Thomas Kratzer is the purchasing manager for the headquarters of a large insurance company chain with a central inventory operation.$$ Thomas's fastest$-$moving inventory item has a demand of $6,100$ units per year. The cost of each unit is $$$$102,$ and the inventory carrying cost is $$$$11$ per unit per year. The average ordering cost is $$$$31$ per order. It takes about $5$ days for an order to$$ arrive, and the demand for $1$ week is $122$ units.$($This is a corporate$$ operation, and there are $250$ working days per$$ year$).$

Part $2$

$$a$)$ What is the$$ EOQ? $185\mathrm{.}42185\mathrm{.}42$ units $($round your response to two decimal$$ places$).$

Part $3$

$$b$)$ What is the average inventory if the EOQ is$$ used? $92\mathrm{.}7192\mathrm{.}71$ units $($round your response to two decimal$$ places$).$

Part $4$

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