Linear Programming: Theory and Applications

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LinearProgramming:TheoryandApplicationsC atherineLewisMay 11, 20081Contents1 Introductionto a linearprogram?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LinearProgrammingProblem. . . . . . . . . . . LinearProgramming. . . . . . . . . . . . SetsandDirections. . . . . . . . . . . . . . . . . . . . .82 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .163 nitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .194 AnOutlineof theProof205 ExamplesWithConvex SetsandExtremePoints Precursorsto theSimplexMethod . . . . . . . . . . .237 TheSimplexMethod In Practice258 Whatif thereis noinitialbasisin theSimplextableau?.

This paper will cover the main concepts in linear programming, including examples when appropriate. First, in Section 1 we will explore simple prop-erties, basic de nitions and theories of linear programs. In order to illustrate some applicationsof linear programming,we will explain simpli ed \real-world" examples in Section 2.

  Programming, Basics, Linear programming, Linear, Concept