Georgia Atlantic Corporation needs to decide on the locations for two new warehouses. The candidate sites are Philadelphia, Tampa, Denver, and Chicago. The following table provides the monthly capacities and the monthly fixed costs for operating warehouses at each potential site:
Philadelphia Capacity 250; Monthly fixed cost $1,000
Tampa Capacity 260; Monthly fixed cost$800
Chicago Capacity 280; Monthly fixed cost $1,200
Denver Capacity 270; Monthly fixed cost $700
The warehouse will need to ship to three marketing areas: North, South, and West. Monthly requirements are 200 units for North, 180 units for South, and 120 units for West. The following table provides the cost to ship one unit between each location and destination:
Warehouse North South West
Philadelphia $4 $7 $9
Tampa $6 $3 $11
Chicago $5 $6 $5
Denver $8 $10 $2
In addition, the following conditions must be met by the final decision: (1) A warehouse must be opened in either Philadelphia or Denver, and (2) if a warehouse is opened in Tampa, then one must also be opened in Chicago. Which two sites should be selected for the new warehouses to minimize total fixed and shipping costs?