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Standard XII

Mathematics

Average Rate of Change

At present a ...

Question

At present a firm manufacturing $2000$ items it is estimated that the rate of change of production (P) with respect to additional number of workers $(x)$ is given by
$\frac{d P}{d x} = 100 - 12 \sqrt{x}$ . If the firm employes $25$ more workers then the new production is?

2500

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3000

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3500

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4500

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Solution

The correct option is A $2500$
Solution-
$\frac{d p}{d x} = 100 - 12 \sqrt{x}$
$p = \int (100 - 12 \sqrt{x}) d x$
$p = 100 x - 8 (x)^{3 / 2} + c$
$c = 0$
$p = 100 \times 2025 - 8 (45)^{3} + c$
$p - 2000 = 100 \times 2025 - 8 (45)^{3} - 100 \times 2000 + 8 (2000)^{3 / 2}$
$p = 25000$
A is correct.

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Similar questions

Q. 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

\frac{d P}{d x} = 100 - 12 \sqrt{x}

. If the firm employs 25 more workers, then the new level of production of items is:

Q. 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

\frac{d P}{d x} = 100 - 12 \sqrt{x}

. If the firm employs

25

more workers, then the new level of production of items is :

Q. Given below is the distribution of total household expenditure of 200 manual workers in a city:

Expenditure (in Rs)	No. of manual workers
1000-1500	24
1500-2000	40
2000-2500	31
2500-3000	28
3000-3500	32
3500-4000	23
4000-4500	17
4500-5000	5

Find the expenditure done by maximum number of manual workers.

Given below is the distribution of total household expenditure of 200 manual workers in a city.
$\begin{matrix} Expenditure (in Rs.) & No. of manual workers 1000 - 1500 & 24 1500 - 2000 & 40 2000 - 2500 & 31 2500 - 3000 & 28 3000 - 3500 & 32 3500 - 4000 & 23 4000 - 4500 & 17 4500 - 5000 & 5 \end{matrix}$
Find the expenditure done by maximum number of manual workers.

Q. If the average wage of

100

workers is

3000

and the average wage of

25

of them is

4500

then find the average wage of the remaining workers.

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At present a firm manufacturing 2000 items it is estimated that the rate of change of production (P) with respect to additional number of workers (x) is given by dPdx=100−12√x. If the firm employes 25 more workers then the new production is?

The correct option is A 2500Solution-dpdx=100−12√xp=∫(100−12√x)dxp=100x−8(x)3/2+cc=0p=100×2025−8(45)3+cp−2000=100×2025−8(45)3−100×2000+8(2000)3/2p=25000A is correct.

At present a firm manufacturing $2000$ items it is estimated that the rate of change of production (P) with respect to additional number of workers $(x)$ is given by
$\frac{d P}{d x} = 100 - 12 \sqrt{x}$ . If the firm employes $25$ more workers then the new production is?

The correct option is A $2500$
Solution-
$\frac{d p}{d x} = 100 - 12 \sqrt{x}$
$p = \int (100 - 12 \sqrt{x}) d x$
$p = 100 x - 8 (x)^{3 / 2} + c$
$c = 0$
$p = 100 \times 2025 - 8 (45)^{3} + c$
$p - 2000 = 100 \times 2025 - 8 (45)^{3} - 100 \times 2000 + 8 (2000)^{3 / 2}$
$p = 25000$
A is correct.