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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.

Constraint Inequalities We rst consider the problem of making all con-straints of a linear programming problem in the form of strict equalities. By introducing new variables to the problem that represent the di erence between the left and the right-hand sides of the constraints, we eliminate this concern.

  Programming, Linear programming, Linear, Constraints

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