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 costs of keeping each warehouse open are $40,000 for New York, $50,000 for Los Angeles, $30,000 for Chicago and $25,000 for Atlanta. Region 1 of the company 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) of sending one unit from a warehouse to a region are attached in the file spreadsheet below. The company wants to meet the 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 also be opened.

At most two warehouses can be opened.

Either the Atlanta or the Los Angeles warehouse must be opened. (Note that either A or B means, one of three possibilities just A, just B or both A and B)

1 Opening warehouses 3 Unit production and shipping costs Region 1 Region 2 Region 3 Fixed cost $40,000 $50,000 $30,000 $25,000 6 From NY LA Chicago Atlanta $15 535 550 526 $18 $35 10 11 Warehouses to open (1 if open, 0 if not) 12 NY Chicago Atlanta 14 15 16 17 Amount produced and shipped Region 1 Region 2 Region 3 Total Logical Capacity 0