Pedro runs a fruit shop. Mondays he opens his shop with a fresh supply of strawberries of \(s\) pounds, which is supposed to satisfy the demand for three days. He knows that for this time span the demand \(X\) is exponentially distributed with a mean value of 200 pounds. Pedro pays \(\$ 2\) for a pound and sells it for \(\$ 4\). So he will lose \(\$ 2\) for each pound he cannot sell, and he will make a profit of \(\$ 2\) out of each pound he sells. What amount \(s=s^{*}\) of strawberries Pedro should stock for a period of three days to maximize his mean profit?