$(15$ pts$)$ Joe Henry's machine shop uses $2,500$ brackets during the course of a year. These brackets are

purchased from a supplier $90$ miles away. The following information is known about the brackers:

a$.(2$ pts$)$ Given the above information, what would be the economic order quantity $($EOQ$)?$

b$.(2$ pts$)$ Given the EOQ what would be the annual inventory holding cost?

c$.(2$ pts$)$ Given the EOQ what would be the annual ordering cost?

d$.(2$ pts$)$ Given the EOQ, what is the total annual inventory cost including purchasing costs?

e$.(4$ pts$)$ Given the following price breaks for purchasing the item, what would be the optimal order

quantity?

f$.(3$ pts$)$ Given Suppose the annual demand is normally distributed with standard deviation of $500.$

What reorder point should they use to achieve $90\%$ service level?