Question 4 Multi-period Inventory Control (9 marks) A retailer operates 365 days of the year. It has an annual demand of food products of 60,000 units with an equal daily demand across the year with the standard deviation of the daily demand of 60 units. The supplier of the products charges the retailer the base rate of the products' price for $200 per unit and the base rate for the ordering cost (including delivery) of $500 per order. The supplier has agreed that it will take four days to fulfil (deliver) the orders for the retailer. The products are kept at the retailer's storage area, and the annual holding cost per unit is 5% of the product's unit price. As part of building a long-term relationship, the supplier offers discounted prices for different order quantities. Any order quantity below 2,000 units, the products and the ordering cost will be priced at the base rate. For any order quantity between 2,000 and 4,999 units, the retailer will receive a 5% discount on the base rate of the products' price and a 10% discount on the base rate of the ordering cost. For any order quantity of 5,000 units or more, the 2 retailer will receive a 10% discount on the base rate of the product's price and a 20% discount of the base rate of the ordering cost. a. Calculate the minimum total inventory costs for each order quantity range, and determine the order quantity that produces the lowest total inventory cost (2 marks) b. Determine the order quantity that has the lowest total cost of the products for the whole year by comparing order quantities of the other ranges. Which order quantity would you recommend to the retailer? (2 marks) c. If the retailer currently sets the service level at 80%, what will be the amount of the safety stock and the re-order point of the products? (1 mark) d. If the retailer wants to increase the service level by 10%, suggest two possible options that it can take to achieve the goal without changing the demand. Show the calculations to support your suggestion as well as (any) factors that need to be considered in the suggestion. (4 marks)