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 $5,750$ units per year. The cost of each unit is $$99,$ and the inventory carrying cost is $$9$ per unit per year. The average ordering cost is $$29$ per order. It takes about $5$ days for an order to arrive, and the demand for $1$ week is $115$ units. $($This is a corporate operation, and there are $250$ working days per year$).$

a$)$ What is the EOQ? $192\mathrm{.}49$ units $($round your response to two decimal places$).$

b$)$ What is the average inventory if the EOQ is used? $96\mathrm{.}25$ 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$)$