The Piecewise Concave Function

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Abstract
An important function which is neither concave nor convex often arises in production and inventory models. This function is herein called piecewise concave and can be considered to be a generalization of the concave function. Essentially it is the maximum of a collection of concave functions. Various properties of piecewise concave functions are explored in this paper. In particular, a theory is developed to locate the point at which such functions are minimized. A short discussion of applications is included.

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