 0.25

The profit contributions per unit are

Product 1 = $25

Product 2 = $28

product 3 = $30

The set up costs are

Product 1 = $400

Product 2 = $550

Product 3 =$600

The labor-hours available are

Department A = 450

Department B = 350

Department C = 50

Formulating a linear programming model, as have

Let X be the number of units produced

Max Z = 25X1 + 28X2 + 30X3 - 400Y1 - 550Y2 - 600Y3

Subjected to (the constraints are)

1.5X1 + 3X2 + 2X3 ≤ 450

2X1 + X2 + 2.5X3 ≤ 350

0.25X1 + 0.25X2 + 0.25X3 ≤ 50

0 ≤ X1 ≤ 175Y1

0 ≤ X2 ≤ 150Y2

0 ≤ X3 ≤ 140Y3

The first three constraints represents the labour hours in departments A, B and C.

While the last three constraints represents the maximum production of product 1,2 and 3.

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