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6 This problem shows why a dual variable y, corresponding to a z constraint in a max problem must satisfy y, < 0. a Using the rules given in the text, find the dual of max z = 3x, + x, X, + x2 s 1 s.t. X1, X2 2 0 b Transform the LP of part (a) into a normal max problem. Now use (16) and (17) to find the dual of the transformed LP. Let y, be the dual variable correspond- ing to the second primal constraint. c Show that, defining ỹ, = -y2, the dual in part (a) is equivalent to the dual in part (b).

6 This problem shows why a dual variable y, corresponding to a z constraint in a max problem must satisfy y, < 0. a Using the rules given in the text, find the dual of max z = 3x, + x, X, + x2 s 1 s.t. X1, X2 2 0 b Transform the LP of part (a) into a normal max problem. Now use (16) and (17) to find the dual of the transformed LP. Let y, be the dual variable correspond- ing to the second primal constraint. c Show that, defining ỹ, = -y2, the dual in part (a) is equivalent to the dual in part (b).

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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6 This problem shows why a dual variable y, corresponding to a z constraint in a max problem must satisfy y, < 0. a Using the rules given in the text, find the dual of max z = 3x, + x, X, + x2 s 1 s.t. X1, X2 2 0 b Transform the LP of part (a) into a normal max problem. Now use (16) and (17) to find the dual of the transformed LP. Let y, be the dual variable correspond- ing to the second primal constraint. c Show that, defining ỹ, = -y2, the dual in part (a) is equivalent to the dual in part (b).
Transcribed Image Text:6 This problem shows why a dual variable y, corresponding to a z constraint in a max problem must satisfy y, < 0. a Using the rules given in the text, find the dual of max z = 3x, + x, X, + x2 s 1 s.t. X1, X2 2 0 b Transform the LP of part (a) into a normal max problem. Now use (16) and (17) to find the dual of the transformed LP. Let y, be the dual variable correspond- ing to the second primal constraint. c Show that, defining ỹ, = -y2, the dual in part (a) is equivalent to the dual in part (b).
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