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.

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. Subtracting a slack variable from a \greater than or equal to" constraint or by adding an excess variable to a \less than or equal to" constraint, trans-forms inequalities into equalities.

  Programming, Linear programming, Linear, Introducing