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Linear Programming Notes VI Duality and Complementary ...

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Linear Programming Notes VIDuality and Complementary Slackness1 IntroductionIt turns out that Linear Programming problems come in pairs. That is, if youhave one Linear Programming problem, then there is automatically another one,derived from the same with an LP written in the form:maxc xsubject toAx b, x 0.(We know from the study of problem transformations that you can write any LPin this form.) I will call this thePrimal. It is useful to keep track of that there arenvariables (components ofx) andmconstraints. Thatmeans thatcisn dimensional,bism dimensional, andAis a matrix withmrows andncolumns. The data of the problem areb,c, andA.

matical relationship is described in what is called the Duality Theorem of Linear Programming. I will have a lot to say about this theorem. The answer to the second question is simple. Before I give the answer, let me explain the question in more detail. I gave you a de nition of the dual of a linear programming problem.

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