Thomas Kratzer is the purchasing manager for the headquarters of a large insurance company chain with a central inventory operation.$$ Thomas's fastest$-$moving inventory item has a demand of $6$ comma $1006,100$ units per year. The cost of each unit is $$$$9898,$ and the inventory carrying cost is $$$$1111$ per unit per year. The average ordering cost is $$$$3131$ per order. It takes about $55$ days for an order to$$ arrive, and the demand for $1$ week is $122122$ units.$($This is a corporate$$ operation, and there are $250250$ working days per$$ 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? $32\mathrm{.}9032\mathrm{.}90$ orders $($round your response to two decimal$$ places$).$

Part $5$

$$d$)$ What is the optimal number of days in between any two$$ orders? $7\mathrm{.}607\mathrm{.}60$ days $($round your response to two decimal$$ places$).$

Part $6$

$$e$)$ What is the annual cost of ordering and holding$$ inventory? $$$$1019\mathrm{.}831019\mathrm{.}83$ per year $($round your response to two decimal$$ places$).$