$*12\mathrm{.}14$ 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 $$30$ per order. It takes about $5$ days for an order to arrive, and the demand for $1$ week is $120$ units. $($This is a corporate operation, and there are $250$ working days per year.$)$ a$)$ What is the EOQ? b$)$ What is the average inventory if the EOQ is used? c$)$ What is the optimal number of orders per year? d$)$ What is the optimal number of days in between any two orders? e$)$ What is the annual cost of ordering and holding inventory? f$)$ What is the total annual inventory cost, including the cost of the $6,000$ units? $12\mathrm{.}15$ Joe Henry's machine shop uses $2,500$ brackets during the course of a year. These brackets are purchased from a supplier $90$ miles away. The following information is known about the brackets: Annual demand: $2,500$ Holding cost per bracket per year: $$1\mathrm{.}50$