The total cost of producing x radio sets per day


The total cost of producing $x$ radio sets per day is Rs $\left(\frac{x^{2}}{4}+35 x+25\right)$ and the price per set at which they may be sold is Rs. ( $50-\frac{x}{2}$ ). Find the daily


Profit =S.P. - C.P.

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

$\Rightarrow P=50 x-\frac{x^{2}}{2}-\frac{x^{2}}{4}-35 x-25$

$\Rightarrow \frac{d P}{d x}=50-x-\frac{x}{2}-35$

For maximum or minimum values of $P$, we must have

$\frac{d P}{d x}=0$

$\Rightarrow 15-\frac{3 x}{2}=0$

$\Rightarrow 15=\frac{3 x}{2}$

$\Rightarrow x=\frac{30}{3}$

$\Rightarrow x=10$


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

So, profit is maximum if daily output is 10 items.

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