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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.

    © BrainMass Inc. brainmass.com October 10, 2019, 5:46 am ad1c9bdddf
    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.

    $2.19