Suppose that the marginal cost for a certain product is given by MC = 1.02(x + 200)0.02 and marginal revenue is given by MR = (2 / √4x + 1) + 1.75, where x is in thousands of units and revenue and cost are in thousands of dollars. Suppose further that fixed costs are $150,000 and production is limited to at most 200 thousand units.
(a) Find C(x) and R(x).
(b) Graph C(x) and R(x) to determine whether a profit can be made.
(c) Determine what level of production yields maximum profit, and find the maximum profit (or minimum loss).