A cable television firm presently serves 7000 households and charges $50 per month. A marketing survey indicates that each decrease of $5 in the monthly charge will result in 1000 new customers. Let p denote the monthly charge in dollars. Answer the following:
(a) Suppose that the number of households is a linear function of the monthly charge p. Determine an equation for .
(b) Determine the revenue function in terms of p.
(c) Determine the value of p that results in maximum monthly revenue. (Round your answer to the nearest cent.)