$1^{st}$ Inventory Management Problem $(3$ pts$)$

Kevin Mills is the inventory manager for a popular online book retailer. One of the retailer's top$-$selling books has an annual demand of $8,000$ copies. The cost of each book is $$25,$ and the inventory carrying cost is $$5$ per book per year. The average ordering cost is $$35$ per order. An order takes about $4$ days to arrive, and the demand for one week is $160$ copies. The retailer operates year$-$round with $250$ 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?