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  • Reduced cost of basic variables are not zero!

    From Z. My@21:1/5 to All on Tue Oct 11 00:32:11 2016
    Hello everyone,

    I am solving a problem with Lingo in which the values of basic variables are not zero. I cannot understand what it means.

    Here is the model and the solution:

    MAX = 25.83 * Xa + 28 * Xb + 28.5 * Xc + 29.33 * Xd + 84.17 * Xe;
    0.25 * Xa + 0.17 * Xb + 0.25 * Xc <= 80;
    0.12 * Xb + 0.12 * Xc + 0.38 * Xd + Xe <=40;
    0.33* Xa + 0.17 * Xb + 0.22 * Xc + 0.25 * Xd + 0.05 * Xe<= 120;
    0.1* Xa + 0.25 * Xb + 0.17 * Xc + 0.1 * Xd + 0.07 * Xe<= 80;
    Xa<=120;
    Xb<=100;
    Xc<=100;
    Xd<=50;
    Xe<=30;
    @GIN(Xa);
    @GIN(Xb);
    @GIN(Xc);
    @GIN(Xd);
    @GIN(Xe);

    Global optimal solution found.
    Objective value: 10096.32
    Objective bound: 10096.32
    Infeasibilities: 0.000000
    Extended solver steps: 0
    Total solver iterations: 0


    Variable Value Reduced Cost
    XA 120.0000 -25.83000
    XB 100.0000 -28.00000
    XC 100.0000 -28.50000
    XD 0.000000 -29.33000
    XE 16.00000 -84.17000

    Row Slack or Surplus Dual Price
    1 10096.32 1.000000
    2 8.000000 0.000000
    3 0.000000 0.000000
    4 40.60000 0.000000
    5 24.88000 0.000000
    6 0.000000 0.000000
    7 0.000000 0.000000
    8 0.000000 0.000000
    9 50.00000 0.000000
    10 14.00000 0.000000

    I would highly appreciate it if anyone can help me.

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  • From Paul@21:1/5 to Z. My on Tue Oct 11 13:33:46 2016
    On Tuesday, October 11, 2016 at 3:32:12 AM UTC-4, Z. My wrote:
    Hello everyone,

    I am solving a problem with Lingo in which the values of basic variables are not zero. I cannot understand what it means.
    ...

    Since you are declaring the variables as general integer, they are not really basic, and there is no reason to expect their reduced costs to be zero.

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