Thomas Kratzer is the purchasing manager for the headquarters of a large insurance con inventory operation. Thomas's fastest$-$moving inventory item has a demand of $6,100$ units unit is $$103,$ and the inventory carrying cost is $$9$ per unit per year. The average ordering about $5$ days for an order to arrive, and the demand for $1$ week is $122$ units. $($This is a col $250$ working days per year$).$

a$)$ What is the EOQ? $198\mathrm{.}27$ units $($round your response to two decimal places$).$

b$)$ What is the average inventory if the EOQ is used? $$ units $($round your response to $t$