Discussion Forum

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   $\frac{dp}{dx}=100-12\sqrt{x}. $ If the firm employees 25 more workers, then the new level of production of items is 

Answer:

Explanation:

Given, $\frac{dP}{dx}= (100-12\sqrt{x})$

 $\Rightarrow$  $ dP= (100-12\sqrt{x})dx$

 On integrating both sides, we get

        $\int_{}^{} dP= \int_{}^{} (100-12\sqrt{x}) dx$

       $P=100x-8x^{3/2}+C$

  When   x=0, then P= 2000

 $\rightarrow$    C=2000

 Now, when x=25  then is

        $P= 100\times 25-8\times(25)^{3/2}+2000$

   = 2500- 8 X 125+2000

   =4500-1000=3500