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

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Solution

We have,

Profit=Revenue-Cost

Therefore,to earn some profit,we must have Revenue > Cost

$\Rightarrow 2 x > 300 + \frac{3}{2} x \Rightarrow 2 x - \frac{3}{2} x > 300 \Rightarrow \frac{4 x - 3 x}{2} > 300 \Rightarrow x > 300 \times 2 \Rightarrow x > 600$

Hence, the manufactures must sell more than 600 cassettes to realize some profit.

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

We have, Profit=Revenue-Cost Therefore,to earn some profit,we must have Revenue > Cost ⇒2x>300+32x⇒2x−32x>300⇒4x−3x2>300⇒x>300×2⇒x>600 Hence, the manufactures must sell more than 600 cassettes to realize some profit.

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