(Solution Download) Complementary slackness describes a relationship between the values of primal variables and dual...
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Complementary slackness describes a relationship between the values of primal variables and dual constraints and between the values of dual variables and primal constraints. Let be a feasible solution to the primal linear program given in (29.16)?(29.18), and let be a feasible solution to thedual linear program given in (29.83)?(29.85). Complementary slackness states that the following conditions are necessary and sufficient for and to be optimal:
a. Verify that complementary slackness holds for the linear program in lines (29.53)?(29.57).
b. Prove that complementary slackness holds for any primal linear program and its corresponding dual.
c. Prove that a feasible solution to a primal linear program given in lines (29.16)?(29.18) is optimal if and only if there exist values = (1, 2,?, m) such that
1. is a feasible solution to the dual linear program given in (29.83)?(29.85),
2. for all j such that and
3. =0 for all i such that
This question was answered on: Oct 24, 2017
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