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Linear Programming-Transportation Simplex

  1. Jun 8, 2012 #1
    I don't know if I've posted this in the right place but I thought I'd give it a go anyway.

    1. The problem statement, all variables and given/known data
    See Attatchment


    2. Relevant equations



    3. The attempt at a solution

    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!
     

    Attached Files:

  2. jcsd
  3. Jun 8, 2012 #2

    Ray Vickson

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    Science Advisor
    Homework Helper

    Your new solution is not basic; you need a basis, and since two previously-basic variables were driven to zero simultaneously, you need to drop one and keep the other at level 0; that is, your new basic solution will be degenerate. Either x13 or x22 should drop out of the basis, leaving the other one in at zero value. One of these choices will lead to optimality. Try one, and if it does not work, then try the other.

    RGV
     
  4. Jun 8, 2012 #3
    Thanks a lot :)
     
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