Question

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 '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 40% in the next year. How will this influence the new store's coordinates?

Answer 1

To determine the location for Todd's Direct new outlet using the center of gravity method, we calculate the weighted averages for both X and Y coordinates based on the given populations and coordinates, then adjust the populations for projected growth in specific census tracts and recalculate as necessary.

Step-by-step explanation:

The subject of the question is Business, specifically related to location planning and analysis using the center of gravity method. To find the optimal location for Todd's Direct new outlet in Mobile, Alabama, we need to calculate the center-of-gravity coordinates first, taking into account the population as weights and the X, Y coordinates for each census tract as location points. The formula for calculating the center of gravity is:

Weighted average of X coordinates (Xcg) = ∑(Population* Xcoordinate) / ∑(Population)

Weighted average of Y coordinates (Ycg) = ∑(Population* Ycoordinate) / ∑(Population)

For the given data:

Xcg = (2000*25 + 5000*25 + 10000*55 + 7000*50 + 10000*80 + 20000*70 + 14000*90) / (2000 + 5000 + 10000 + 7000 + 10000 + 20000 + 14000)

Ycg = (2000*45 + 5000*25 + 10000*45 + 7000*20 + 10000*50 + 20000*20 + 14000*25) / (2000 + 5000 + 10000 + 7000 + 10000 + 20000 + 14000)