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 \(p \le 26\)), then the number of books sold per month is \(130-5p\). What price should the store charge to maximize its revenue?
I know that his is a repost but the other ansewer was not correct.
Thanks in advance.
To solve this, I started experimenting the profit of books going down from the price of $26 AND going up from the price of 0$
I realized that 0 and 26 had the same profit, the same as 1 and 25. This pattern continues on with the profit always going on a increase.
Because of this trend, we can find the median number between 1 and 25, which is 13.
So the book store should make its books cost $13 to maximize its revenue.
Revenue will be given by the price x number of books sold
-5p^2 + 130p = revenue (this is a dome shaped parabola)
Max will be p = -b/2a = - (130)/((2* -5) = 13 dollars (just as CU found !)