Daily demand for a certain product is normally distributed with a mean of $100$ and a standard deviation of $15.$ The supplier is reliable and maintains a constant lead time of $5$ days. The cost of placing an order is $$10$ and the cost of holding inventory is $$0\mathrm{.}50$ per unit per year. There are no stock$-$out costs, and unfilled orders are filled as soon as the order arrives. Assume sales occur over $360$ days of the year.

Your goal here is to find the order quantity and reorder point to satisfy a $90$ percent probability of not stocking out during the lead time.