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 prices of a one year membership. The demand function for the club is q = 3000 - 20q.
a. Use the demand function to write cost and revenue functions of p.
b. Graph cost and revenue as a function of p, on the same axes. (Note that price does not go above $170 and that the annual costs of running the club reach $120,000.)
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.