1)

At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P  with respect to an additional number of workers x is given by   dpdx=10012x. If the firm employees 25 more workers, then the new level of production of items is 


A) 2500

B) 3000

C) 3500

D) 4500

Answer:

Option C

Explanation:

Given, dPdx=(10012x)

   dP=(10012x)dx

 On integrating both sides, we get

        dP=(10012x)dx

       P=100x8x3/2+C

  When   x=0, then P= 2000

     C=2000

 Now, when x=25  then is

        P=100×258×(25)3/2+2000

   = 2500- 8 X 125+2000

   =4500-1000=3500