A health club has cost and revenue functions given by C = 10,000 + 35q and R = pq, where
Chapter 1, Problem 30(choose chapter or problem)
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 oneyear 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. (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.
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