Luxe is a new optic store located in Florence which has been operating for a couple of years. Luxe is open for six days in a week and assume there are 48 weeks in a year. There are two types of glasses that Luxe sells: regular glasses and sunglasses. The distributors for both glasses are in China. It to place an order to place an order for sunglasses. The lead time of the orders is expected to be six weeks. The orders of the regular glasses and sunglasses are independent from each other.

For the regular glasses, Luxe can observe the inventory daily. Past data indicates that most of the regular glasses are sold on Fridays and Saturdays, and the least on Tuesdays. On the other hand, based on your forecasting results in Case I, you assume that the weekly demand follows a stationary normal distribution with a mean of 140 glasses and a standard deviation of 22 glasses (disregarding the variation within the week). The demand is practically observed continuously. Luxe purchases regular glasses for 40 per unit and sells them for 90 per unit. It costs per unit to keep regular glasses for one year in the inventory. Any demand that cannot be met on time is backlogged, incurring a shortage cost that is 20% of the selling price, that is, 18 per unit.

Luxe wants to keep track of the inventory more precisely and decides to apply a continuous review (Q,R) policy. Calculate the optimal order quantity and reorder level as well as the expected total annual cost.