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A manufacturer has cost and revenue functions C(x) = 2x + 80 and R(x) = 5x + 20, where x denotes the number of items produced and sold. For the manufacturer to make a profit, how many items must be sold?

1. more than 20
2. more than or equal to 20
3. more than 25
4. None of these

Correct answer: more than 20

Solution

To determine when the manufacturer makes a profit, we set the revenue function R(x) greater than the cost function C(x). Solving the inequality 5x + 20 > 2x + 80 leads to x > 20, indicating that selling more than 20 items is necessary for profit.

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