Cost Minimization Problems Treated by Geometric Means

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Abstract
It is supposed that the cost of an engineering design is a generalized polynomial function in the design parameters. The terms of such a polynomial are products of the parameters raised to powers. Fractional and negative powers are permitted but the coefficients of the terms are taken to be positive. The problem of concern is the adjustment of the parameters so as to minimize the cost. By use of the classical inequality to the effect that the arithmetic mean exceeds the geometric mean it is found that the cost function exceeds a certain function termed the dual. Moreover it is shown that the maximum of the dual function gives the minimum cost. This relation furnishes a simple method of estimating the minimum cost.