A shoe company manufacturing 4000 items. It is estimated that the rate of change of production P with respect to additional no. of worker x is given by \frac{dP}{dx}=200-24\sqrt{x}. If the company has 100 more workers then the new level of production of items is

a. 8000

b. 6000

c. 12000

d. 0

Answers (1)

\frac{dP}{dx}=200-24\sqrt x

P=200x-24.\frac{2}{3}x^{\frac{3}{2}}+ C

P=200x-16x^{\frac{3}{2}}+ C    - (i)

Given if x = 0, P = 4000

\Rightarrow C=4000

Hence (i) becomes

P=200x-16x^{\frac{3}{2}}+ 4000

If\ x=100

P=200(100)-16(10^2)^{\frac{3}{2}}+ 4000

=20000-16000+ 4000

=8000

Hence, (a) is the correct answer.

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