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Earl’s Biking Company manufactures and sells bikes.

Each bike costs £40 to make, and the company’s fixed costs are £$5000$.

In addition, Earl knows that the price of each bike comes from the price function $f(x) = 300 – 2x$ where $x$ denotes the number of bikes produced per year.

1. Show that the revenue in terms of $x$ is given by the formula $R(x) = 300 x – 2 x^2$.
2. Show that the cost in terms of $x$ is given by the formula $C(x) = 5000 + 40 x$.
3. Show that the company’s profit function, in terms of $x$, is $P(x)= –5000+260x–2x^2$.
4. Find the output level that maximizes the company’s profit, and the maximum profit.

## Vocabulary

• Timeline: chronologie
• Bike vs bicycle: bike is a general word used to describe all vehicles having two wheels though it originated with bicycles which were invented first ; bike today includes engine powered motorcycles while bicycles are propelled by the man riding them using his legs (source: https://www.differencebetween.com).