Todd\'s Direct, a major TV sales chain headquartered in New Orleans, is about to

Question

Todd's Direct, a major TV sales chain headquartered in New Orleans, is about to open its frst outlet in Mobilo, Alabama, and wands to select a she that wil place the new outet in the center of Mobile's population base Todd examines the seven oensus tracts in Mobile, plots the coordinatos 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 CensusX. Y Map Tract Coordina 102 103 104 105 106 107 1800 5,200 10,500 7.200 10.200 18,000 12,000 24 44) 24.25) (57 42) (52,18) (784B) 72.20) 96,22) a) The center-of-gravity coordinates for the location af the proposed outlet in Moblie, Alabama should be x = ? (round your rosponse to two decimal places). y(round your response to two decimal places) Enter your answer in each of the answer boxes. 20 esc 5 0

Explanation / Answer

Let coordinates of center of gravity outlet is ( P,Q )

Therefore , as per center of gravity method ,

Sum of population in census tract x P = Sum of all ( X coordinate x Corresponding population in census tract )

Or, ( 1800 + 5200 + 10500 + 7200 + 10200 + 18000 + 12000) x P = 24 x 1800 + 24 x 5200 + 57 x 10500 + 52 x 7200 + 76 x 10200 + 72 x 18000 + 96 x 12000

Or, 64900 x P = 43200 + 124800 + 598500 + 374400 + 775200 + 1296000

Or, 64900 x P = 3212100

Or, P = 3212100 / 64900

Or, P = 49.49

Sum of population in census tract x Q = Sum of all ( Y coordinate x Corresponding population in census tract )

Or, ( 1800 + 5200 + 10500 + 7200 + 10200 + 18000 + 12000) x Q = 44 x 1800 + 25 x 5200 + 42 x 10500 + 18 x 7200 + 48 x 10200 + 20 x 18000 + 22 x 12000

Or, 64900 x Q = 79200 + 130000 + 441000 + 129600 + 489600 + 360000 + 264000

Or, 64900 x Q = 1893400

Or, Q = 1893400/ 64900

Or, Q = 29.17

X COORDINATE = 49.49

Y COORDINATE = 29.17

X COORDINATE = 49.49

Y COORDINATE = 29.17

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