$(6)$ A retailer uses continuous review method to manage its inventory. A certain product has a daily demand of $25$ units; the retailer operates the store $360$ days a year. The purchase price of the product is $$40$; holding cost is determined to be $15\%$ of cost$.$ Ordering cost is determined to be $$93\mathrm{.}4.$ Do$/$answer the following.

$($i$)$ What is the annual demand? $(5)$

$($ii$)$ What is the optimal order quantity? $(15)$

$($iii$)$ What is the maximum inventory? Calculate the average inventory and the total annual holding cost. $(10)$

$($iv$)$ What would be your estimate of annual ordering cost based on your calculations so far? You have to briefly state the rationale. $(5)$

$($v$)$ Annually, how many times are orders placed? $(5)$

$($vi$)$ Given that the lead time is FOUR days, what would be the ROP under constant demand rate assumption? $(5)$

$($vii$)$ What is the probability of being stock out during lead time if you used your answer in $($vi$)$ as ROP? What is the service rate if ROP is $136?(5+10)$

$($viii$)$ Calculate the ROP and safety stock for a service rate of $97\mathrm{.}5\%.(15)$

$($ix$)$ What is the average maximum and minimum inventory levels with the policy of using safety stock? Calculate the average inventory and the increment in holding cost due to safety stock. $(10)$