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Math Help - linear programming/solver

  1. #1
    Newbie
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    Mar 2009
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    linear programming/solver

    i am completely stuck on this problem, i cannot figure out all of the contraints or what Z is. can i have to equations for Z? i know how to do in solver but i just cant figure out out to fomulate the problem

    Frandec Company manufactures, assembles, and rebuilds material handling equipment used in warehouses and distribution centers. One product, called a Liftmaster, is assembled from four components: a frame, a motor, two supports, and a metal strap. Frandecís production schedule calls for 5000 Liftmasters to be made next month. Frandec purchases the motors from an outside supplier, but the frames, supports and straps may either be manufactured by the company or purchased from an outside supplier. Manufacturing and purchase costs per unit are shown.
    Component
    Manufacturing Cost
    Purchase Cost
    Frame
    $38.00
    $51.00
    Support
    11.50
    15.00
    Strap
    6.50
    7.50

    Three departments are involved in the production of these components. The time (in minutes per unit) required to process each component in each department and the available capacity (in hours) for the three departments are as follows.
    capacity (in hours) for the three departments are as follows.
    DEPARTMENT
    Component
    Cutting
    Milling
    Shaping
    Frame
    3.5
    2.2
    3.1
    Support
    1.3
    1.7
    2.6
    Strap
    1.8
    ---
    1.7
    Capacity (hours)
    350
    420
    680


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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by thrasher View Post
    i am completely stuck on this problem, i cannot figure out all of the contraints or what Z is. can i have to equations for Z? i know how to do in solver but i just cant figure out out to fomulate the problem

    Frandec Company manufactures, assembles, and rebuilds material handling equipment used in warehouses and distribution centers. One product, called a Liftmaster, is assembled from four components: a frame, a motor, two supports, and a metal strap. Frandecís production schedule calls for 5000 Liftmasters to be made next month. Frandec purchases the motors from an outside supplier, but the frames, supports and straps may either be manufactured by the company or purchased from an outside supplier. Manufacturing and purchase costs per unit are shown.

    Component
    Manufacturing Cost
    Purchase Cost
    Frame
    $38.00
    $51.00
    Support
    11.50
    15.00
    Strap
    6.50
    7.50

    Three departments are involved in the production of these components. The time (in minutes per unit) required to process each component in each department and the available capacity (in hours) for the three departments are as follows.
    capacity (in hours) for the three departments are as follows.
    DEPARTMENT
    Component
    Cutting
    Milling
    Shaping
    Frame
    3.5
    2.2
    3.1
    Support
    1.3
    1.7
    2.6
    Strap
    1.8
    ---
    1.7
    Capacity (hours)
    350
    420
    680


    Let the variables be R, U and T the number of frames, supports and straps manufactured. The objective to be mininmise is the total cost:

    f(R,U,T)=38R+51(5000-R)+11.5U+15(5000-U)+6.5T+7.5(5000-T)

    or:

    f(R,U,T)=367500-13R-3.5U-T

    which if you prefer is minimised by maximising:

    g(R,U,T)=13R+3.5U+T.

    Then we have the capacity constraints:

    3.5R+1.3U+1.8T \le 350

    2.2R+1.7U \le 420

    3.1R+2.6U+1.7T \le 680

    Then the usual positivity constraints and also:

    R \le 5000

    U \le 5000

    T \le 5000.

    CB
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