Todd\'s Direct, a major TV sales chain headquartered in New? Orleans, is about t
ID: 428157 • Letter: T
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 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.
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Census Tract
Population in Census Tract
?X, Y Map Coordinates
101
2,000
?(25?,45?)
102
4,800
?(25?,24?)
103
9,500
?(57?,42?)
104
7,000
?(50?,22?)
105
10,400
?(76?,52?)
106
18,000
?(72?,22?)
107
15,000
?(96?,22?)
?a) The? center-of-gravity coordinates for the location of the proposed outlet in? Mobile, Alabama should? be:
x? = 68.78
y? = 30.36
?b) Census tracts 103 and 105 are each projected to grow by 20% in the next year. The new? center-of-gravity coordinates for the location of the proposed outlet in? Mobile, Alabama should? be:
x? =
y =
(round your response to two decimal? places).
Census Tract
Population in Census Tract
?X, Y Map Coordinates
101
2,000
?(25?,45?)
102
4,800
?(25?,24?)
103
9,500
?(57?,42?)
104
7,000
?(50?,22?)
105
10,400
?(76?,52?)
106
18,000
?(72?,22?)
107
15,000
?(96?,22?)
Explanation / Answer
To be calculated:
The centre-of-gravity coordinates for the location of the proposed outlet in Mobile, Alabama.
Given values:
7 census tracts, population in census tract and X,Y map coordinates
Solution:
(a) The centre-of-gravity coordinates can be calculated as;
X-coordinate = Sum of [Xi x Population] / Total population in census tract
Total population in census tract = 2000 + 4800 + 9500 + 7000 + 10400 + 18000 + 15000
Total population in census tract = 66700
X-coordinate = [(25 x 2000) + (25 x 4800) + (57 x 9500) + (50 x 7000) + (76 x 10400) + (72 x 18000) + (96 x 15000)] / 66700
X-coordinate = 68.78
Y-coordinate = Sum of [Yi x Population] / Total population in census tract
Y-coordinate = [(45 x 2000) + (24 x 4800) + (42 x 9500) + (22 x 7000) + (52 x 10400) + (22 x 18000) + (22 x 15000)] / 66700
Y-coordinate = 30.36
Answer: X = 68.78, Y = 30.36
(b) Census tracts 103 and 105 are projected to grow by 20% in the next year.
Census tract 103 = 9500 + (0.20 x 9500) = 11400
Census tract 105 = 10400 + (0.20 x 10400) = 12480
Total population in census tract = 2000 + 4800 + 11400 + 7000 + 12480 + 18000 + 15000
Total population in census tract = 70680
X-coordinate = [(25 x 2000) + (25 x 4800) + (57 x 11400) + (50 x 7000) + (76 x 12480) + (72 x 18000) + (96 x 15000)] / 70680
X-coordinate = 68.68
Y-coordinate = [(45 x 2000) + (24 x 4800) + (42 x 11400) + (22 x 7000) + (52 x 12480) + (22 x 18000) + (22 x 15000)] / 70680
Y-coordinate = 31.31
Answer: X = 68.68, Y = 31.31
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