Question

A company manufactures cassettes. Its cost and revenue functions are $C\left(x\right)=26,000+30x$ and $R\left(x\right)=43x$, respectively, where $x$ is the number of cassettes produced and sold in a week. How many cassettes must be sold by the company to realise some profit?

Answer 1

Given :

Cost function $C\left(x\right)=26,000+30x$

Revenue function $R\left(x\right)=43x$

$R\left(x\right)>C\left(x\right)$ (For profit)

$\Rightarrow 43x>26000+30x$

$\Rightarrow 13x>26000$

$\Rightarrow x>2000$

Hence, more than $2000$ cassettes should be sold to realise some profit .