TeePee Store Location

TeePee is a convenience store chain that is attempting to determine the best location for a new outlet. Management would like to select a location that will draw customers from three population centers. Letting (x,y) represent the map coordinates of the three population centers, their locations are as follows: Center 1 is at (2,8), Center 2 is at (6,6), and Center 3 is at (1,1).

If the new outlet is located at (x=3,y=2), then it considered to be at a distance of (3-1)+(2-1)=3 miles from Center 3 (i.e., distance is measured as the sum of the east-west and north-south coordinate differences).

1. Formulate a goal programming model to determine the location for the new outlet that will minimize the total combined distance from the three population centers.
2. Population Center 1 is four times as large as Center 3 and Center 2 is twice as large as Center 3. The firm feels that the importance of locatiing near a population center is proportional to its population. Develop a new goal programming model that reflects these importances.