Question

The cost, C, of producing a custom-made T-shirt is given by the formula $C=110+\frac{x}{2}$, where $x$ is the number of T-shirts produced. The revenue obtained from selling every T-shirt produced is given by $R=15x-\frac{x^2}{10}$. Which one of the following would be the formula for the net profit from producing and selling $x$ T-shirts?

• A. $-\frac{x^2}{10}-\frac{31}{2}x+110$
• B. $-\frac{x^2}{10}-\frac{29}{2}x+110$
• C. $-\frac{x^2}{10}+\frac{29}{2}x-110$
• D. $-\frac{x^2}{10}+\frac{31}{2}x-110$

Answer 1

Answer: (C)

$-\frac{x^2}{10}+\frac{29}{2}x-110$

Given the cost of T-shirts is $C=110+\frac{x}{2}$ where $x$ is number of T-shirts

And revenue received is $R=15x-\frac{x^2}{10}$

Profit $=(15x-\frac{x^2}{10})-(110+\frac{x}{2})$

$\Rightarrow P=15x-\frac{x^2}{10}-110-\frac{x}{2}$

$\Rightarrow P=-\frac{x^2}{10}+\frac{29}{2}x-110$