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3. (Submit, 8pts) XYZ plc sells a wide range of products. The daily demand for one such product has a Normal distribution N(20,36). If stock falls to a fixed level R, an order is placed with the local wholesaler for a fixed quantity Q, which will arrive exactly five days later. The cost of placing an order is 42. The wholesaler charges 30 per unit but XYZ can usually sell it for 49.99. Stockholding costs average out at 9% per unit per year. If demand cannot be met from stock, then it is held over until the order arrives, and XYZ will pay a stockout cost to the customer in the form of a discount on average 1 per unit per year. The management determined 8% as the tolerated probability of stockout before the order arrives. XYZ plc is open for business 300 days a year. a. What are the values for K,c,h,p ? What is the average demand d per time unit? Use 1 year as the time unit. 2 b. Use the EOQ model with planned shortages to find the approximately optimal order quantity Q for XYZ plc. c. Given the tolerated stockout probability, find the optimal reorder point R. (Recall that the sum of two normal distributions N(1,12) and N(2,22) is the normal distribution N(1+2,22+22). You may use the distribution tables attached.)