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1. For each of the following linear programming models, give your recommendation on which is the more efficient way (probably) to obtain an optimal solution: by applying the simplex method directly to this primal problem or by applying the simplex method directly to the dual problem instead. Explain. (a) Maximize Z = 10x₁ - 4x₂ + 7x3 subject to 3x1x₂ + 2x3 ≤ 25 x12x2 + 3x3 ≤ 25 5x₁ + x₂ + 2x3 ≤ 40 x₁ + x₂ + x3 ≤ 90 2x₁x₂ + x3 ≤ 20 and x₁ ≥ 0, x₂ ≥ 0, x3 ≥ 0. (b) Maximize Z = 2x₁ + 5x₂ + 3x3 + 4x4 + x5 subject to 3x₁ + 3x₂ + 2x3 + 3x4 + x5 ≤6 4x₁ + 6x₂ + 5x3 + 7x4 + x5 ≤ 15 and x; ≥ 0, for j = 1, 2, 3, 4, 5.

1. For each of the following linear programming models, give your recommendation on which is the more efficient way (probably) to obtain an optimal solution: by applying the simplex method directly to this primal problem or by applying the simplex method directly to the dual problem instead. Explain. (a) Maximize Z = 10x₁ - 4x₂ + 7x3 subject to 3x1x₂ + 2x3 ≤ 25 x12x2 + 3x3 ≤ 25 5x₁ + x₂ + 2x3 ≤ 40 x₁ + x₂ + x3 ≤ 90 2x₁x₂ + x3 ≤ 20 and x₁ ≥ 0, x₂ ≥ 0, x3 ≥ 0. (b) Maximize Z = 2x₁ + 5x₂ + 3x3 + 4x4 + x5 subject to 3x₁ + 3x₂ + 2x3 + 3x4 + x5 ≤6 4x₁ + 6x₂ + 5x3 + 7x4 + x5 ≤ 15 and x; ≥ 0, for j = 1, 2, 3, 4, 5.

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. For each of the following linear programming models, give your recommendation on which is the more efficient way (probably) to obtain an optimal solution: by applying the simplex method directly to this primal problem or by applying the simplex method directly to the dual problem instead. Explain. (a) Maximize subject to Z=10x₁4x2 + 7x3 - x₂ + 2x3 ≤ 25 3x1 x₁2x₂ + 3x3 ≤ 25 - 5x₁ + x₂ + 2x3 ≤ 40 x₁ + x₂ + x3 ≤ 90 2x₁ - x₂ + x3 ≤ 20 and x₁ ≥ 0, x₂ ≥ 0, x3 ≥ 0. (b) Maximize Z = 2x₁ +5x₂ + 3x3 + 4x4 + X5 subject to 3x₁ + 3x₂ + 2x3 + 3x4 + x5 ≤ 6 4x₁ + 6x₂ + 5x3 + 7x4 + x5 ≤ 15 and x; ≥ 0, for j = 1, 2, 3, 4, 5.
Transcribed Image Text:1. For each of the following linear programming models, give your recommendation on which is the more efficient way (probably) to obtain an optimal solution: by applying the simplex method directly to this primal problem or by applying the simplex method directly to the dual problem instead. Explain. (a) Maximize subject to Z=10x₁4x2 + 7x3 - x₂ + 2x3 ≤ 25 3x1 x₁2x₂ + 3x3 ≤ 25 - 5x₁ + x₂ + 2x3 ≤ 40 x₁ + x₂ + x3 ≤ 90 2x₁ - x₂ + x3 ≤ 20 and x₁ ≥ 0, x₂ ≥ 0, x3 ≥ 0. (b) Maximize Z = 2x₁ +5x₂ + 3x3 + 4x4 + X5 subject to 3x₁ + 3x₂ + 2x3 + 3x4 + x5 ≤ 6 4x₁ + 6x₂ + 5x3 + 7x4 + x5 ≤ 15 and x; ≥ 0, for j = 1, 2, 3, 4, 5.
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