4.5 Weekly demand of packs of AAA batteries in BVE store is normally distributed with a mean of 1000 and a standard deviation of 50. The xed ordering cost is $130 per order. The inventory holding cost is $1.5per pack of batteries per year. The replenishment lead time is 2weeks. The company uses a continuous review policy with an order lot size of 3000. BVE makes a prot of $1.7 per pack of batteries. Currently demand during stockout is lost.

(a) What is the optimal CSL? What is the level of safety inventory that BVE needs to carry?

(b) BVE is considering a plan to backlog customer demand and mail the batteries to customers when the inventory is replenished. It does not offer any discount but the mailing cost is estimated to be $1 per pack of batteries. What is the optimal CSL under this plan?