Linear Prog COP4355_Part_7

Linear Prog COP4355_Part_7 - 32 Chapter 3 Linear...

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32 Chapter 3 Linear Programming: Graphical Analysis

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Solutions Manual and Workbook 33 Chapter 4 Linear Programming: The Simplex Algorithm 4.1 MAX Z: 8X + 6Y + 0S 1 + 0S 2 Subject to: 6X + 12Y + 1S 1 + 0S 2 = 72 5X + 2Y + 0S 1 + 1S 2 = 20 (X, Y, S i 0) Initial Tableau X Y Slack 1 Slack 2 Cj 8 6 0 0 Bi Θ Slack 1 0 6 12 1 0 72 12 Slack 2 0 5* 2 0 1 20 4 Zj 0 0 0 0 0 Zj 8 6 0 0 Entering: X Leaving: Slack 2 Tableau 2 X Y Slack 1 Slack 2 Cj 8 6 0 0 Bi Θ Slack 1 0 0 9.60* 1 -1.20 48 5 X 8 1 0.40 0 0.20 4 10 Zj 8 3.20 0 1.60 32.00 Zj 0 2.80 0 -1.60 Entering: Y Leaving: Slack 1
34 Chapter 4 Linear Programming: The Simplex Algorithm 4.1 (continued) Optimal Tableau X Y Slack 1 Slack 2 Cj 8 6 0 0 Bi Y 6 0 1 0.10 -0.13 5 X 8 1 0 -0.04 0.25 2 Zj 8 6 0.29 1.25 46 Zj 0 0 -0.29 -1.25 Optimal Solution: X = 2, Y = 5, Z MAX = 46 *The numerical value enclosed by the red square represents the pivot element. 4.2 MIN Z: 8X + 10Y +0S 1 + 0S 2 + MA 1 +MA 2 Subject to: 3X + 6Y - S

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Linear Prog COP4355_Part_7 - 32 Chapter 3 Linear...

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