Problem $1)(12$ points$)$

A produce distributor uses $5,400$ packing crates a month, and each crate is purchased at a cost of $$16.$ The manager has assigned an annual carrying cost of $25$ percent of the purchase price per crate. Ordering cost is $$225.$ Currently the manager orders once a month.

a$)$ What is the Economic Order Quantity $($EOQ$)$ for this product? $(4$ pts$)$

b$)$ How much could the firm save annually in total holding and ordering costs by ordering at the EOQ level? $(8$ pts $)($Show the computations for the total holding and ordering costs in detail$)$