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Linear Programming: Theory and Applications

LinearProgramming:TheoryandApplicationsC atherineLewisMay 11, 20081 Contents1 Introductionto a linearprogram?.. LinearProgrammingProblem.. LinearProgramming.. SetsandDirections..82 ..163 nitions..194 AnOutlineof theProof205 ExamplesWithConvex SetsandExtremePoints Precursorsto theSimplexMethod ..237 TheSimplexMethod In Practice258 Whatif thereis noinitialbasisin theSimplextableau? ..319 .. 'sRule.. [2].. Ruleto Use?..3910 Sensitivity .. Analysisfora costcoe cient .. Analysisfora right-hand-sidevalue..4111 CaseStudy:BusingChildrento .. Function.. Together.. Prices..5712 Conclusion5721 Introductionto LinearProgrammingLinearprogrammingwas developedduringWorldWar II, whena systemwithwhich to maximizethee ciencyof resourceswas of \Program-ming"was a militarytermthatreferredto activitiessuch as planningschedulese cientlyor deployingmenoptimally.

plore an outline of the proof of the GRT and in Section 5 we work through a few examples related to the GRT. After learning the theory behind linear programs, we will focus methods of solving them. Section 6 introduces concepts necessary for introducing the Simplex algorithm, which we explain in Section 7. In Section 8, we explore

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