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A firm currently makes 2000 items. The rate of change of production P with the number of extra workers x is dP/dx = 100 - 12*sqrt(x). If 25 more workers are hired, what is the new production level?

1. 2500
2. 3000
3. 3500
4. 4500

Correct answer: 3500

Solution

Integrating gives P(x) = 100x - 8x^(3/2) + 2000; at x = 25 this equals 3500.

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