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{dP}{dx} = 100 - 12 \sqrt{x}. If the firm employs 25 more workers, then the new level of production of items is :

Engineering

Mathematics

Variable Separable Differential Equation

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 $\frac{dP}{dx} = 100 - 12 \sqrt{x}$ . If the firm employs 25 more workers, then the new level of production of items is :

4500

2500

3000

3500

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$\frac{dP}{dx} = 10 - 12 \sqrt{x}$

$\int_{2000}^{P} dP = \int_{0}^{25} (100 - 12 \sqrt{x}) dx$

P – 2000 = 100 × x – ${\frac{12 x^{\frac{3}{2}}}{3 / 2} |}_{0}^{25}$

$= 100 x - {8 x^{\frac{3}{2}} |}_{0}^{25}$ = 2500 – 8 × 125

P = 3500. Ans.

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