Demand for a product is Normally distributed with a mean of $400$ units a month and a standard deviation of $30$ units a month. Lead time is also Normally distributed with a mean of $2$ months and a standard deviation of $0\mathrm{.}5$ months. What reorder level gives a $95\%$ cycle service level? What is the best reorder quantity if reorder cost is $$400$ and the holding cost is $$10$ a unit a month?