Question

A company manufactures cassettes and its cost equation for a week is $C=300+1.5x$ and its revenue equation is $R=2x$, where $x$ is the number of cassettes sold in a week. How many cassettes must be sold for the company to realize a profit?

Answer 1

Step 1:

Given data:

Cost equation,$C=300+1.5x$

Revenue, $R=2x$

Here, $x$ is the number of cassettes sold in a week.

Step 2:

Find the number of cassettes to be sold:

$\mathrm{Profit}=\mathrm{Total}\mathrm{Revenue}-\mathrm{Total}\mathrm{Expenses}$

For, the company to realize a profit,

$$\begin{gathered} \mathrm{Revenue}>\mathrm{Cost} \\ \Rightarrow 2x>300+1.5x \\ \Rightarrow 2x–1.5x>300 \\ \Rightarrow 0.5x>300 \\ \Rightarrow x>\frac{300}{0.5}\left[\mathrm{Divide}\mathrm{by}0.5\mathrm{on}\mathrm{both}\mathrm{sides}.\right] \\ \therefore x>600 \end{gathered}$$

Therefore, more than $600$ cassettes must be sold for the company to realize a profit.