$2.$ Q$$Well$,$ located in Guelph, is a large online retailer of refillable water bottles. Q$$Well operates

$280$ days a year and sells an average of $250$ one litre water bottles a day. They order bottles from

a manufacturer in China. After ordering, bottles always arrive in exactly $18$ days. Annual

holding costs per bottle are estimated to be $15\%$ of the cost of bottles. The ordering cost is $$200$

per order. The cost of a one litre bottle is $$4.$

a$.$ What is the optimal order quantity for Q$$Well$?$ What is the average inventory? What is the

expected total number of orders per year?