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


Answered 1 year ago
Answered 1 year ago
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Let's remember that the total cost can be determined as

Total cost=Fixed cost+Variable costC(q)=Fixed cost+qItem cost(1)\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

Revenue=PriceQuantityR(q)=pq(2)\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

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

where qq number of items, pp the price per item.

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