Cost Price (CP) for producing x amount = 500 + \(\frac{x}{5}\)
Selling Price (SP) per producing x amount = 5 - \(\frac{x}{100}\)
Selling Price (SP) per producing x amount = 5x - \(\frac{x^2}{100}\)
Profit P = SP - CP
x = 240
Therefore,
\(\frac{d^2P}{dx^2}\) = \(-\frac{1}{50}\) < 0
Thus,
x = 240 is a point of maxima.
Thus for maximum profit,
x should be 240.