CPM Homework Help : A2C Problem 4-150

The amount of profit (in millions) made by Scandal Math, a company that writes math problems based on tabloid articles, can be found by the equation $P\left(n\right) = −n^{2} + 10n$ , where n is the number of textbooks sold (also in millions). Find the maximum profit and the number of textbooks that Scandal Math must sell to attain this maximum profit.

Hint:

To find the maximum, you need to find the vertex of the parabola. Write the equation in graphing form so you can find the vertex.

Hint 2:

It is easier to complete the square without the $−n^{2}$ . Start by multiplying both sides by $−1$ so $−P\left(n\right) = n^{2} − 10n$ . Now complete the square.

Hint 3:

Do not forget to multiply again by $−1$ after you complete the square.

More Help:

The vertex is your maximum y-value.