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    bkzd1989's Avatar
    bkzd1989 Posts: 2, Reputation: 1
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    #1

    Oct 16, 2013, 06:26 AM
    Linear Programming with Singular Constraint
    How am I going to go about solving this with only a singular constraint and an unknown?

    Refer to the following LP Formulation with unknown number S:

    Max x1+x2

    S.t

    Sx1+x2 <= 1 x1,x2 => 0

    How do I identify the unknown S to

    (a) Having an optimal solution (b) Being infeasible (c) Being Unbound
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #2

    Oct 16, 2013, 09:20 AM
    If you set S=0 then X1 can take on any value you like. Therefore the max value of X1 + X2 is infinity. You get a similar result if S is a negative number. If 0<S<1 then you maximize x1+x2 by making x1=1/S and x2=0. If S = 1 then pick an X1 betyween 0 and 1 and set X2= 1-X1. If S>0 then set x1=0 and x2=1.

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