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 $150 for Atlanta.
Region 1 of the country requires 80 units per week, region 2 requires 70 units per week, and region 3 requires 40 units per week. The costs (including production and shipping costs) of sending one unit from a plant to a region are shown in Table.
|
From |
To ($) |
||
|
Region 1 |
Region 2 |
Region 3 |
|
|
New York |
20 |
40 |
50 |
|
Los Angeles |
48 |
15 |
26 |
|
Chicago |
26 |
35 |
18 |
|
Atlanta |
24 |
50 |
35 |
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.
