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.

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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.
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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