URGENT!! Please show all work and answer the questions fully! I will give excellent ratings if you answer it fully, so I can fully understand.

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?

b$.$ What are the total annual holding costs of the stock for Q'Well? What are the total annual

ordering costs?

c$.$ If Q'Well orders in quantities of $8,000$ or more, it can get a $$0\mathrm{.}05$ discount per bottle. Should

Q'Well take the quantity discount? If so$,$ how much should Q'Well order?

d$.$ Using the same numbers as the first part of the question $($without the discount$),$ assume now

that the daily demand normally distributed with a mean of $250,$ a variance of $25$ bottles per day,

and lead time is assumed to be normally distributed with a mean of $18$ days and a variance of $4$

days. Assume that management has specified that no more than a $5\%$ risk of a stockout is

acceptable. What is the standard deviation of demand during lead time? What is the safety stock

needed to attain a $5\%$ risk of stockout during lead time? What is the demand during lead time?

What should be the reorder point? What is the annual holding cost of maintaining the level of

safety stock needed to support a $5\%$ risk of a stockout?