A company is considering opening warehouses in four cities: New York, Los Angeles, Chicago, and Atlanta. Each warehouse can ship 100 units per week. The weekly fixed cost of keeping each warehouse open is $400 for New York, $500 for Los Angeles, $300 for Chicago, and $150 for Atlanta. Region 1 of the country requires 80 units per week, region 2 requires 70 units per week, and region 3 requires 40 units per week. The costs (including production and shipping costs) of sending one unit from a plant to a region are shown in Table.
To ($)
From Region 1 Region 2 Region 3
New York 20 40 50
Los Angeles 48 15 26
Chicago 26 35 18
Atlanta 24 50 35
We want to meet weekly demands at minimum cost, subject to the preceding information and the following restrictions:
1 If the New York warehouse is opened, then the Los Angeles warehouse must be opened.
2 At most two warehouses can be opened.
3 Either the Atlanta or the Los Angeles warehouse must be opened.
Formulate an IP that can be used to minimize the weekly costs of meeting demand.