$12\mathrm{.}14$ 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 $6,000$ units per year. The cost of each unit is $$100,$and the inventory carrying cost is $$10$ per unit per year. The average ordering cost is $$30$ per order. It takes about $5$ days for anorder to arrive, and the demand for $1$ week is $120$ units. $($This is a corporate operation, and there are $250$ working days per year.$)$a$)$ What is the EOQ?b$)$ What is the average inventory if the EOQ is used?c$)$ What is the optimal number of orders per year?d$)$ What is the optimal number of days in between any two orders?e$)$ What is the annual cost of ordering and holding inventory?f$)$ What is the total annual inventory cost, including the cost of the $6,000$ units?