CPM Homework Help : CCA2 Problem 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.

Hint:

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

More Help:

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

$P(3)=−(3)^2+10(3)\\=−(9)+30\\=21$

Answer:

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.