Solve this LP problem: 1. Maximize z = 3x₂ + 3x₂ + 3x3 Subject to: 2x₁ + x₂ + x3 ≤ 2 3x₂ + 4x₂ + 3x₂ ≥ 8 , X₂, X₂ ≥ 0 X₁, X₂¹ Requirements: a) Use the M-Technique to show that the optimal solution includes an artificial basic variable, but at zero level. b) Does the problem have a feasible optimal solution? Verify using the Two - Phase Technique and applying the procedure described on the next slide.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter2: Systems Of Linear Equations
Section2.4: Applications
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Solve this LP problem:
1. Maximize z = 3x₂ + 3x₂ + 3x3
Subject to: 2x₁ + x₂ + x3 ≤ 2
3x₂ + 4x₂ + 3x₂ ≥ 8
, X₂, X₂ ≥ 0
X₁, X₂¹
Requirements:
a)
Use the M-Technique to show that the optimal solution includes an
artificial basic variable, but at zero level.
b)
Does the problem have a feasible optimal solution? Verify using the Two -
Phase Technique and applying the procedure described on the next slide.
Transcribed Image Text:Solve this LP problem: 1. Maximize z = 3x₂ + 3x₂ + 3x3 Subject to: 2x₁ + x₂ + x3 ≤ 2 3x₂ + 4x₂ + 3x₂ ≥ 8 , X₂, X₂ ≥ 0 X₁, X₂¹ Requirements: a) Use the M-Technique to show that the optimal solution includes an artificial basic variable, but at zero level. b) Does the problem have a feasible optimal solution? Verify using the Two - Phase Technique and applying the procedure described on the next slide.
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