a$)$ Given that it is trying to minimize its ordering and holding cost, what lot size will the retailer ask for in each order? What is the annual ordering and holding cost for the retailer as a result of this policy? What is the annual ordering and holding cost for Crunchy as a result of this policy? What is the total inventory cost across both parties as a result of this policy?

b$)$ What lot size minimizes the inventory costs $($ordering$,$ delivery, and holding$)$ across this entire supply chain $($both Crunchy and the retailer$)?$ What is the total inventory. cost of this supply chain?

c$)$ Compare the results obtained in a$)$ and b$)$ and discuss your observations.

Problem $4$

A shop owner uses a reorder point approach to restocking a certain raw material. Lead time is $10$ days. Usage of the material is normally distributed with a mean of $80$ pounds per day and a daily standard deviation of $8$ pounds. When should the raw material be reordered if the acceptable risk of a stockout is $2\%($Customer service level is $98\%)?($Hint: You need to calculate the standard deviation during the lead time$)$