Demand for pools. Tropical Pools sells an above ground model for p dollars each. The monthly revenue for this model is given by the formula
R (p) = - 0.08p2 + 300p.
Revenue is the product of the price p and the demand (quantity sold).
a) Factor out the price on the right-hand side of the formula.
b) Write a formula D (p) for the monthly demand.
c) Find D (3000).
d) Use the accompanying graph to estimate the price at which the revenue is maximized. Approximately how many pools will be sold monthly at this price?
e) What is the approximate maximum revenue?
f) Use the accompanying graph to estimate the price at which the revenue is zero.