Question 6 (17 marks) YY Auto HK LTD. imports Toyota Alphard from Japan at the price of $400,000 per car. Assume that the demand, ordering costs, carrying costs and lead time are known and constant: The demand in Hong Kong market is 12,000 cars per year or 1,000 cars per month; The ordering cost is $1,000,000 per purchase order and it takes one month to deliver the ordered cars from Japan to Hong Kong: YY Auto requires 5% annual return on investment; warehouse maintenance and rental fees for one year is $4,000 per car; and there is no other carrying costs. Required: a. Calculate the total carrying cost per unit of stock for 1 year. (3 marks) b. What is the optimal quantity of each order if YY Auto wants to minimize the relevant total inventory cost? (2 marks) How many orders per year? (1 mark) C. At what point should YY Auto reorder a new batch of cars, assuming that both demand and purchase-order lead time are known and constant. (3 marks) d. If the monthly demand fluctuates from time to time, the maximum demand is 1.200 cars per month while the average demand is 1,000 cars per month. Given that the distribution of the fluctuated demand is unknown and YY Auto does not want to run out of stock at any time, please help YY Auto to determine the safety stock (2 marks). In this case, how the safety stock will affect YY Auto's reorder point (2 marks)? e. Now assume that YY Auto knows about the probability distribution of fluctuated monthly demand, as shown in the following table. It is costly to run out of stock: if YY Auto runs out of stock, it would have to rush order the cars at an additional cost of $10,000 per car. In this scenario, how much safety stock should the company hold to minimize the total relevant costs (4 marks)? Demand level per month Probability of demand 800 cars 5% 900 cars 20% 1,000 cars 50% 1,100 cars 20% 1,200 cars 5% Average: 1,000 cars Total: 100%