At present, a firm is manufacturing 2000...

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 `(d P)/(dx)=100-12sqrt(xdot)` If the firm employs 25 more workers, then the new level of production of items is (1) 3000 (2) 3500 (3) 4500 (4) 2500

3000

3500

4500

2500

Text Solution

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The correct Answer is:

`(dP)/(dx)=100-12sqrt(x)`
Integrating, we get
`P=100x-12. 2/3x^(3//2)+C`
`therefore p=100x-8x^(3//2)+C` ……………….(1)
Given, if `x=0, p=2000`
`rArr C=2000`
So, (1) becomes
`P=100x-8x^(3//2)+2000`
`=2500-1000+2000=3500`

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