At present,a firm is manufacturing 1000 items | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given the rate of change of production: $\frac{dP}{dx} = 100 - 12\sqrt{x}$.Integrating both sides with respect to $x$:$\int dP = \int (100 - 12x^{

Vedclass · Accepted Answer

$1684$

Vedclass · Answer

(A) Given the rate of change of production: $\frac{dP}{dx} = 100 - 12\sqrt{x}$.Integrating both sides with respect to $x$:$\int dP = \int (100 - 12x^{1/2}) dx$$P = 100x - 12 \cdot \frac{x^{3/2}}{3/2} + C$$P = 100x - 8x^{3/2} + C$Given that the initial production $P = 1000$ when $x = 0$:$1000 = 100(0) - 8(0)^{3/2} + C \implies C = 1000$.Thus,the production function is $P(x) = 100x - 8x\sqrt{x} + 1000$.For $x = 9$ additional workers:$P(9) = 100(9) - 8(9)\sqrt{9} + 1000$$P(9) = 900 - 8(9)(3) + 1000$$P(9) = 900 - 216 + 1000 = 1684$.The new level of production is $1684$ items.

At present,a firm is manufacturing $1000$ items. It is estimated that the rate of change of production $P$ with respect to the additional number of workers $x$ is given by $\frac{dP}{dx} = 100 - 12\sqrt{x}$. If the firm employs $9$ more workers,then the new level of production of items is:

Similar Questions

$A$ ladder of length $13 \ m$ has one end resting against a vertical wall and the other on the ground. If the lower end moves away from the wall at a speed of $2 \ m/min$,then the speed (in $m/min$) at which the upper end falls when the bottom is $5 \ m$ away from the wall is

$A$ closed conical vessel is filled with water fully and is placed with its vertex down. The water is let out at a constant speed. After $21 \, min$,it was found that the height of the water column is half of the original height. How much more time in minutes does it require to empty the vessel?

$A$ particle moves in a straight line such that $s = \sqrt{t}$,then its acceleration is proportional to

$A$ balloon which always remains spherical is being inflated by pumping in $10 \text{ cm}^3$ of gas per second. Find the rate at which the radius of the balloon is increasing when the radius is $15 \text{ cm}$.

The rate of change of the diagonal $R$ of a square with respect to its area $A$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module