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.

The goal is to maximize profit.

Profit will be represented by the letter Z in the model.

The restrictions are the labor-hours available in each department.

Department A hours ≤ 450

Department B hours ≤ 350

Department C hours ≤ 50

The decisions variables are:

X1 = Units to produce of Product 1

X2 = Units to produce of Product 2

X3 = Units to produce of Product 3

MODEL:

Maximize Z = $25X1 + $28X2 + $30X3

Subject to: X1 + X2 + X3 ≤ 450

X1 + X2 + X3 ≤ 350

X1 + X2 + X3 ≤ 50

X1, X2, X3 ≥ 0