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20 September, 12:46

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.

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  1. 20 September, 13:04
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    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
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