Linear Programming in Matrix Form B

Linear Programming in Matrix form Appendix B. We first introduce Matrix concepts in Linear Programming by developing a variation of the simplex method called the revised simplex method. This algorithm, which has become the basis of all commercial computer codes for Linear Programming , simply recognizes that much of the information calculated by the simplex method at each iteration, as described in Chapter 2, is not needed. Thus, efficiencies can be gained by computing only what is absolutely required. Then, having introduced the ideas of matrices, some of the material from Chapters 2,3, and 4 is recast in Matrix terminology. Since matrices are basically a notational convenience, this reformulation provides essentially nothing new to the simplex method, the sensitivity analysis, or the duality theory. However, the economy of the Matrix notation provides added insight by streamlining the previous material and, in the process, highlighting the fundamental ideas.

B.1 A Preview of the Revised Simplex Method 507 Tableau B.2 Basic Current variables values x4 x5 x6 x2 42 7 1 7 3 35 x6 1 4 7 2 7 1 14 1 x1 63 7 2 7 1 14 (z) 513 7 11 14 1 35 reflect a summary of all of the operations that were performed on the objective function during this process.

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