A larger and more modern main post office is to be constructed at a new location

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 14

Explanation / Answer

(A)

The center of gravity "X" coordinate = (823/56) = 14.696 = 15

The center of gravity "Y" coordinate = (472/56) = 8.429 = 8

(B)

The load-distance score to M is = 451.20

The load-distance to the center of gravity = 371

Mail Source Point Rounds trips per day(W) X Y W*X W*Y 1 7 12 16 84 112 2 4 17 17 68 68 3 6 7 6 42 36 4 18 17 2 306 36 5 8 16 6 128 48 6 2 12 3 24 6 7 4 13 17 52 68 M 7 17 14 119 98 Sum 56 823 472

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