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Complementary slackness

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

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This question was answered on: Oct 24, 2017

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