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L07_Artificial Variable techniques - Two Phase Method(Continued)

L07_Artificial Variable techniques - Two Phase Method(Continued)

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Minimize 2 1 7 5 x x z + = Subject to the constraints 0 , 18 60 4 3 42 3 2 2 1 2 1 2 1 2 1 + + + x x x x x x x x We shall solve this problem by two phase method.

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Phase I: Minimize Subject to the constraints 1 2 1 1 1 2 2 2 1 2 3 3 1 2 1 2 3 1 2 3 2 3 42 3 4 60 18 , , , , , , , 0 x x s R x x s R x x s R x x s s s R R R + - + = + - + = + - + = Here s 1 ,s 2 ,s 3 are surplus variables; R 1 ,R 2 ,R 3 are artificial variables. 1 2 3 r R R R = + +
r 1 0 0 0 0 0 -1 -1 -1 0 Basic r x1 x2 s1 s2 s3 R1 R2 R3 Sol 6 8 -1 -1 -1 0 0 0 120 R1 0 2 3 -1 0 0 1 0 0 42 R2 0 3 4 0 -1 0 0 1 0 60 R3 0 1 1 0 0 -1 0 0 1 18 x2 0 2/3 1 -1/3 0 0 1/3 0 0 14 r 1 2/3 0 5/3 -1 -1 -8/3 0 0 8 R2 0 1/3 0 4/3 -1 0 -4/3 1 0 4 R3 0 1/3 0 1/3 0 -1 -1/3 0 1 4

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r 1 2/3 0 5/3 -1 -1 -8/3 0 0 8 Basic r x1 x2 s1 s2 s3 R1 R2 R3 Sol x2 0 2/3 1 -1/3 0 0 1/3 0 0 14 R2 0 1/3 0 4/3 -1 0 -4/3 1 0 4 R3 0 1/3 0 1/3 0 -1 -1/3 0 1 4 x2 0 3/4 1 0 -1/4 0 0 1/4 0 15 r 1 1/4 0 0 1/4 -1 -1 -5/4 0 3 s1 0 1/4 0 1 -3/4 0 -1 3/4 0 3 R3 0 1/4 0 0 1/4 -1 0 -1/4 1 3
r 1 1/4 0 0 1/4 -1 -1 -5/4 0 3 Basic r x1 x2 s1 s2 s3

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