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(Question 5) Solved a 3-variable maximisation Linear Program with the objective function of z = 4x₁ + 3x₂ + 7x3. The Linear Program has two "s" constraints, and its optimal solution is (x₁, x₂, x3, S₁, S₂ ) = (7, 0, 0, 2, 0), z = 28. First situation: the objective function changes to maximise z = 4x₁ + 7x₂ + 7x3. Second situation: the objective function changes to maximise: z = 3x₁ + 3x₂ + 7x3. Analyse separately and specifically for each situation, what must be checked if were to determine whether the current basis remains optimal after the change is made. Justify the answers.

(Question 5) Solved a 3-variable maximisation Linear Program with the objective function of z = 4x₁ + 3x₂ + 7x3. The Linear Program has two "s" constraints, and its optimal solution is (x₁, x₂, x3, S₁, S₂ ) = (7, 0, 0, 2, 0), z = 28. First situation: the objective function changes to maximise z = 4x₁ + 7x₂ + 7x3. Second situation: the objective function changes to maximise: z = 3x₁ + 3x₂ + 7x3. Analyse separately and specifically for each situation, what must be checked if were to determine whether the current basis remains optimal after the change is made. Justify the answers.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.4: Linear Programming
Problem 15E
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INTRODUCTION TO OPERATIONS RESEARCH

 

Introduction to operations research Question (Question 5) Solved a 3-variable maximisation Linear Program with the objective function of z = 4x₁ + 3x₂ + 7x3. The Linear Program has two "<" constraints, and its optimal solution is (x₁, x₂, x3, S₁, S₂ ) = (7, 0, 0, 2, 0), z* = 28. First situation: the objective function changes to maximise z = 4x₁ + 7x₂ + 7x3. Second situation: the objective function changes to maximise: z = 3x₁ + 3x₂ + 7x3. Analyse separately and specifically for each situation, what must be checked if were to determine whether the current basis remains optimal after the change is made. Justify the answers.
Transcribed Image Text:Introduction to operations research Question (Question 5) Solved a 3-variable maximisation Linear Program with the objective function of z = 4x₁ + 3x₂ + 7x3. The Linear Program has two "<" constraints, and its optimal solution is (x₁, x₂, x3, S₁, S₂ ) = (7, 0, 0, 2, 0), z* = 28. First situation: the objective function changes to maximise z = 4x₁ + 7x₂ + 7x3. Second situation: the objective function changes to maximise: z = 3x₁ + 3x₂ + 7x3. Analyse separately and specifically for each situation, what must be checked if were to determine whether the current basis remains optimal after the change is made. Justify the answers.
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