$2.$ Consider a product for which the average demand is $20$ items per day $($for $365$ days per year$)$ and the standard deviation of demand is $6$ per day. The item value is $$200,$ the order cost is $$30$ per order, and the inventory carrying cost is $20\%$ per year. The stockout cost is $$50$ per unit short. The probability of being in stock is to be $90\%.$ The supplier has an average lead time of $6$ days with a standard deviation of $1$ day.

$(5$ pts$.)$ a$)$ Design a reorder point system using the $90\%$ probability of being in stock and $($i$)$ state the policy $($order size and when to order$)$ and $($ii$)$ the total annual cost.