Todd's Direct, a major TV sales chain headquartered in New Orleans, is about to open its first outlet in Mobile, Alabama, and wants to select a site that will place the new outlet in the center of Mobile's population base. Todd examines the seven census tracts in Mobile, plots the coordinates of the center of each from a map, and looks up the population base in each to use as a weighting. The information gathered appears in the following table.
|
Census Tract
|
Population in Census Tract
|
X, Y Map Coordinates
|
|
101
|
2,000
|
(25, 45)
|
|
102
|
5,000
|
(25, 25)
|
|
103
|
10,000
|
(55, 45)
|
|
104
|
7,000
|
(50, 20)
|
|
105
|
10,000
|
(80, 50)
|
|
106
|
20,000
|
(70, 20)
|
|
107
|
14,000
|
(90, 25)
|
a) At what center-of-gravity coordinates should the new store be located?
b) Census tracts 103 and 105 are each projected to grow by 20% in the next year. How will this influence the new store's coordinates?