A Diet Model with Protein Quality Variable

Malnutrition is a serious obstacle to development in many countries. To deal with it effectively we must know how to provide adequate nutrition in an economical way. Linear programming will determine the most economical set of foods or production activities if the set of nutrients needed can be specified in absolute amounts or as fixed ratios, but this will not suffice for one of the most pressing nutritional problems—the protein problem. It is impossible to specify the quantity of protein required in this way. That quantity depends upon the concentration of protein in the diet and the “quality” of the protein (its amino acid composition). The greater the concentration, the less efficiently the protein is used; the better the quality, the more efficiently. For a least-cost diet, quality and quantity must be determined simultaneously, but the relationships are nonlinear. This paper presents a model, with one nonlinear restraint, that determines a least-cost diet in which the quality and the quantity of the protein are jointly and optimally determined.