Question

Todd’s Direct, a major TV sales chain headquar-tered in New Orleans, is about to open its first outlet in Mobile, Alabama, and wants to select a site that will place the new out-let 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 1. 101 2,000(25, 45) 2. 102 5,000 (25, 25) 3. 103 10,000 (55, 45) 4. 104 7,000 (50, 20) 5. 105 10,000 (80, 50) 6. 106 20,000 (70, 20) 7. 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

Answer 1

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Solution:
		Coordinate
Location	Population	X	Y
101	2000	25	45
102	5000	25	25
103	10000	55	45
104	7000	50	20
105	10000	80	50
106	20000	70	20
107	14000	90	25
a). At what center of gravity coordinates should the new store be located?
	X coordinate =	∑Population_i*xi/∑Population_i	=	66.69
	Y coordinate =	∑Population_i*yi/∑population_i	=	30.22
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?
		Coordinate
Location	Population	X	Y
101	2000	25	45
102	5000	25	25
103	12000	55	45	population increased by 20 %
104	7000	50	20
105	12000	80	50	population increased by 20 %
106	20000	70	20
107	14000	90	25
At what center of gravity coordinates should the new store be located?
	X coordinate =	∑Population_i*xi/∑Population_i	=	66.74
	Y coordinate =	∑Population_i*yi/∑population_i	=	31.18

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