At present, a firm is manufacturing 2 0 0 0 items. It is estimated that the rate of change of production P w…

At present, a firm is manufacturing 2 00 0 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by dPdx=100-12x. If the firm employs 2 5 more workers, then the new level of production of items is
  1. 3500
  2. 4500
  3. 2500
  4. 3000

Solution

dPdx=100-12x

⇒∫dP=∫100-12xdx

⇒P=100x-8x3/2+C

Now, x=0

⇒P=2000⇒C=2000

hence, P=100x-8x32+2000

∵  x=25

P=2500-1000+2000

P=3500

Asked in: JEE Main 2013 (07 Apr)

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