Exp$-$smooth:

#$4.$ A retailer uses continuous review method to manage its inventory. A certain product has an annual demand of $14,800$ ; the retailer operates the store $360$ days a year. The purchase price of the product is $$60$; holding cost is determined to be $20\%$ of cost$.$ Ordering cost is determined to be $$320\mathrm{.}0.$ Answer the following.

$($i$)$ Currently the managers orders $1800$ units every time she$/$he paces and order. $($a$)$ Determine HC $($annual holding cost$),($b$)$ annual number of orders on average, $($c$)$ SC$,$ annual ordering cost and $($d$)$ TC$,$ the total cost of inventory management. $(20$ pts$.)$

$($ii$)$ What is the optimal order quantity to minimize TC$?$ Determine the TC with the optimal order quantity and calculate the savings it generates. $(20$ pts$.)$