Use of the Quadratic Growth Response to Dietary Protein and Energy Concentrations in Least-Cost Feed Formulation

Quadratic growth responses to cumulative protein and energy intakes were observed in birds fed corn-soybean meal-wheat middlings and poultry oil-based diets. The linear and quadratic parts of a fitted equation identified diminishing marginal productivity of protein and energy; the interaction term identified the effect of the marginal physical product of one being a function of the other (R2>.99). The ingredient and nutrient coefficient matrices of one of the United States’ leading broiler producing firms were combined with the response equation by appropriate transformations. Ingredient prices were also added, and the resulting model was analyzed to indicate an exact point of economic efficiency (least cost per kilogram of broiler produced). As the price of corn increased, the concentrations of protein and energy in the diet that maximized weight gain for a given bird cost were affected only slightly. As the price of soybean meal increased, protein concentrations giving maximum gains decreased, and energy concentrations giving maximum gains increased. Quadratic programming (QP) constraints (maximum gain per input) produced a 1.84-kg broiler for 1.54¢ less than linear programming constraints (those suggested by the National Research Council, 1977). This was due to higher protein and lower energy concentrations by QP that resulted in a technical feed conversion that was of least cost with respect to the protein and energy values inherent at available feed ingredient prices.