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Math Help - Linear Programming model

  1. #1
    Juggler
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    Linear Programming model

    I was having a problem developing the optimal solution. I tried to find the objective function, and decision variables/constraints but I got confused. Any pointers would be appreciated. Thanks.

    Tots Toys makes a plastic tricycle that is composed of three major components: a handlebar-front wheel-pedal assembly, a seat and frame unit, and rear wheels. The company has orders for 12,000 of these trikes.

    As indicated in the table below, the company obviously does not have the resources available to manufacture everything needed for the completion of 12000 tricycles, so it has arranged to purchase additional components, as necessary. Develop a linear programming model to tell the company how many of each component should be manufactured and how many should be purchased in order to provide 12000 fully completed tricycles at the minimum cost.


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  2. #2
    Junior Member
    Joined
    Feb 2006
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    Let F_p, and F_m refer to front parts manufactured and produced... Similarly S_p, S_m refers to seat, and W_p, W_m refers to rear wheels.

    We wish to minimize the cost:

    \text{Cost} = 12F_p + 8F_m + 9S_p + 6S_m + 3W_p + W_m

    given the following constraints:

    we want 12000 parts, and 24000 rear wheels:
    F_p + F_m = 12000, S_p + S_m = 12000, W_p + W_m = 24000

    and we have limited parts/time/space available so:
    3F_m+4S_m + 5W_m \leq 50000

    10F_m + 6S_m + 2W_m \leq 160000

    2F_m + 2S_m + W_m \leq 30000


    then one would use some magical linear programming techniques to find the optimal values for F_m, F_p, S_m, S_p, W_m, W_p
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