Question

A company manufactures cassettes and its cost and revenue functions for a week are $C=300+\frac{3}{2}x\mathrm{and}R=2x$ 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?

Answer 1

To realise profit, revenue must be greater than the cost.

$$\begin{gathered} \therefore 2x>300+\frac{3}{2}x \\ \Rightarrow 2x-\frac{3}{2}x>300 \\ \Rightarrow \frac{1}{2}x>300 \\ \Rightarrow x>600 \\ \mathrm{Thus},\mathrm{the}\mathrm{company}\mathrm{must}\mathrm{sell}\mathrm{more}\mathrm{than}600\mathrm{cassettes}\mathrm{in}\mathrm{a}\mathrm{week}\mathrm{to}\mathrm{reali}se\mathrm{profit}. \end{gathered}$$