Q$2.($Total $60$ points$)$

Harvey's Specialty Shop is a popular spot that specializes in international gourmet foods. One of the items that Harvey sells is a popular mustard that he purchases from an English company. The mustard costs Sio a jar and requires a $2-$month lead time for replenishment of stock. The replenishment time is constant. Harvey uses a $20\%$ annual interest rate to compute holding costs. Bookkeeping expenses for placing an order amount to about $$50.$ During the $2-$month supply time, Harvey estimates that he sells an average of $100$ jars but there is substantial variation. He estimates the standard deviation of demand for each $2-$month period is $25.$ Assume that total demand during lead time duration is described by a normal distribution. points