Consider the equipment replacement problem over a period of n years. A new piece of equipment costs c dollars, and its resale value after t years in operation is s1t2 = n - t for n 7 t and zero otherwise. The annual revenue is a function of the age t and is given by r1t2 = n2 - t2 for n 7 t and zero otherwise.

(a) Formulate the problem as a DP model.

(b) Find the optimal replacement policy given that c = $10,000, n = 5, and the equipment is 2 years old.