Question

Manufacturer can sell x items at a price of Rs. $(5-\frac{x}{100})$ each. The cost price is Rs. $(\frac{x}{5}+500).$ Then, find the number of items he should sell to earn maximum profit.

Answer 1

$Profitfunctionf\left(x\right)=x\times (5-(\frac{x}{100})-(\left(\frac{x}{5}\right)+500)=5x-(\frac{x^2}{100})-(\frac{x}{5})-500=(\frac{1}{100}\left)\right[500x-x^2-20x-50000\left]f^{\prime }\right(x)=500-2x-20=0\therefore 2x=500-20\therefore x=(\frac{480}{2})=240whichisapointofmaxima$