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Question

# A company producing jigsaw puzzles has fixed costs of $\ 6000$ and variable costs of $\ 2$ per puzzle. The company sells the puzzles for $\ 5$ each. Find formulas for the cost function, the revenue function, and the profit function.

Solution

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Let's remember that the total cost can be determined as

\begin{aligned} \text{Total cost}&=\text{Fixed cost}+\text{Variable cost}\\ C(q)&=\text{Fixed cost}+q\cdot\text{Item cost}\tag{1} \end{aligned}

and the revenue can be determined as

\begin{aligned} \text{Revenue}&=\text{Price}\cdot\text{Quantity}\\ R(q)&=p\cdot q\tag{2} \end{aligned}

Also, the profit can be calculated as

\begin{aligned} \text{Profit}&=\text{Revenue}-\text{Cost}\\ \pi&=R(q)-C(q) \tag{3}\end{aligned}

where $q$ number of items, $p$ the price per item.

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