Thomas Kratzer is the purchasing manager for the headquarters of a large insurance company chain with a central inventory operation. Thomass fastest$-$moving inventory item has a demand of $6,100$ units per year. I he cost of each unit is $$96,$ and the inventory carrying cost is $$11$ 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 $122$ units. $($This is a corporate operation, and there are $250$ working days per year$).$

a$)$ What is the EOQ? $185\mathrm{.}42$ units $($round your response to two decimal places$).$

b$)$ What is the average inventory if the EOQ is used? $92\mathrm{.}71$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$).$