At present,a firm is manufacturing 1000 items | vedclass

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(A) 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^{

Vedclass · Accepted Answer

$1684$

Vedclass · Answer

(A) 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$$P = 100x - 12 \cdot \frac{x^{3/2}}{3/2} + C$$P = 100x - 8x^{3/2} + C$Given that the initial production $P = 1000$ when $x = 0$:$1000 = 100(0) - 8(0)^{3/2} + C \implies C = 1000$.Thus,the production function is $P(x) = 100x - 8x\sqrt{x} + 1000$.For $x = 9$ additional workers:$P(9) = 100(9) - 8(9)\sqrt{9} + 1000$$P(9) = 900 - 8(9)(3) + 1000$$P(9) = 900 - 216 + 1000 = 1684$.The new level of production is $1684$ items.

At present,a firm is manufacturing $1000$ 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 $9$ more workers,then the new level of production of items is:

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