A gourmet coffee shop in downtown San Francisco is open $200$ days a year and sells an average of $75$ pounds of Kona coffee beans a day. $($Demand can be assumed to be distributed normally, with a standard deviation of $15$ pounds per day.$)$ After ordering

$($fixed cost $=$ $$16$ per order$)$

$,$ beans are always shipped from Hawaii within exactly $4$ days. Per$-$pound annual holding costs for the beans are $$3.$

a$.(3$ points$)$ What is the economic order quantity $($EOQ$)$ for Kona coffee beans?

b$.(3$ points$)$ What are the total annual holding costs of stock for Kona coffee beans?

c$.(3$ points$)$ What are the total annual ordering costs for Kona coffee beans?

d$.(3$ points$)$ Assume that management has specified that no more than a $1\%$ risk during stockout is acceptable. What should the reorder point $($ROP$)$ be$?$

e$.(3$ points$)$ What is the safety stock needed to attain a $1\%$ risk of stockout during the lead time?