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Math Help - Linear Programming-Transportation Simplex

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    Linear Programming-Transportation Simplex

    I don't know if I've posted this in the right place but I thought I'd give it a go anyway.

    For question see attachment below.

    So for part a) max z:150X11+350X12+300X13+100X21+500X22+400X23

    s.t. X11+X12+X13≤40
    X21+X22+X23≤90
    X11+X21≥30
    X12+X22≥40
    X13+X23≥60

    For (b) eliminate first constraint and label constraints: u2,v1,v2,v3

    Then solve for us and vs and i get u1=0 u2=100 v1=0 v2=400 and v3=300

    Then c*12=50 so not optimal

    (c) Enter X12 into basis create loop etc. but that give new solution as X12=40, X21=30 and X23=60. But then when you go through us and vs again to test for optimality, you've got 5 variables to solve for and only four equations so I'm stuck. Help please!
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