# 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 isa. 8000b. 6000c. 12000d. 0

H Harsh Kankaria

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

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

$P=200x-16x^{\frac{3}{2}}+ C$    - (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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