Amos Mbewe is the owner of Mbewe and Sons Stores, the largest car dealership in its part of the country. His most popular car model is the BMW, so his largest costs are those associated with ordering these cars from the factory and maintaining an inventory of BMW on the lot. Therefore, Amos Mbewe has asked his general manager, Catherine Gama, who once took a course in operations research, to use this background to develop a cost-effective policy for when to place these orders for BMW and how many to order each time. Catherine decides to use the stochastic continuous-review model to determine Re-order and Quantity (R. Q) policy. After some investigation, she estimates that the administrative cost for placing each order is MWK 150,000 (a lot of paperwork is needed for ordering cars), the holding cost for each car is MWK300,000 per year (15 percent of the agency's purchase price of MWKK200,000), and the shortage cost per car short is MWK100,000 per year (an estimated probability of 1/3 of losing a car sale and its profit of about MWK300,000). After considering both the seriousness of incurring shortages and the high holding cost, Amos and Catherine agree to use a 95 percent service level (a probability of 0.95 of not incurring a shortage between the time an order is placed and the delivery of the cars ordered). Based on previous experience, they also estimate that the BMW sell at a relatively uniform rate of about 3,600 per year. After an order is placed, the cars aredelivered in about two thirds of a month. Catherine's best estimate of the probability distribution of demand during the lead time before a delivery arrives is a normal distribution with a mean of 50 and a standard deviation of 15.a) Calculate the order quantity (Q).b) Calculate the Re-order point (R).c) Calculate the safety stock.(6 marks)(4 marks)(4 marks)d) Suppose, Amos and Catherine agree to change the service level from 95 percent to 99.5 percent (a probability of 0.995 of not incurring a shortage between the time an order is placed and the delivery of the cars ordered). What could be the new:. Re-order point (R)?ii. Safety stock?