The Art of Problem Solving has begun selling a cookbook called "What Would Euler Eat?" If the price of the cookbook is dollars ()

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)

The Baking store is actually the name. My sister put that.