Transcription of Linear Programming: Theory and Applications
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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. GeorgeDantzig,a member of ,developedtheSimplexmethod of optimizationin 1947in ordertoprovidean e cient ,expertsfroma variety of elds,especiallymathematicsandeconomics,h ave developedthetheorybehind\linearprogrammi ng"andexploreditsapplications[1].
Linear programming was developed during World War II, when a system with which to maximize the e ciency of resources was of utmost importance. New war-related projects demanded attention and spread resources thin. \Program-ming" was a military term that referred to activities such as planning schedules
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