Maximize z = 2x1 + 2x2 + 4x3   subject to:   2x1 + x2 + x3 <= 2   3x1 + 4x2 + 2x3 >= 8   x1, x2, x3 >= 0   (a) Show that Phase I will terminate with an artificial basic variable at zero level (you may use TORA for convenience).   (b) Remove the zero artificial variable prior to the start of Phase II, then carry out Phase II iterations.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter7: Nonlinear Optimization Models
Section: Chapter Questions
Problem 52P
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Consider the following problem:

 

Maximize z = 2x1 + 2x2 + 4x3

 

subject to:

 

2x1 + x2 + x3 <= 2

 

3x1 + 4x2 + 2x3 >= 8

 

x1, x2, x3 >= 0

 

(a) Show that Phase I will terminate with an artificial basic variable at zero level (you may use TORA for convenience).

 

(b) Remove the zero artificial variable prior to the start of Phase II, then carry out Phase II iterations.

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