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A company manufactures cassettes. Its cost and revenue functions are $C(x)=26000+30 x$ and $R(x)=43 x$, respectively, where $\mathrm{x}$ is the number of cassettes produced and sold in a week.
Find the number of cassettes that must be sold by the company to realise some profit.
Find the number of cassettes that must be sold by the company to realise some profit.
Solution:
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Verified Answer
Given, $C(x)=26000+30 x$
and $R(x)=43 x$
$\therefore \quad$ Profit $=\mathrm{R}(\mathrm{x})-\mathrm{C}(\mathrm{x})$
$=43 x-(26000+30 x)=13 x-26000$
For some profit, $13 x-26000>0$
$\Rightarrow 13 x>26000$
$\Rightarrow x>2000$
and $R(x)=43 x$
$\therefore \quad$ Profit $=\mathrm{R}(\mathrm{x})-\mathrm{C}(\mathrm{x})$
$=43 x-(26000+30 x)=13 x-26000$
For some profit, $13 x-26000>0$
$\Rightarrow 13 x>26000$
$\Rightarrow x>2000$
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