Suppose that marginal cost for a certain product is given by MC = 1.05(x + 180)0.05 and marginal revenue is given by MR = (1 / √0.5x + 4) + 2.8, where x is in thousands of units and both revenue and cost are in thousands of dollars. Fixed costs are $200,000 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 the level of production that yields maximum profit, and find the maximum profit (or minimum loss).