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Linear Prog COP4355_Part_10

# Linear Prog COP4355_Part_10 - 44 4.10 Chapter 4 Linear...

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44 Chapter 4 Linear Programming: The Simplex Algorithm 4.10 (continued) Solution: X = 200 square feet, Y = 800 square feet, S 3 = 400 square feet, S 4 = 400 square feet. Meaning: Devote 200 square feet to decorations and 800 square feet to toys. S 3 is the amount by which the minimum toy space is exceeded and S 4 is the amount by which the space devoted to toys exceeds twice that devoted to decorations.

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Solutions Manual and Workbook 45 4.11 MAX Z: 2X 1 + 3X 2 + 5X 3 Subject to: X 1 + X 2 + X 3 = 10 X 1 X 3 4 X 2 3 (X 1 , X 2 , X 3 0) Tableau 1 X 1 X 2 X 3 A1 S2 A2 S3 Cj 2 3 5 - M 0 - M 0 Bi Θ A1 - M 1 1 1 1 0 0 0 10 10 A2 - M 1 0 -1 0 -1 1 0 4 4 S3 0 0 1 0 0 0 0 1 3 + Zj -2 M - M 0 - M M - M 0 -14 M Zj 2+2 M 3+ M 5 0 - M 0 0 Entering: X 1 Leaving: Artificial 2 Optimal Tableau X 1 X 2 X 3 A1 S2 A2 S3 Cj 2 3 5 - M 0 - M 0 Bi X 3 5 0 0.50 1 0.50 0.50 -0.50 0 3 X 1 2 1 0.50 0 0.50 -0.50 0.50 0 7 S3 0 0 1 0 0 0 0 1 3 Zj 2 3.50 5 3.50 1.50 -1.50 0 29 Zj 0 -0.50 0 -3.5- M -1.50 1.5- M 0 Solution: X 1 = 7,000 acres, X 3 = 3,000 acres, S 3 = 3,000 acres.
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