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.

Guest Aug 12, 2019

#1**+3 **

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.**

CalculatorUser Aug 12, 2019

#2**+1 **

Revenue will be given by the price x number of books sold

p (130-5p)

-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 !)

ElectricPavlov Aug 12, 2019

#3

#4**0 **

Yah....that is the maximum revenue , but the question only asked for the price which would generate that maximum....

ElectricPavlov
Aug 12, 2019