A bookstore is deciding what price it should charge for a certain book. After research, the store finds that if the book's price is p dollars (where p is greater than or equal to 32 ), then the number of books sold per month is 128-4p. What price should the store charge to maximize its revenue?
Let r(p) be the revenue.
r(p) = p(128-4p) = -4p^2 + 128p
Completing the square, r(p) = -4(p^2-32p) = -4(p-16)^2 + 1024.
Therefore, if the price is 16 dollars, the revenue will be maximized, which will be 1024 dollars.