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

 

  • Option 1)

    4500

  • Option 2)

    2500

  • Option 3)

    3000

  • Option 4)

    3500

 

Answers (1)

best_answer

As we have learned

Variable Separation Method -

integrating, we get

\int f\left ( x \right )dx+\int \phi \left ( y \right )dy =c

-

 

\frac{dp}{dx}= 100 12 \sqrt x

\Rightarrow \int dP = \int 100 dx - \int 12 \sqrt x dx

\Rightarrow P = 100x - \frac{12 x^{3/2}}{3/2}+ C

\Rightarrow P = 100 x -8x^{3/2 } +C \\ now, 2000 = 100 x_0 -8 x_{0}^{3/2}+C ....(1)

and   P' = 100 (x_0+25 )- 8 (x_0+25 )^{3/2}+C ......(2)

We have x_0 = 0 \\ so , on (2)-(1), P ' -2000 = 2500 - 8\times 125=1500

 

 

 

 

 

 


Option 1)

4500

Option 2)

2500

Option 3)

3000

Option 4)

3500

Posted by

Himanshu

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