$2(50$ pts$)$ A local distributor for a national tire company expects to sell approximately $9,600$ steel$-$belted radial tires of a certain size and tread design next year. Annual carrying cost is $$16$ per tire, and ordering cost is $$\frac{75}{?}$ order. The distributor operates $288$ days a year, and the lead time to receive an order from its upstream supplier is three working days.

$($a$)(10$pts$)$ What is the Economic Order Quantity $($EOQ$)?$

$($b$)(5$pts$)$ How many orders per year are expected?

$($c$)(5$pts$)$ What is the expected time between orders?

$($d$)(10$pts$)$ Find the total annual inventory costs if the EOQ quantity is ordered.

$($e$)(10$pts$)$ If ordering costs were to increase by $$5$ per year, how much would that affect the minimum total annual cost?

$($f$)(10$pts$)$ What is the reorder point?