9. Consider Example 5b of Chapter 4, but now suppose that the seasonal demand is a continuous random variable having probability density function *f*. Show that the optimal amount to stock is the value *s* that satisfies

$$F(s) = \frac{b}{b + \ell}$$

where *b* is net profit per unit sale, *l* is the net loss per unit unsold, and *F* is the cumulative distribution function of the seasonal demand.