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Math Help - Linear Programming help

  1. #1
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    Linear Programming help

    Have great difficult getting my head around this LP problem in university. Any help would be greatly appreciated. Have LP solver but can't lay out question

    A wooden factory has 4 machines to create different size chairs. The machines operate differently and are of different sizes. The firm has been contracted to produce 3 products, 400 units of product 1, 570 of product 2 and 320 of product 3. Productions times are as follows:

    ----------Machine
    Product -1--2 --3--4
    --1-----35-41--34--39
    --2-----40-36--32--43 ------(Mins)
    --3-----38-37--33--40

    Machine 1 is available for 150 hours, machine 2 for 240, machine 3 for 200 and machine 4 for 250. The products have different profits depending on which machine they’re produced on, as follows

    ------------Machine
    Product----1----2---3----4
    1-------7.8--7.8--8.2--7.9
    2-------6.7--8.9--9.2--6.3 (Profit)
    3-------8.4--8.1--9.0--5.8

    How many units should be produced on each machine to maximise profit?
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  2. #2
    MHF Contributor
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    Pretty difficult to "teach" that here (not a classroom).

    Did you Google "linear programming"?
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by bannana View Post
    Have great difficult getting my head around this LP problem in university. Any help would be greatly appreciated. Have LP solver but can't lay out question

    A wooden factory has 4 machines to create different size chairs. The machines operate differently and are of different sizes. The firm has been contracted to produce 3 products, 400 units of product 1, 570 of product 2 and 320 of product 3. Productions times are as follows:

    ----------Machine
    Product -1--2 --3--4
    --1-----35-41--34--39
    --2-----40-36--32--43 ------(Mins)
    --3-----38-37--33--40

    Machine 1 is available for 150 hours, machine 2 for 240, machine 3 for 200 and machine 4 for 250. The products have different profits depending on which machine they’re produced on, as follows

    ------------Machine
    Product----1----2---3----4
    1-------7.8--7.8--8.2--7.9
    2-------6.7--8.9--9.2--6.3 (Profit)
    3-------8.4--8.1--9.0--5.8

    How many units should be produced on each machine to maximise profit?
    Let's assume you cannot identify the variables involved. These should be N_{i,j},\ i=1..3,\ j=1,..4 where N_{i,j} is the number of chair type i produced on machine j. Call these x_k,\ k=1, .., 12 if that helps.

    Now formulate the constraints and the objective in terms of these variables.

    CB
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