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 $$26$ a jar and requires a $3-$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 $ $60.$ During the $3-$month supply time, Harvey estimates that he sells an average of $150$ jars but there is substantial variation. He estimates the standard deviation of demand for each $3-$month period is $25.$ Assume that demand is described by a normal distribution. $(5+5+5+12+13+20=60$ points $)$ a$)$ What is the optimal order quantity? b$)$ What will be the average time between transactions? c$)$ How much safety stock should be maintained for $96\%$ cycle service level?