A large supplier of electronic components has decided to control the inventory of a certain item by a periodic review, order up to R policy. The mean demand rate for this item is 500 units per year. The lead time ? is nearly constant at three months. The demand in the time ? + T can be represented by a normal distribution with mean 500 (? + T) and the variance 800(? + T). The cost of each unit is $10, the inventory carrying cost rate is 0.10, the cost of making a review and placing an order is $15, and the cost of backorder is estimated to be $30. Find the optimal quantity and period for this problem.