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Duality theory

  1. Oct 11, 2005 #1
    Consider a PRoblem in standard form;
    Max { Sum of (c_j * x_j) }
    Sum of (a_i,j * x_j) <= b_i , i = 1,.....,m
    x_j >= 0 , j= 1,.....,n

    Assume that x* = (x*_1,.....x*_n ) is an optimal solution to this
    problem and that the first constraint is not satisfied at equality
    i.e. Sum of (a_1,j * x*_j) < b_1.

    Show using Duality Theory, that x* is also an optimal solution for the
    problem obtained by deleting the first constraint i.e. the problem
    Maximize Sum of (c_j * x_j)

    s.t. Sum of (a_i,j * x_j) <= b_i , i= 2,.....,m
    x_j >= 0

    note: Sum of sign has n on the top and j=1 on the bottom
    >= means > or equal to..
    <= means < or equal to...

    any hint or help please.thanks


    I understnad what the optimal solution is...but not quite sure what
    duality theory is..
  2. jcsd
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