At present,a firm is manufacturing 2000 items | vedclass

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(C) Given the rate of change of production: $\frac{dP}{dx} = 100 - 12\sqrt{x}$.Integrating both sides with respect to $x$:$\int dP = \int (100 - 12x^{

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$3500$

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(C) Given the rate of change of production: $\frac{dP}{dx} = 100 - 12\sqrt{x}$.Integrating both sides with respect to $x$:$\int dP = \int (100 - 12x^{1/2}) dx$$P = 100x - 12 	imes \frac{x^{3/2}}{3/2} + C$$P = 100x - 8x^{3/2} + C$Initially,when $x = 0$,the production $P = 2000$. Substituting these values:$2000 = 100(0) - 8(0)^{3/2} + C \Rightarrow C = 2000$.So,the production function is $P = 100x - 8x^{3/2} + 2000$.For $x = 25$ additional workers,the new production level is:$P = 100(25) - 8(25)^{3/2} + 2000$$P = 2500 - 8(125) + 2000$$P = 2500 - 1000 + 2000$$P = 3500$.

At present,a firm is manufacturing $2000$ items. It is estimated that the rate of change of production $P$ with respect to the 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:

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