A health club has cost and revenue functions given by C = 10,000 + 35q and R = pq, where q is the number of annual club members and p is the price of a one year membership. The demand function for the club is q = 3000 − 20p.
(a) Use the demand function to write cost and revenue as functions of p.
(b) Graph cost and revenue as a function of p, on the same axes.
(c) Explain why the graph of the revenue function has the shape it does.
(d) For what prices does the club make a profit?
(e) Estimate the annual membership fee that maximizes profit. Mark this point on your graph.