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Consider the LP problem max 2x₁ + 2x2 subject to x1 + x3 + x4 +x2 + x3 x4 x1 + x2 + 2x3 X1, X2, X3, X4 ≥ 0. ≤1 ≤1 <3 a). Determine the dual problem. b). Assuming that Y* = (1,1,1) is an optimal solution point to the dual problem, determine an optimal solution point, X*, to the primal. c). Show that for this pair of solutions, X*, Y*, for each j, x > 0 implies that the slack in the corresponding dual constraint is zero.

Consider the LP problem max 2x₁ + 2x2 subject to x1 + x3 + x4 +x2 + x3 x4 x1 + x2 + 2x3 X1, X2, X3, X4 ≥ 0. ≤1 ≤1 <3 a). Determine the dual problem. b). Assuming that Y* = (1,1,1) is an optimal solution point to the dual problem, determine an optimal solution point, X*, to the primal. c). Show that for this pair of solutions, X*, Y*, for each j, x > 0 implies that the slack in the corresponding dual constraint is zero.

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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Linear Programming
2. Consider the LP problem max 2x1 + 2x₂ subject to X1 + x3 + x4 +x2 + x3 x4 x1 + x2 + 2x3 X1, X2, X3, X4 ≥ 0. ≤1 VI VI VI ≤1 <3 a). Determine the dual problem. b). Assuming that Y* = (1,1,1) is an optimal solution point to the dual problem, determine an optimal solution point, X*, to the primal. c). Show that for this pair of solutions, X*, Y*, for each j, x > 0 implies that the slack in the corresponding dual constraint is zero.
Transcribed Image Text:2. Consider the LP problem max 2x1 + 2x₂ subject to X1 + x3 + x4 +x2 + x3 x4 x1 + x2 + 2x3 X1, X2, X3, X4 ≥ 0. ≤1 VI VI VI ≤1 <3 a). Determine the dual problem. b). Assuming that Y* = (1,1,1) is an optimal solution point to the dual problem, determine an optimal solution point, X*, to the primal. c). Show that for this pair of solutions, X*, Y*, for each j, x > 0 implies that the slack in the corresponding dual constraint is zero.
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