Demand for walnut fudge ice cream at the sweet cream dairy can be approximated by a normal distribution with a meanof 21 gallons per week and a standard deviation of 3.5 gallons per week. the new manager desires a service level of 90percent. lead time is two days, and the dairy is open seven days a week. (hint: work in terms of weeks.)a. if an rop model is used, what rop would be consistent with the desired service level? how many days of supply are onhand at the rop, assuming average demand? b. lf a fixed-interval model is used instead of an rop model, what order size would be needed for the 90 percent servicelevel with an order interval of 10 days and a supply of 8 gallons on hand at the order time? what is the probability ofexperiencing a stockout before this order arrives? c.5uppose the manager is using the rop model described in part a. one day after placing an order with the supplier, themanager receives a call from the supplier that the order will be delayed because of problems at the supplier’s plant. thesupplier promises to have the order there in two days. after hanging up, the manager checks the supply of walnut fudgeice cream and finds that 2 gallons have been sold since the order was placed. assuming the supplier’s promise is valid, what is the probability that the dairy will run out of this flavor before the shipment arrives?