7 Farmer Jones is trying to raise a prize steer for the Bloomington 4-H show. The steer now weighs w0 pounds.

Each week, farmer Jones must determine how much food to feed the steer. If the steer weighs w pounds at the beginning of a week and is fed p pounds of food during a week, then at the beginning of the next week, the steer will weigh g(w, p) pounds. It costs farmer Jones c(p) dollars to feed the steer p pounds of food during a week. At the end of the 10th week (or equivalently, the beginning of the 11th week), the steer may be sold for $10/lb. Formulate a dynamic programming recursion that can be used to determine how farmer Jones can maximize profit from the steer.