A company is considering opening warehouses 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...

A company is considering opening warehouses 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, and $25,000 for Atlanta. Region 1 of the country requires 8000 units per week, region 2 requires 7000 units per week, and region 3 requires 4000 units per week. The costs (including production and shipping costs) of sending one unit from a warehouse to a region are shown in the file P06_50.xlsx. 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 opened, 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.