Problem 1 Consider the following LP: min 5x₁ + 4x2 s.t. x₁ + x₂ ≥ 1 2x1 - x₂ ≥ 1 3x2 ≤ 2 x1, x₂ > 0. 1. Write down the dual of this LP. 2. We know that by strong duality, we can either solve this LP or its dual form to get the same optimal objective value. If you apply the simplex algorithm, which one would you rather solve? Make your choice and apply the simplex algorithm to solve it.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter7: Nonlinear Optimization Models
Section: Chapter Questions
Problem 59P
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Problem 1 Consider the following LP:
min 5x₁ + 4x2
s.t. x₁ + x2 ≥ 1
2x₁ − x₂ ≥ 1
3x₂ ≤ 2
x1, x2 > 0.
1. Write down the dual of this LP.
2. We know that by strong duality, we can either solve this LP or its dual form to get the same
optimal objective value. If you apply the simplex algorithm, which one would you rather
solve? Make your choice and apply the simplex algorithm to solve it.
Transcribed Image Text:Problem 1 Consider the following LP: min 5x₁ + 4x2 s.t. x₁ + x2 ≥ 1 2x₁ − x₂ ≥ 1 3x₂ ≤ 2 x1, x2 > 0. 1. Write down the dual of this LP. 2. We know that by strong duality, we can either solve this LP or its dual form to get the same optimal objective value. If you apply the simplex algorithm, which one would you rather solve? Make your choice and apply the simplex algorithm to solve it.
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