A larger and more modern main post office is to be constructed at a new location
ID: 448107 • Letter: A
Question
A larger and more modern main post office is to be constructed at a new location In Davis, California. Growing suburbs caused a shift in the population density from where it was 40 years ago, when the current facility was built. Annette Work, the postmaster. asked her assistants to draw a grid map of the seven points where mail is picked up and delivered in bulk. The coordinates and trips per day to and from the seven mail source points and the current main post office, M, are shown in the following table. M will continue to act as a mail source point after relocation.
Mail Source Point
A. Calculate the center of gravity as a possible location for the new facility (round to the nearest whole number).
The center of gravity "X" coordinate= _____________
The center of gravity "Y" coordinate= _____________
B) Compare the load-distance scores for the location in part (a) and the current location using rectilinear distance.
1)The load-distance score to M is _______ (enter answer as an integer)
2)The load-distance to the center of gravity ______. (round to nearest whole number)
Mail Source Point
Round trips per day x Coordinate (miles) Y Coordinate (miles) 1 7 12 16 2 4 17 17 3 6 7 6 4 18 17 2 5 8 16 6 6 2 12 3 7 4 13 17 M 7 17 14Explanation / Answer
Mail Source Point Round trips per day (l) x Coordinate (miles) Y Coordinate (miles) l*x l*y load distance to M: (17,14) laod distance to center of gravity (15,8) 1 7 12 16 84 112 49 77 2 4 17 17 68 68 12 44 3 6 7 6 42 36 108 60 4 18 17 2 306 36 216 144 5 8 16 6 128 48 72 24 6 2 12 3 24 6 32 16 7 4 13 17 52 68 20 44 M 7 17 14 119 98 0 56 total 56 823 472 509 465 The center of gravity "X" coordinate= (total sum of l*x)/ sum of l 15 The center of gravity "Y" coordinate= (total sum of l*y) / sum of l 8 The load-distance score to M is 509 The load-distance to the center of gravity 465
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