An Experimental Method for Profit Maximization

Abstract

This paper develops a procedure for locating profit maximizing operating conditions when the input variables are subject to control by the experimenter and observations on physical output may be taken subject to experimental error at any combination of these inputs. This procedure uses the Box-Wilson technique, a well-known statistical search procedure, together with the pria of the output and the cost of the inputs so as to search for maximum profit points rather than maximum output points. The result is an experimental search method which maximizes profit when the functional form of the physical response surface (production function) is unknown. In this case, of course, standard mathematical programming models are of no use in the absence of the required functional forms. This functional form, though unknown, is determined by the existing investment in capital equipment. These procedures, like the Box-Wilson technique, are more likely to be applicable to flow process reactor systems in the chemical and oil industries, but are certainly not limited to such applications.