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Mathematics, 08.11.2019 05:31 emmapizano

Recall that for a linear program in canonical form the condition of complimentary slackness is that two particular pairs of vectors are complimentary to each other, in contrast to a linear program in standard form wherein the condition of complimentary slackness is that a single particular pair of vectors are complimentary to each other. consider a generic linear program in canonical form (lp) mincz such that az 2 b and z 0, and convert it to standard form in the usual way by subtracting slack variables. your task is to show and explain how the single complimentarity condition of (lp) in standard form precisely expresses both complimentarity conditions of (lp) in canonical form. (hint: in order to answer this question in general and to get an appreciation for the question-it will be to first play with a specific example of (lp) by putting in actual numbers, writing out the two forms of lp and their respective compli- mentary slackness conditions. if done properly the explanation will be transparent.)

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