A company is considering opening a warehouse in four cities: New York, Los Angeles, Chicago, and Atlanta. Each warehouse can ship 10,000 units per week. The weekly fixed cost of keeping each warehouse open is $40,000 for New York, $50,000 for Los Angeles, $30,000 for Chicago, an $25,000 for Atlanta. Region 1 of the country requires 8,000 units per week, region 2 requires 7,000 units per week, and region 3 requires 4,000 units per week. The costs (including production and shipping costs of sending one unit from a warehouse to a region are in the table below: From/ To Region 1 Region 2 Region 3 New York $20 $40 $50 Los Angeles $48 $15 $26 Chicago $26 $35 $18 Atlanta $24 $50 $35 The company wants to meet weekly demands at minimum cost, subject to the preceding information and the following restrictions: If the New York warehouse is open, then the Los Angeles warehouse must be opened. At most two warehouses can be opened. Either the Atlanta or the Los Angeles warehouse must be opened. a. What is the optimal minimum total cost and the operational plan for distributing the units from the warehouses to the regions? b. Suppose the COO insists that the Atlanta and Los Angeles warehouses be open. What would be the operational plan for distributing the units to the regions? How much worse is this plan?

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