You have 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 as follows: (x₁, x₂, x3, S₁, S₂) = (7,0,0,2,0), z* = 28. Consider the following situations: • The objective function changes to maximise z = 4x₁ + 7x2 + 7x3. • The objective function changes to maximise z = 3x₁ + 3x2 + 7x3. For each situation above, analyse separately and specifically what must be checked if you were to determine whether the current basis remains optimal after the change is made. Justify your answers.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter9: Decision Making Under Uncertainty
Section: Chapter Questions
Problem 34P
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You have 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 as follows:
(x₁, x₂, x3, S₁, S₂) = (7,0,0,2,0), z* = 28.
Consider the following situations:
• The objective function changes to maximise z = 4x₁ + 7x2 + 7x3.
• The objective function changes to maximise z = 3x₁ + 3x2 + 7x3.
For each situation above, analyse separately and specifically what must be checked if you
were to determine whether the current basis remains optimal after the change is made. Justify
your answers.
Transcribed Image Text:You have 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 as follows: (x₁, x₂, x3, S₁, S₂) = (7,0,0,2,0), z* = 28. Consider the following situations: • The objective function changes to maximise z = 4x₁ + 7x2 + 7x3. • The objective function changes to maximise z = 3x₁ + 3x2 + 7x3. For each situation above, analyse separately and specifically what must be checked if you were to determine whether the current basis remains optimal after the change is made. Justify your answers.
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