Abstract

The problems of linear and nonlinear programming are reviewed using a geometrical representation, with a general discussion of the various types of solutions arising to the problem of finding a maximum or minimum of a property z = f(x1, …, xn) when the variables xi are subject to a certain number of constraints. A special type of nonlinear programming is considered when the departure from linearity is due to a systematic drift toward a saturation level as is the case when profit actually decreases after the rate of production attains its optimum value. The mathematical model satisfying this requirement is one for which a linear factor dominates the profit function for small rates of production and a negative exponential for high rates of production. A solution with illustrative examples is presented to this problem.

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