# A firm manufacturing 2000 items.It estimated that the rate of change of production P with the respect to additional number of workers x is given by dP/dx=100-12x^.5.If the firm employees 25 more workers,then the new level of production of the items is?

Apr 6, 2018

New level of production is $3000$

#### Explanation:

As the rate of change of production $P$ with the respect to additional number of workers $x$ is given by $\frac{\mathrm{dP}}{\mathrm{dx}} = 100 - 12 {x}^{0.5}$

As $x$ changes by $25$ i.e. $\Delta x = 25$,

$\Delta P = \Delta x \times \frac{\mathrm{dP}}{\mathrm{dx}} = 25 \left(100 - 12 \cdot {25}^{0.5}\right)$

= $25 \cdot \left(100 - 12 \cdot 5\right) = 25 \cdot 40 = 1000$

and new level of production is $2000 + 1000 = 3000$