$3.$ Weekly demand for Lego at a Wal$-$Mart store is $2500$ boxes. The replenishment lead time is two weeks; the cost of ordering is $ $231$ and cost of holding $($per item per year$)$ is $20\%$ of item cost, which is $$3$ per unit. We are assuming there are $52$ weeks in one year.

a$.$ Find the economic order quantity $($round to the nearest thousand$),$ reorder point, time between orders, average inventory level, and total annual variable cost, assuming there is no uncertainty in demand.b$.$ Use a continuous review approach. Use EOQ as the order quantity. Find the reorder point, order$-$up$-$to level, safety stock quantity, average inventory level, and total annual variable cost, assuming demand is normally distributed with a weekly average of $2500$ and a weekly standard deviation of $500$ and a desired service level of $90\%.$ Compare total cost you find to that in part $1.$ What is the difference in cost$?$

c$.$ Now use a periodic review approach with the periodicity derived from the initial EOQ analysis in part $1.$ Find the safety stock, order$-$up$-$to level, average inventory level, and total annual variable cost with the same average demand and standard deviation of weekly demand, and the same desired service level as in part $1.$ Compare the total cost to those in parts $1$ and $2,$ what are the differences?

d$.$ Comment on your findings.