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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Similar questions

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2000

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

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