Problem 2 Simplex Approaches. Consider the following LP and its dual Primal Minimize x₁ + x2 s.t. 2x1 + x2 > 1 -x12x2 ≥ −2 -X2 -0.5 x1, x2 > 0 Dual Maximize y1 - s.t. - 2y2 - 0.5y3 2y1 - y2 ≤ 1 y12y2y3 ≤ 1 Y1, 92, 93 > 0 Use the simplex method to find an optimal solution to the primal LP. Use the Weak LP Dual- ity Theorem to justify the optimality of your solution. Hint: The proof of the Strong LP Duality Theorem involves deriving the optimal dual solution from the primal. Additionally, the dual of the dual is the primal.
Problem 2 Simplex Approaches. Consider the following LP and its dual Primal Minimize x₁ + x2 s.t. 2x1 + x2 > 1 -x12x2 ≥ −2 -X2 -0.5 x1, x2 > 0 Dual Maximize y1 - s.t. - 2y2 - 0.5y3 2y1 - y2 ≤ 1 y12y2y3 ≤ 1 Y1, 92, 93 > 0 Use the simplex method to find an optimal solution to the primal LP. Use the Weak LP Dual- ity Theorem to justify the optimality of your solution. Hint: The proof of the Strong LP Duality Theorem involves deriving the optimal dual solution from the primal. Additionally, the dual of the dual is the primal.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter5: Network Models
Section5.5: Shortest Path Models
Problem 30P
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![Problem 2 Simplex Approaches. Consider the following LP and its dual
Primal
Minimize x₁ + x2
s.t.
2x1 + x₂ ≥ 1
−x1 − 2x2 ≥ −2
-x2 ≥ -0.5
Xx1, x2 > 0
Dual
Maximize y₁ - 2y2 - 0.5y3
2y1 - y2 ≤ 1
Y1 - 2y2 - Y3 ≤ 1
Y1, Y2, Y3 ≥ 0
s.t.
Use the simplex method to find an optimal solution to the primal LP. Use the Weak LP Dual-
ity Theorem to justify the optimality of your solution. Hint: The proof of the Strong LP Duality
Theorem involves deriving the optimal dual solution from the primal. Additionally, the dual of the
dual is the primal.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7ade660a-35f4-4d6c-9b74-ecbeda94ccc4%2Fc19456cd-4b85-46ae-8a40-3e922122e61f%2F5l84dpc_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 2 Simplex Approaches. Consider the following LP and its dual
Primal
Minimize x₁ + x2
s.t.
2x1 + x₂ ≥ 1
−x1 − 2x2 ≥ −2
-x2 ≥ -0.5
Xx1, x2 > 0
Dual
Maximize y₁ - 2y2 - 0.5y3
2y1 - y2 ≤ 1
Y1 - 2y2 - Y3 ≤ 1
Y1, Y2, Y3 ≥ 0
s.t.
Use the simplex method to find an optimal solution to the primal LP. Use the Weak LP Dual-
ity Theorem to justify the optimality of your solution. Hint: The proof of the Strong LP Duality
Theorem involves deriving the optimal dual solution from the primal. Additionally, the dual of the
dual is the primal.
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