3. Consider the following dual problem Minimize Z = 7x1 + 2x2 + 5x3 + 4x4 subject to 2x1 + 4x2 + 7x3 + x4 ≥ 5 8x1 + 4x2 + 6x3 + 4x4 ≥ 8 3x1 +8x2 + x3 + 4x4 ≥ 4 and x1 ≥0, x2 ≥ 0, x3 ≥ 0, x4 ≥ 0. (a) Construct the primal problem corresponding to this problem. (b) Solve the primal problem by the original simplex method (in tabular form) step by step. Identify the complementary basic solution for the dual problem obtained at each iteration. (c) Use the dual simplex method manually to solve the dual problem. Compare the resulting sequence of basic solutions with the complementary basic solutions obtained in part (b).
3. Consider the following dual problem Minimize Z = 7x1 + 2x2 + 5x3 + 4x4 subject to 2x1 + 4x2 + 7x3 + x4 ≥ 5 8x1 + 4x2 + 6x3 + 4x4 ≥ 8 3x1 +8x2 + x3 + 4x4 ≥ 4 and x1 ≥0, x2 ≥ 0, x3 ≥ 0, x4 ≥ 0. (a) Construct the primal problem corresponding to this problem. (b) Solve the primal problem by the original simplex method (in tabular form) step by step. Identify the complementary basic solution for the dual problem obtained at each iteration. (c) Use the dual simplex method manually to solve the dual problem. Compare the resulting sequence of basic solutions with the complementary basic solutions obtained in part (b).
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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Transcribed Image Text:3. Consider the following dual problem
Minimize Z = 7x₁ + 2x₂ + 5x3 + 4x4
subject to 2x₁ + 4x₂ + 7x3 + x4 ≥ 5
8x₁ + 4x2 + 6x3 + 4x4 ≥ 8
3x₁ + 8x₂ + x3 + 4x4 ≥ 4
and x₁ ≥ 0, x₂ ≥ 0, X3 ≥ 0, X4 ≥ 0.
(a) Construct the primal problem corresponding to this problem.
(b) Solve the primal problem by the original simplex method (in tabular form) step by step.
Identify the complementary basic solution for the dual problem obtained at each iteration.
Use the dual simplex method manually to solve the dual problem. Compare the resulting
sequence of basic solutions with the complementary basic solutions obtained in part (b).
(c)
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