Thomas Kratzer is the purchasing manager for the headquarters of a large insurance company chain with a central inventory operation. Thomas's fastest$-$moving inventory item has a demand of $5,800$ units per year. The cost of each unit is $$102,$ and the inventory carrying cost is $$8$ per unit per year. The average ordering cost is $$31$ per order. It takes about $5$ days for an order to arrive, and the demand for $1$ week is $116$ units. $($This is a corporate operation, and there are $250$ working days per year$).$

a$)$ What is the EOQ? units $($round your response to two decimal places$).$

b$)$ What is the average inventory if the EOQ is used? units $($round your response to two decimal places$).$

c$)$ What is the optimal number of orders per year? orders $($round your response to two decimal places$).$

d$)$ What is the optimal number of days in between any two orders? $|$ days $($round your response to two decimal places$).$

e$)$ What is the annual cost of ordering and holding inventory? $ per year $($round your response to two decimal places$).$

f$)$ What is the total annual inventory cost, including the cost of the $5,800$ units? $ per year $($round your response to two decimal places$).$