Notes on Linear Programming: Part XLIII

A Feasibility Algorithm for One-Way Substitution in Process Analysis

by Kenneth Arrow, Selmer Martin Johnson

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A proof that an algorithm for the most efficient assignment of machines to tasks solves an equivalent linear-programming problem. The study assumes that with a certain number of machines (not all of the same capability) with which to do a certain number of tasks (not all of the same difficulty), it is better to use a more capable machine for a more difficult task.

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