Question:
A company manufactures cassettes and its cost and revenue functions for a week are $C=300+\frac{3}{2} x$ and $R=2 x$ respectively, where $x$ is the number of cassettes produced and sold in a week. How many cassettes must be sold for the company to realize a profit?
Solution:
To realise profit, revenue must be greater than the cost.
$\therefore 2 x>300+\frac{3}{2} x$
$\Rightarrow 2 x-\frac{3}{2} x>300$
$\Rightarrow \frac{1}{2} x>300$
$\Rightarrow x>600$
Thus, the company must sell more than 600 cassettes in a week to reali se profit.