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. Consider the cost function C(x) given below. (Round your answers to the nearest cent.)
C(x) = 24,000 + 170x + 6x^3/2
(a) Find the total cost (in dollars) at a production level of 1,000 units.
(b) Find the average cost (in dollars per unit) at a production level of 1,000 units.
(c) Find the marginal cost (in dollars per unit) at a production level of 1,000 units.
(d) Find the production level (in units) that will minimize the average cost.
(e) What is the minimum average cost (in dollars per unit)?