sol4 - AMS 540 / MGT 540 (Fall, 2010) Estie Arkin Homework...

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Unformatted text preview: AMS 540 / MGT 540 (Fall, 2010) Estie Arkin Homework Set # 4: Solution notes 1). Solve using the big M method: Set up a standard form, with a 1 and a 2 the artificial variables: max z = 2 x 1- 5 x 2 + x 3- Ma 1- Ma 2 s . t .- x 1 + x 2 + x 3- x 4 + a 1 = 5 x 1 + x 2- x 3 + a 2 = 1 5 x 1 + 3 x 2- x 3 + x 5 = 9 x 1 ,x 2 ,x 3 ,x 4 ,x 5 ,a 1 ,a 2 after cleaning up the objective row, the first tableau is: z x 1 x 2 x 3 x 4 x 5 a 1 a 2 RHS z 1-2 5-2M-1 M-6M a 1-1 1 1-1 1 5 a 2 1 1-1 1 1 x 5 5 3-1 1 9 pivot x 2 in and a 2 out and get second tableau: z x 1 x 2 x 3 x 4 x 5 a 1 a 2 RHS z 1 2M-7 4-2M M 2M-5-5-4M a 1-2 2-1 1-1 4 x 2 1 1-1 1 1 x 5 2 2 1-3 6 pivot x 3 in and a 1 out get third tableau: z x 1 x 2 x 3 x 4 x 5 a 1 a 2 RHS z 1-3 2 M-2 M-3-13 x 3-1 1-0.5 0.5-0.5 2 x 2 1-0.5 0.5 0.5 3 x 5 4 1 1-1-2 2 At this point we have a feasible solution to the original problem, we could remove the artificial columns, if we want. Pivot x 1 in and x 5 out to get the last (optimal) tableau: z x 1 x 2 x 3 x 4 x 5 a 1 a 2 RHS z 1 2.75 0.75 M-2.75 M-4.5-11.5 x 3 1-0.25 0.25 0.25-1 2.5 x 2 1-0.5 0.5 0.5 3 x 1 1 0.25 0.25-0.25-0.5 0.5 Note that M appears throughout only in the objective row, and at the final tableau only in the coefficients of the artificial variables. The optimal solution isthe coefficients of the artificial variables....
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This note was uploaded on 01/31/2011 for the course AMS 540 taught by Professor Arkin,e during the Fall '08 term at SUNY Stony Brook.

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sol4 - AMS 540 / MGT 540 (Fall, 2010) Estie Arkin Homework...

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