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.

\Program-ming" was a military term that referred to activities such as planning schedules e ciently or deploying men optimally. George Dantzig, a member of the U.S. Air Force, developed the Simplex method of optimization in 1947 in order to

  Programs, Programming, Linear programming, Linear, Ming, Pro gramming