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Linear Prog COP4355_Part_14

Linear Prog COP4355_Part_14 - Chapter 5 Linear Programming...

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60 Chapter 5 Linear Programming: Computer Applications 5.1 (b) (continued) Tableau 2 X Y S1 A1 S2 A2 Cj 8 10 0 M 0 M Bi Θ Y 10 0.50 1.00 -0.17 0.17 0.00 0.00 6 12 A2 M 0.50 0.00 0.17 -0.17 -1.00 1.00 4 8 Zj 5+.5 M 10 -1.7+.17 M 1.7-.17 M - M M 60+4 M Zj 3-.5 M 0 1.7-.17 M -1.7+1.17 M M 0 Entering: X Leaving: A2 Optimal Tableau X Y S1 A1 S2 A2 Cj 8 10 0 M 0 M Bi Y 10 0.00 1.00 -0.33 0.33 1.00 -1.00 2 X 8 1.00 0.00 0.33 -0.33 -2.00 2.00 8 Zj 8 10 -0.67 0.67 -6 6 84.00 Zj 0 0 0.67 -.67+ M 6 -6+ M Optimal Solution: X = 8, Y = 2, Z MIN = 84 5.1 (c) MAX Z: 5X + Y Subject to: X + Y 6 2X + Y 8 (X, Y 0)

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Solutions Manual and Workbook 61 5.1 (c) (continued) Initial Tableau X Y S1 A1 S2 Cj 5 1 0 - M 0 Bi Θ A1 - M 1.00 1.00 -1.00 1.00 0.00 6 6 S2 0 2.00 1.00 0.00 0.00 1.00 8 4 Zj - M - M M - M 0 -6 M Zj M M - M 0 0 Entering: X Leaving: S2 Tableau 2 X Y S1 A1 S2 Cj 5 1 0 - M 0 Bi Θ A1 - M 0.00 0.50 -1.00 1.00 -0.50 2 4 X 5 1.00 0.50 0.00 0.00 0.50 4 8 Zj 5 2.5-.5 M M - M 2.5-.5 M 20-2 M Zj 0 -1.5+.5 M - M 0 -2.5-.5 M Entering: Y Leaving: A1 Optimal Tableau X Y S1 A1 S2 Cj 5 1 0 - M 0 Bi Y 1 0.00 1.00 -2.00 2.00 -1.00 4 X 5 1.00 0.00 1.00 -1.00 1.00 2 Zj 5 1 3 -3 4 14 Zj 0 0 -3 - M +3 -4 Optimal Solution: X = 2, Y = 4, Z MAX = 14
62 Chapter 5 Linear Programming: Computer Applications 5.1 (d) MAX Z:

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Linear Prog COP4355_Part_14 - Chapter 5 Linear Programming...

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