Thomas Kratzer is the purchasing manager for the headquarters of a large insurance company chain with a central inventory operation.$$ Thomas's fastest$-$moving inventory item has a demand of $5,800$ units per year. The cost of each unit is $$$$96,$ and the inventory carrying cost is $$$$8$ per unit per year. The average ordering cost is $$$$31$ per order. It takes about $5$ days for an order to$$ arrive, and the demand for $1$ week is $116$ units.$($This is a corporate$$ operation, and there are $250$ working days per$$ year$).$

Part $2$

$$a$)$ What is the$$ EOQ? $212\mathrm{.}01212\mathrm{.}01$ units $($round your response to two decimal$$ places$).$

Part $3$

$$b$)$ What is the average inventory if the EOQ is$$ used? $106\mathrm{.}01106\mathrm{.}01$ units $($round your response to two decimal$$ places$).$

Part $4$

$$c$)$ What is the optimal number of orders per$$ year? $27\mathrm{.}3427\mathrm{.}34$ orders $($round your response to two decimal$$ places$).$

Part $5$

$$d$)$ What is the optimal number of days in between any two$$ orders? $9\mathrm{.}149\mathrm{.}14$ days $($round your response to two decimal$$ places$).$

Part $6$

$$e$)$ What is the annual cost of ordering and holding$$ inventory? $$$enter your response here per year $($round your response to two decimal$$ places$).$