Question points$]$:

Freeport Corporation finds that demand for surfboards has average demand of $10$ units per day, with a standard deviation of $3$ units. Lead time from the supplier averages $12$ days, with a standard deviation of $2$ days. The item costs $$50$ and the inventory carrying cost is $30\%.$

a$.$ Suppose management decides to offer a $95\%$ service level. That is$,$ it is willing to experience a stockout probability of $5\%$ during the order cycle. How much safety stock should be carried?

b$.$ How much is the annual inventory carrying cost of the safety stock because of this decision?

c$.$ You decide that you want this company to give better service to its customers. You decide that a $99\%$ service level is appropriate. How much safety stock must be carried to offer this service level?

d$.$ What is the additional inventory carrying cost that will be incurred on this item because of your decision to increase the service level? I