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  • Provide solution for RD Sharma maths class12 Chapter Maxima and Minima exercise 17.5 question 36.

Provide solution for RD Sharma maths class12 Chapter Maxima and Minima exercise 17.5 question 36.

Answers (1)

10 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 ( 50-\frac{x}{2} \right )-\left ( \frac{x^2}{4}+35x+25 \right )

Solution: P= x\left ( 50-\frac{x}{2} \right )-\left ( \frac{x^2}{4}+35x+25 \right )

\begin{aligned} &P=50 x-\frac{x^{2}}{2}-\frac{x^{2}}{4}-35 x-25 \\ &\frac{d P}{d x}=50-x-\frac{x}{2}-35 \\ &\frac{d P}{d x}=0 \\ &15-\frac{3 x}{2}=0 \\ &15=\frac{3 x}{2}, x=\frac{30}{3}=10 \end{aligned}

Now,

\frac{d^2P}{dx^2}==\frac{-3}{2}<0

Profit is the maximum if daily output is 10 units.

 

Posted by

infoexpert24

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