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Math Help - Finding LP dual for this general LP problem

  1. #1
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    Finding LP dual for this general LP problem

    I have this LP problem:

    max (x1-2x2)

    subject to:

    x1 + 2x2 - x3 + x4>=0
    4x1 + 3x2 + 4x3 - 2x4<=3
    -x1 - x2 + 2x3 + x4=1

    end

    x2,x3>=0 and x1 and x4 are uncontrained

    and i am trying to figure out the dual, i arrived to this:

    min 3x2+x3

    subject to

    x1+4x2-x3 = 1
    2x1+3x2-x3>=-2
    -x1+4x2+2x3>=0
    x1-2x2+x3=0

    end

    The problem is that the optimums are not equal. I am a beginner when it comes to LP and i think i'm missing a simple thing there. Where's the catch?
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  2. #2
    Member kjchauhan's Avatar
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    x_3 and  x_4 are unrestricted in sign.

    So take

    x_3=x'_3-x''_3 ; where x'_3 \;and \;x''_3\geq 0

    and

    x_4=x'_4-x''_4 ; where x'_4 \;and \;x''_4\geq 0

    and solve..
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  3. #3
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    Yes you can find the dual in that way too, my question is why does the results for the optimum are different considering that the primal is bounded and feasible?
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