The baking store has begun selling a cookbook called "What Would Euler Eat?" If the price of the cookbook is 
dollars (
), then it will sell 
copies. What price (in dollars) will maximize the total revenue we receive for the books?
+23254 The profit is determined by the number of books sold times the price per book.
We want to graph points where the x-value represents the cost per book, n, and where the y-value represents the amount of money taken in.
When n = 0, the amount of money taken in will be 0; again, when n = 72, the amount of money will again be 0.
This graph will be a parabola.
As n increases from 0, to 1, to 2, etc., the amount of money taken in will increase until it hits a maximum at 36; after 36, the amount of money taken in will decrease.
Let y = amount of money taken in: x = price per book: y = x(720-10x)
y = 720 - 10x²
Either graph this and find the maximum point , or find the vertex (the maximum point) by completing the square.
y = -10x² + 720x
y = -10(x² - 72x)
y - 12960 = -(x² - 72x + 1296) <--- complete the square.
y - 12960 = -(x - 3)²
Vertex: (36, 12960)
