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Question:

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√x. If the firm employs 25 more workers, then the new level of production of items is:

4500

3000

3500

2500

Solution:

∫2000P dP = ∫025 (100√x) dx
(P|2000P) = 25 × 100 × (2/3)(25)3/2
P = 3500.