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Maximize subject to Z= x₁ - x₂ + 2x3, 2x12x2 + 3x3 ≤ 5 X₁ + X₂ X₁ X₂ and X3 ≤3 X3 ≤2

Maximize subject to Z= x₁ - x₂ + 2x3, 2x12x2 + 3x3 ≤ 5 X₁ + X₂ X₁ X₂ and X3 ≤3 X3 ≤2

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1 5.2-5. Work through the matrix form of the simplex method step by step to solve the model given in Prob. 4.9-6. D 5.3-1.* Consider the following problem. Z = x₁ - x₂ + 2x3, Maximize subject to 2x12x2+3x3 X₁ + X₂ X₁ X₂ and x₁ ≥ 0, X₂ ≥ 0, x3 ≥ 0. Let x4, X5, and x6 denote the slack variables for the respective con- straints. After you apply the simplex method, a portion of the final simplex tableau is as follows: ≤5 X3 ≤ 3 X3 ≤ 2 Basic Variable Eq. (0) Z X₂ X6 X3 (2) (3) N 1 000 Coefficient of: X₁ X2 X3 X4 1 1 0 1 X5 X6 1 0 3 - 2 1 2 0 OIO 0 Right Side (a) Use the fundamental insight presented in Sec. 5.3 to identify the missing numbers in the final simplex tableau. Show your calculations. (b) Identify the defining equations of the CPF solution correspond- ing to the optimal BF solution in the final simplex tableau.
Transcribed Image Text:1 5.2-5. Work through the matrix form of the simplex method step by step to solve the model given in Prob. 4.9-6. D 5.3-1.* Consider the following problem. Z = x₁ - x₂ + 2x3, Maximize subject to 2x12x2+3x3 X₁ + X₂ X₁ X₂ and x₁ ≥ 0, X₂ ≥ 0, x3 ≥ 0. Let x4, X5, and x6 denote the slack variables for the respective con- straints. After you apply the simplex method, a portion of the final simplex tableau is as follows: ≤5 X3 ≤ 3 X3 ≤ 2 Basic Variable Eq. (0) Z X₂ X6 X3 (2) (3) N 1 000 Coefficient of: X₁ X2 X3 X4 1 1 0 1 X5 X6 1 0 3 - 2 1 2 0 OIO 0 Right Side (a) Use the fundamental insight presented in Sec. 5.3 to identify the missing numbers in the final simplex tableau. Show your calculations. (b) Identify the defining equations of the CPF solution correspond- ing to the optimal BF solution in the final simplex tableau.
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