AlgebraVery hardCounting production levels that make a profit
Algebra practice question
A workshop can make at most 60 chairs a week. Each chair sells for $15 and costs $6 in materials, and the workshop has fixed weekly costs of $450. For how many possible whole numbers of chairs made in a week would the workshop make a profit?
Answer: 10
Profit = 15n − 6n − 450 = 9n − 450 > 0 gives n > 50. With n ≤ 60, the possible values are 51 to 60: ten of them.
Common wrong answers
- If you answered 9
- 9 leaves out n = 60.
- If you answered 11
- 11 wrongly includes n = 50, where profit is 0.
- If you answered 50
- 50 is the break-even number of chairs.
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