SATHEE: Differential Equations 3 Question 5

Differential Equations 3 Question 5

5.

At present, a firm is 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 employees $25$ more workers, then the new level of production of items is

(2013 Main)

(a) 2500

(b) 3000

(d) 4500

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Answer:

Correct Answer: 5. (c)

Solution:

Given, $\frac{d P}{d x} = (100 - 12 \sqrt{x}) \Rightarrow d P = (100 - 12 \sqrt{x}) d x$

On integrating both sides, we get

$\begin{matrix} \int d P = \int (100 - 12 \sqrt{x}) d x \\ P = 100 x - 8 x^{3 / 2} + C \end{matrix}$

When $x = 0$ , then $P = 2000 \Rightarrow C = 2000$

Now, when $x = 25$ , then is

$\begin{aligned} P & = 100 \times 25 - 8 \times (25)^{3 / 2} + 2000 \\ = 2500 - 8 \times 125 + 2000 \\ = 4500 - 1000 = 3500 \end{aligned}$

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Differential Equations 3 Question 5

5.

Answer:

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