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Math Help - Finding the optimal solution to a Linear Program

  1. #1
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    Finding the optimal solution to a Linear Program

    Hi there,

    It's the beginning of a new quarter and I can tell my basic linear algebra is failing me at this point. I just need help solving a multi-dimensional linear program. So far this is the LP.

    Maximize: 6*x1 + 3*x2 + 8*x3 + 3*x4 + 9*x5 + 5*x6
    Subject to:
    x1 + x2 <= 480
    x3 + x4 <= 400
    x5 + x6 <= 230
    x1 + x3 + x5 <= 420
    x2 + x4 + x6 <= 250
    x1, x2, ..., x6 >= 0

    From there I have no idea where to go. I know how to solve a two-dimensional LP graphically but I just can't figure this one out.

    Thanks in advance! :)
    Last edited by hjhart; October 7th 2009 at 10:34 PM. Reason: Errors
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  2. #2
    Grand Panjandrum
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    someplace
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    Quote Originally Posted by hjhart View Post
    Hi there,

    It's the beginning of a new quarter and I can tell my basic linear algebra is failing me at this point. I just need help solving a multi-dimensional linear program. So far this is the LP.

    Maximize: 6*x1 + 3*x2 + 8*x3 + 3*x4 + 9*x5 + 5*x6
    Subject to:
    x1 + x2 <= 480
    x3 + x4 <= 400
    x5 + x6 <= 230
    x1 + x3 + x5 <= 420
    x2 + x4 + x6 <= 250
    x1, x2, ..., x6 >= 0

    From there I have no idea where to go. I know how to solve a two-dimensional LP graphically but I just can't figure this one out.

    Thanks in advance!
    If you have never done a course that covered solving multidimensional LP problems then you will not get far with this, but here is the Wikipedia article on the simplex algorithm. Also the solver in Excel (and most other spreadsheet programs) will solve LP problems.

    CB
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  3. #3
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    Sep 2009
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    Seattle, WA
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    Thanks CaptainBlack, we've just gotten into the Simplex method this week. :)
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