linear programming notes

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1、LinearProgrammingNotesCarlW.LeeDepartmentofMathematicsUniversityofKentuckyLexington,KY40506lee@ms.uky.eduJanuary3,1996LatestRevision:Fall2003iContents1References12Exercises:LinearAlgebra23Introduction53.1Example......................................53.2D

2、efinitions.....................................63.3BacktotheExample...............................74Exercises:LinearPrograms95TheoremsoftheAlternatives135.1SystemsofEquations...............................135.2Fourier-MotzkinElimination—AStartingExample..

3、............155.3ShowingourExampleisFeasible........................185.4AnExampleofanInfeasibleSystem......................195.5Fourier-MotzkinEliminationinGeneral.....................215.6MoreAlternatives.................................236Exercises:Sy

4、stemsofLinearInequalities257Duality287.1EconomicMotivation...............................287.2TheDualLinearProgram............................297.3TheDualityTheorems..............................317.4CommentsonGoodCharacterization......................36

5、7.5ComplementarySlackness............................367.6DualsofGeneralLP’s..............................377.7GeometricMotivationofDuality........................428Exercises:Duality449TheSimplexMethod509.1BasesandTableaux...............................

6、.509.2Pivoting......................................579.3The(Primal)SimplexMethod..........................62ii10Exercises:TheSimplexMethod7411TheSimplexMethod—FurtherConsiderations7811.1Uniqueness....................................7811.2RevisedSimplexM

7、ethod.............................7811.3DualSimplexMethod..............................8111.4RevisedDualSimplexMethod..........................8311.5SensitivityAnalysis................................8511.5.1RightHandSides.............................861

8、1.5.2ObjectiveFunctionCoefficients.....................8811.5.3NewVariable...............................9111.5.4NewConstraint..............................9211.6LP’sWithEquations...............................9311.7LP’sWith