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The Princeton Companion to Mathematics by Imre Leader, June Barrow-Green, Timothy Gowers

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III.84 The Simplex Algorithm

Richard Weber

1 Linear Programming

The simplex algorithm is the preeminent tool for solving some of the most important mathematical problems arising in business, science, and technology. In these problems, which are called linear programs, we are to maximize (or minimize) a linear function subject to linear constraints. An example is the diet problem posed by the U.S. Air Force in 1947: find quantities of seventy-seven differently priced foodstuffs (cheese, spinach, etc.) to satisfy a man’s minimum daily requirements for nine nutrients (protein, iron, etc.) at least cost. Further applications occur in choosing the elements of an investment portfolio, rostering an airline’s crew, and finding optimal strategies in ...

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