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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.

 Aug 12, 2019
 #1
avatar+2856 
+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.

 Aug 12, 2019
 #2
avatar+25913 
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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 !)

 Aug 12, 2019
 #3
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THX.

The other answer was $845. 

 Aug 12, 2019
 #4
avatar+25913 
0

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

ElectricPavlov  Aug 12, 2019

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