**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.

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