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Standard XII

Mathematics

Linear Differential Equations of First Order

At present, a...

Question

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:

3000

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3500

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4500

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2500

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Solution

The correct option is B 3500
$\int_{2000}^{P} d P = \int_{0}^{25} (100 - 12 \sqrt{x}) d x$
$(P - 2000)$ $= 25 \times 100 - \frac{12 \times 2}{3} (25)^{3 / 2}$
$P = 3500.$

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Shetty&Co is a firm manufacturing paper bags in Odisha. It has employed female workers in the company and manufactures paper bags from recycling paper and thereafter sells them to various firms at economic rates. State the value being followed by the company.

Polycons Ltd. is a firm manufacturing paper bags in Odisha. It has employed female workers in the company and manufactures paper bags from recycling paper and thereafter sells them to various firms at economic rates.___ function of management has been ignored above?

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[1 mark]

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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 dPdx=100−12√x. If the firm employs 25 more workers, then the new level of production of items is:

The correct option is B 3500∫P2000dP=∫250(100−12√x) dx(P−2000) =25×100−12×23(25)3/2P=3500.

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:

The correct option is B 3500
$\int_{2000}^{P} d P = \int_{0}^{25} (100 - 12 \sqrt{x}) d x$
$(P - 2000)$ $= 25 \times 100 - \frac{12 \times 2}{3} (25)^{3 / 2}$
$P = 3500.$