A product that is sold seasonally yields a net profit of b dollars for each unit sold and a net loss of L dollars for each unit left unsold when the season ends. The number of units of the product that are ordered at a specific department store during any season is a continuous random variable having probability density function f. (We thus assume that any portion of the product may be sold.) Show that the optimal amount to stock in order to maximize the expected profit is the value s* that satisfies F(s*) = b/(b+L). F is the cumulative distribution function of the seasonal demand. Let X denote the number of units ordered. If s units are stocked, then the profit can be expressed as P(s) = bx - (s-x)L if x >= s, and s*b if X > s.