### Home > CCA2 > Chapter Ch2 > 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. Homework Help ✎

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.