Cost Price (CP) for producing x amount = \(\frac{x^2}{4}+35x+25\)
Selling Price (SP) per producing x amount = (50 - \(\frac{x}{2}\))
Selling Price (SP) for producing x amount = 50x - \(\frac{x^2}{2}\)
Profit P = SP - CP
Therefore,
\(\frac{d^2P}{dx^2}\) = \(-\frac{3}{2}\)
Maxima exits, therefore we will get maximum profit at x = 10.