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At present, a firm is manufacturing 2 0 0 0 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by d P d x = 1 0 0 - 1 2 x . If the firm employs 2 5 more workers, then the new level of production of items is

Options

  1. A3500
  2. B4500
  3. C2500
  4. D3000

Correct answer

A. 3500

Step-by-step solution

d P d x = 1 0 0 - 1 2 x ⇒ ∫ d P = ∫ 100 - 12 x d x ⇒ P = 1 0 0 x - 8 x 3 / 2 + C Now, x = 0 ⇒ P = 2000 ⇒ C = 2000 hence, P = 100 x - 8 x 3 2 + 2000 ∵     x = 25 P = 2500 - 1000 + 2000 P = 3500

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