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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.

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Systems Of Equations And Inequalities
Section6.6: Linear Programming
Problem 33E
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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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