Cattle purchasing, feeding, and selling decisions are described by a free-time optimal control model. The nutrient constraints of the National Research Council and a recently published dry matter intake constraint augment the model and make it nonlinear in the feed ingredients, the daily gain, and the weight of the cattle. Optimal feeding programs are calculated by nonlinear programming under two scenarios: first, when the feedlot has excess capacity and, second, when animals must be sold to make room in the feedlot before more can be purchased. An approximately optimal feeding program is calculated by nonlinear programming and is all but identical to the dynamically optimal programs.