Linear Prog COP4355_Part_11

Linear Prog COP4355_Part_11 - 48 Chapter 4 Linear...

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48 Chapter 4 Linear Programming: The Simplex Algorithm 4.14 (continued) Primal Tableau 2 X1 X2 S1 A1 S2 A2 S3 A3 Cj 2 3 0 M 0 M 0 M Bi Θ X2 3 0 1 -0 0.50 0 0 0 0 2 + A2 M 1 0 0 0 -1 1 0 0 3 3 A3 M 1 0 0.5 -0.50 0 0 -1 1 6 6 Zj 2 M 3 .5 M -.5 M - M M - M M 9 M Zj -2 M 0 -.5 M 1.5 M M 0 M 0 Entering: X 1 Leaving: Artificial 2 Dual Tableau 2 Y1 Y2 Y3 S’1 S’2 Cj 4 3 8 0 0 Bi Θ Y3 8 0 1 1 1 0 2 + S’2 0 2 -1 0 -1 1 1 0.50 Zj 0 8 8 8 0 16 Zj 4 -5 0 -8 0 Entering: Y1 Leaving: Slack 2
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Solutions Manual and Workbook 49 4.14 (continued) Primal Tableau 3 X1 X2 S1 A1 S2 A2 S3 A3 Cj 2 3 0 M 0 M 0 M Bi Θ X2 3 0 1 -.50 0.5 0 0 0 0 2 + X1 2 1 0 0 0 -1 1 0 0 3 -3 A3 1 M 0 0 0 -0.5 1 -1 -1 1 3 3 Zj 2 3 .5 M -.5M M -M - M M 3 M Zj 0 0 -.5M 1.5 M -M 2 M M 0 Entering: Slack 2 Leaving: Artificial 3 Optimal Primal Tableau X1 X2 S1 A1 S2 A2 S3 A3 Cj 2 3 0 M 0 M 0 M Bi X2 3 0 1 -0.50 .50 0 0 0 0 2 X1 2 1 0 0.50 -.50 0 0 -1 1 6 S2 0 0 0 0.50 -.50 1 -1 -1 1 3 Zj 2 3 -0.50 .50 0 0 -2 2 18 Zj 0 0 0.50 -.50+ M 0 M 2 -2+ M Dual Optimal Tableau Y1 Y2 Y3 S’1 S’2 Cj 4 3 8 0 0 Bi Y3 8 0 1 1 1 0 2 Y1 4 1 -0.50 0 -0.50 0.50 0.50 Zj 4 6 8 6 2 18 Zj 0 -3 0 -6 -2
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