Suppose a large company makes 25,000 gadgets per year in batches of x items at a time. After analyzing setup costs to produce each batch and taking into account storage costs, it has been determined that the total cost C(x) of producing 25,000 gadgets in batches of x items at a time is given by

C(x) = 1,250,000 + 125,000,000 / x + 1.5x.

a. Determine the marginal cost and average cost functions. Graph and interpret these functions.

b. Determine the average cost and marginal cost when x = 5000.

c. The meaning of average cost and marginal cost here is different from earlier examples and exercises. Interpret the meaning of your answer in part (b).