Question: Consider 2 identical retailers, with the same costs and characteristics, facing random demand for a single product. We compare the two systems, the decentralized and centralized one. In the centralized pooled system, the retailers together operate a joint inventory facility and take items out of the pooled inventory to meet demand. In the decentralized system, each retailer individually orders from the manufacturer to meet demand. We consider a single period of random demand. The probabilistic forecast of demand faced by each retailer is depicted in the following table: Demand Probabilistic 5,000 12% 6,000 10% 7,000 30% 8,000 23% 9,000 15% 10,000 10% Meanwhile, the wholesale price is $40 per unit, the selling price of $65 per unit, salvage value of $10 per unit, and production cost of $15 per unit. If the order quantity must be multiples of 1,000 units:| a. What's each retailer's best order quantity in a period in each system? b. What is the retailer's expected profit? c. Manufacturer's profit in each system