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

2500

3000

3500

4500

Text Solution

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The correct Answer is:

We have , `(dp)/(dx)=100 -12 sqrt(x)` Integrating both sides with respect to x , we get
`P=int(100 -12 sqrt(x))dx`
`rArr P=100x -8x^(3//2)+C` . . . (i)
Initially x = 0 , P = 2000
`therefore2000=C`
Putting C= 2000 in (i) , we get
P`=100 x-8x^(3//2)+2000`
When x 25 , we get
P`=2500 - 8 (25)^(3//2)+2000 = 3500`
Hence , the new level of production is 3500 items.

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