A company manufactures cassettes and its cost and revenue functions for a week are $C = 300 + \frac{3}{2} x$ and $= 2 x$ respectively where $x$ is the number of cassettes produced and sold in a week. How many cassettes must be sold for the company to realise a profit?

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Solution

We know that for profit, $R e v e n u e > C o s t$ .

$2 x > 300 + \frac{3}{2} x$

$2 x > 300 + 1.5 x$
$2 x - 1.5 x > 300$
$0.5 x > 300$

$x > \frac{300}{0.5}$

$x > 600 C a s s e t t e s$

$∴ 600$ Cassettes must be sold for the company to realize a profit.

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A company manufactures cassettes and its cost and revenue functions for a week are C=300+32x and =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 realise a profit?

We know that for profit, Revenue > Cost.2x>300+32x2x>300+1.5x2x−1.5x>3000.5x>300x>3000.5x>600 Cassettes∴600 Cassettes must be sold for the company to realize a profit.

A company manufactures cassettes and its cost and revenue functions for a week are $C = 300 + \frac{3}{2} x$ and $= 2 x$ respectively where $x$ is the number of cassettes produced and sold in a week. How many cassettes must be sold for the company to realise a profit?

We know that for profit, $R e v e n u e > C o s t$ .

$2 x > 300 + \frac{3}{2} x$

$2 x > 300 + 1.5 x$
$2 x - 1.5 x > 300$
$0.5 x > 300$

$x > \frac{300}{0.5}$

$x > 600 C a s s e t t e s$

$∴ 600$ Cassettes must be sold for the company to realize a profit.