linear programming

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The Pyrotec Company produces three electrical products-clocks, radios and toasters. These products have the following resources requirements :
Resource Requirements
Cost/Unit Labor Hours/Unit
Clock $7 2
Radio 10 3
Toaster 5 2

The manufacturer has a daily production budget of $2,000 and maximum of 660 hours of labor. Maximum daily customer demand is for 200 clocks, 300 radios, and 150 toasters. Clocks sell for $15, radios for $20, and toasters for $12.The company wants to know the optimal product mix that will maximize profit.
a) Formulate a linear programming model for this problem;
b) Solve the model by using the computer.

  • linear programming -

    Given:

    Cost/Unit Labor Hours/Unit
    Clock $7 2
    Radio 10 3
    Toaster 5 2

    Implicitly, all quantities produced daily are to be positive, so
    =>
    c ≥ 0
    r ≥ 0
    t ≥ 0

    The manufacturer has a daily production budget of $2,000
    =>
    7c+10r+5t ≤ 2000

    and maximum of 660 hours of labor.
    =>
    2c+3r+2t ≤ 660

    Maximum daily customer demand is for 200 clocks, 300 radios, and 150 toasters.
    =>
    c ≤ 200
    r ≤ 300
    t ≤ 150

    Clocks sell for $15, radios for $20, and toasters for $12.The company wants to know the optimal product mix that will maximize profit.
    =>
    profit for clocks = 15-7 = 8
    profit for radios = 20-10 = 10
    profit for toasters = 12-5 = 7
    Also, labour cost is not provided, so the 600 hours will be assumed a fixed cost.
    =>
    Z=8c+10r+7t (objective function)


    Feed in all these inequalities to your linear programming solver.
    I get c=178, r=0, t=150
    for Z=2474, 656 hours, and cost = $1996
    Check my results.

    Check my

  • linear programming -

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