### Home > CCA2 > Chapter 2 > Lesson 2.1.2 > Problem2-22

2-22.

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 $P(n)=−n^2+10n$, 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 realize this maximum profit.

Draw the graph and look for the maximum value. One way to draw the graph is to start by making a table.

When you substitute a number into the equation, pay close attention to the Order of Operations. Here’s an example:

$P(3)=−(3)^2+10(3)\\=−(9)+30\\=21$

The maximum $P(n)$-value is $25$, which occurs when $n=5$. Therefore, the maximum profit is $\25$ million and $5$ million books need to be sold.