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

Options

A. 2500
B. 3000
C. 3500
D. 4500

Answer

c

Explanation

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.