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At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by dP/dx = 100 - 12√x. If the firm employs 25 more workers, then the new level of production of items is
- 2500
- 3000
- 3500
- 4500
Correct answer: 3500
Solution
Increase = integral from 0 to 25 of (100 - 12*sqrt(x)) dx = [100x - 8*x^(3/2)] from 0 to 25 = 2500 - 1000 = 1500. New production = 2000 + 1500 = 3500.
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