Linear Prog COP4355_Part_12

# Linear Prog COP4355_Part_12 - 52 Chapter 4 Linear...

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52 Chapter 4 Linear Programming: The Simplex Algorithm (b) MAX Z: 3Y 1 + 2Y 2 Subject to: 2Y 1 + Y 2 8 Y 2 2 -Y 1 -1 MAX Z: 3Y 1 + 2Y 2 + 0S 1 + 0S 2 + 0S 3 Subject to: 2Y 1 + Y 2 + S 1 = 8 Y 2 + S 2 = 2 -Y 1 + S 3 = -1 Using Dual Simplex Initial Tableau Y1 Y2 S1 S2 S3 Cj 3 2 0 0 0 Bi S1 0 2 1 1 0 0 8 S2 0 0 1 0 1 0 2 Zj 0 0 0 0 0 0 Zj 3 2 0 0 0

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Solutions Manual and Workbook 53 4.16 (b) continued Y1 Y2 S1 S2 S3 Cj 3 2 0 0 0 Bi S1 0 0 1 1 0 2 6 S2 0 0 1 0 1 0 2 Y1 3 1 0 0 0 -1 1 Zj 3 0 0 0 -3 3 Zj 0 2 0 0 3 The solution is now feasible. We proceed to optimality by regular simplex. Y1 Y2 S1 S2 S3 Cj 3 2 0 0 0 Bi S3 0 0 0.5 0.5 0 1 3 S2 0 0 1 0 1 0 2 Y1 3 1 0.5 0.5 0 0 4 Zj 3 1.5 1.5 0 0 12 Zj 0 0.5 -1.5 0 0 Y1 Y2 S1 S2 S3 Cj 3 2 0 0 0 Bi S3 0 0 0 0.5 -0.5 1 2 Y2 2 0 1 0 1 0 2 Y1 3 1 0 0.5 -0.5 0 3 Zj 3 2 1.5 0.5 0 13 Zj 0 0 -1.5 -0.5 0 Optimal Solution: Y 1 = 3, Y 2 = 2, Z MAX = 13
54 Chapter 4 Linear Programming: The Simplex Algorithm 4.17 Primal Initial Tableau X1 X2 S1 S2 S3 S4 S5 Cj 3 1 0 0 0 0 0 B i A1 M 1 5 -1 0 0 0 0 15 A2 M 2 4 0 -1 0 0 0 24 A3 M 3 3 0 0 -1 0 0 18 A4 M 4 2 0 0 0 -1 0 24 A5 M 5 1 0 0 0 0 -1 15 Zj 15M 15 - M - M - M - M - M 116M Zj 3-15M 1-15M M M M M M Initial Tableau (omitting columns for artificial variables).

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