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  • 8/6/2019 CA427Simplex BigM Example

    1/2

    Simplex Big M Method

    Maximise 3X1 + 4X2

    Subject to 2X1 + X2 = 0

    Not in canonical form because there is no basic variable in the fourthequation. Therefore we add an artificial variable to that equation (R1) and

    give it a large negative coefficient in the objective function, to penalise

    it:

    Maximise 3X1 + 4X2

    Subject to 2X1 + X2 + S1 = 600

    X1 + X2 + S2 = 225

    5X1 + 4X2 +S3 = 1000X1 + 2X2 - S4 + R1 = 150

    X1 , X2 , S1 , S2 , S3 , S4 , R1 >= 0

  • 8/6/2019 CA427Simplex BigM Example

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    X1 X2 S4 S1 S2 S3 R1 B

    Z -3 -4 0 0 0 0 +M

    S1 2 3 0 1 0 0 0 600

    S2 1 1 0 0 1 0 0 225S3 5 4 0 0 0 1 0 1000

    R1 1 2 -1 0 0 0 1 150

    Not in Canonical form because of +M entry on Z row for one basic variable (R1).

    Pivot to replace +M on Z row by zero - Z row M*R1 row:

    X1 X2 S4 S1 S2 S3 R1 b

    Z (-3-M) (-4-2M) M 0 0 0 0 -150M

    S1 2 3 0 1 0 0 0 600

    S2 1 1 0 0 1 0 0 225

    S3 5 4 0 0 0 1 0 1000

    R1 1 2 -1 0 0 0 1 150

    X1 X2 S4 S1 S2 S3 R1 b

    Z -1 0 -2 0 0 0 M 800

    S1 0 3/2 1 0 0 -3/2 375

    S2 0 0 1 0 - 150S3 3 0 2 0 0 1 -2 700

    X2 1 - 0 0 0 75

    X1 X2 S4 S1 S2 S3 R1 b

    Z -1/3 0 0 4/3 0 0 M 800

    S4 1/3 0 1 2/3 0 0 -1 250

    S2 1/3 0 0 -1/3 1 0 0 25

    S3 7/3 0 0 -4/3 0 1 0 200

    X2 2/3 1 0 1/3 0 0 0 200

    X1 X2 S4 S1 S2 S3 R1 b

    Z 0 0 0 1 1 0 M 825

    S4 0 0 1 1 -1 0 -1 225

    X1 1 0 0 -1 3 0 0 75

    S3 0 0 0 1 -7 1 0 25

    X2 0 1 0 1 -2 0 0 250

    Optimal tableau: Solution: X1* = 75 X2* = 150 Z* = 825


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