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Math Help - Dual-Primal / Simplex

  1. #1
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    Lightbulb Dual-Primal / Simplex

    Hi

    I have solved the PRIMAL problem given in the attached image using in the Big M/ Charne's Penalty method. I am pretty sure that the solution obtained is correct because I have verified with the software "TORA".

    Now, I would like to know how to read the solution of the DUAL of this problem. Can someone help me with that please?


    Thanks,
    Max,
    Attached Thumbnails Attached Thumbnails Dual-Primal / Simplex-dual.jpg  
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  2. #2
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    Exclamation A minor error

    Hi,

    I fell into confusion because I was stupid enough to overlook a small mistake in the input data. This led me into believing that there was a big doubt in my understanding of the dual - primal concept. But I've realized my mistake and have posted the correct output result in the attachment.

    As for people who would need a guidance in reading the solution of the dual from the primal problem, here are the steps I usually work out.

    We start with the dual constraints corresponding to the starting solution of the primal. In this case, we have the 3 artificial variables A1, A2 and A3 as the starting solution variables of the primal.

    The corresponding dual constraints are, x1<= M, x2<=M and x3<=M

    Now using the property of primal-dual relationship, we equate the co-efficients of these three variables in the optimal primal table.

    x1 -M = -M => x1 =0
    x2 -M = 100-M => x2 = 100
    x3 -M = 230-M => x3 = 230.

    Hence the solution of the dual would be 0,100 and 230.

    Hope it helped someone
    Attached Thumbnails Attached Thumbnails Dual-Primal / Simplex-dual.jpg  
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  3. #3
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    Quote Originally Posted by MAX09 View Post
    Hi,

    I fell into confusion because I was stupid enough to overlook a small mistake in the input data. This led me into believing that there was a big doubt in my understanding of the dual - primal concept. But I've realized my mistake and have posted the correct output result in the attachment.

    As for people who would need a guidance in reading the solution of the dual from the primal problem, here are the steps I usually work out.

    We start with the dual constraints corresponding to the starting solution of the primal. In this case, we have the 3 artificial variables A1, A2 and A3 as the starting solution variables of the primal.

    The corresponding dual constraints are, x1<= M, x2<=M and x3<=M

    Now using the property of primal-dual relationship, we equate the co-efficients of these three variables in the optimal primal table.

    x1 -M = -M => x1 =0
    x2 -M = 100-M => x2 = 100
    x3 -M = 230-M => x3 = 230.

    Hence the solution of the dual would be 0,100 and 230.

    Hope it helped someone
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