(a) If C(x) is the cost of producing x units of a commodity, then the average cost per unit is c(x) = C(x)/x. Show that if the average cost is a minimum, then the marginal cost equals the average cost.

(b) If C(x) = 16,000 + 200x + 4x^3/2, in dollars, find (i) the cost, average cost, and marginal cost at a production level of 1000 units; (ii) the production level that will minimize the average cost; and (iii) the minimum average cost.