4. [26 points] Report four digits after the decimal for prob…
4. Report four digits after the decimal for probability-related values. Report two digits after the decimal for quantity-related values. One Love Pub serves craft beers from microbrewers nationwide. The manager buys a particular sour beer from a brewing company in Maine that requires three weeks for delivery. The sour beer costs $1 a bottle and may be purchased in any quantity. The fixed ordering cost is $70, and inventory holding costs are calculated using an annual inventory carrying rate of 22%. Based on historical data, the weekly demand for this sour beer is normally distributed with a mean of 120 bottles and a standard deviation of 40 bottles. The manager currently has a policy to place a replenishment order when there is 4-weeks’ supply left. Each order consists of 6-weeks of supply. For your calculations, you may assume that there are 48 weeks in a year and that all excess demand is fully backlogged. What are the reorder level and order quantity currently used for the sour beer? What is the proportion of demand that cannot be satisfied immediately from stock under the current policy? What reorder level and order quantity should the manager use if she wishes to ensure that the probability of not stocking out during the lead time is 95 percent?