Todd\'s Direct, a major TV sales chain headquartered in New Orleans, is about to
ID: 429019 • 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 to use as a weighting. The information gathered appears in the following table. population base in each Census Tract 101 102 103 104 105 106 107 X, Y Map Coordinates (25,44) (25,24) (55,48) (52,20) (84,52) (68,18) (90,25) Population in Census Tract 2,100 4,800 10,500 7,000 10,400 18,000 12,000 a) The center-of-gravity coordinates for the location of the proposed outlet in Mobile, Alabama should be x(round your response to two decimal places)Explanation / Answer
a) The center of gravity coordinates for the location of proposed output is determined as below:
X = SUMPRODUCT of X coordinate * Population divided by the sum of population
= (2100*25 + 4800*25 + 10500*55 + 7000*52 + 10400*84 + 18000*68 + 12000*90) / (2100 + 4800 + 10500 + 7000 + 10400 + 18000 + 12000)
= 66.23
Y = SUMPRODUCT of Y coordinate * Population divided by the sum of population
= (2100*44 + 4800*24 + 10500*48 + 7000*20 + 10400*52 + 18000*18 + 12000*25) / (2100 + 4800 + 10500 + 7000 + 10400 + 18000 + 12000)
= 31.12