Question

A company manufactures cassettes and its cost and revenue functions for a week are \[C = 300 + \frac{3}{2}x \text{ and } R = 2x\] 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.  

\[\therefore 2x > 300 + \frac{3}{2}x\]
\[ \Rightarrow 2x - \frac{3}{2}x > 300\]
\[ \Rightarrow \frac{1}{2}x > 300\]
\[ \Rightarrow x > 600\]
\[\text { Thus, the company must sell more than 600 cassettes in a week to realise profit } . \]
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