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  • Provide solution for RD Sharma maths class12 Chapter Maxima and Minima exercise 17.5 question 37.

Provide solution for RD Sharma maths class12 Chapter Maxima and Minima exercise 17.5 question 37.

Answers (1)

240 items

Hint: For maximum or minimum value of P, we must have \frac{dP}{dx}=0

Given: Profit = S.P - C.P

P= x\left ( 5-\frac{x}{100} \right )-\left ( 500+\frac{x}{5} \right )

Solution: P= x\left ( 5-\frac{x}{100} \right )-\left ( 500+\frac{x}{5} \right )

\begin{aligned} &P=5 x-\frac{x^{2}}{100}-500-\frac{x}{5} \\ &\frac{d P}{d x}=5-\frac{x}{50}-\frac{1}{5} \\ &\frac{d P}{d x}=0 \\ &5-\frac{x}{50}-\frac{1}{5}=0 \\ &\frac{24}{5}=\frac{x}{50}, x=\frac{24 \times 50}{5}=240 \end{aligned}

Now,

\frac{d^2P}{dx^2}=\frac{-1}{50}<0

Profit is maximum if 240 items are sold.

 

Posted by

infoexpert24

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