III. [Vinopoly, 6 points] Vinopoly is a web-based wine retailer that currently ships all orders from a single fulfillment center (FC) at the center of the country. Based on the dispersion of the vineyards it obtains its wines from, the inbound transportation cost (from vineyard to FC) is $0.20 per bottle. The outbound transportation cost (from FC to customer) per bottle of wine is $1.80. Vinopoly's daily demand for wines has mean (average) 2000 bottles and standard deviation 5000 bottles. The FC maintains an inventory policy of ordering 2000 bottles every day from its suppliers, while maintaining a safety stock of half the standard deviation of daily demand. Annual holding cost per bottle of wine is $100, and is incurred for cycle and safety inventory. There are no other costs. Part a (2 points) Compute the total annual cost incurred by Vinopoly. Part b (4 points) Vinopoly is considering decentralizing its fulfillment to three regional FCs, labeled FC1, FC2, and FC3 respectively. Vinopoly expects that 40% of the total demand will be served by FC1, 20% by FC2, and 40% by FC3. Each regional FC will still place a daily order exactly equal to the mean (average) demand at that FC, and will maintain safety stock equal to one-half the standard deviation of daily demand at that FC. Holding costs remain the same under the decentralized network. Inbound transportation costs will increase to $0.40 per bottle, while outbound costs will decrease to $1.00 per bottle. Do you recommend for decentralization? Support your answer with complete financial justification.