Precision Machine Company produces a unique and high-quality machinefor sale. The company is a price maker in the domestic market.The total cost and marginal cost functions for machine production areTC = 20,000 + 0.25q2;MC = 0.5q. where q is the quantity of machines produced.The demand curve facing theprice-making firm is given by q = 500 -P.That is, P = 500 -q.

a) Find the total revenue (TR) function for the company (in terms of q).

b)Find the company's marginal revenue (MR) function (in terms of q).

c)Using the MR = MC rule, determine the profit-maximizing level of output.

d)Calculate profits for the company.