Let the coordinates of the main source point = P,Q from mail source point at Dav
ID: 373693 • Letter: L
Question
Let the coordinates of the main source point = P,Q from mail source point at Davis, California
Accordingly ,
Sum of round trips per day x P = Sum of all ( X coordinate x round trip per day )
( 2 + 5 + 4 + 9 + 4 + 5 + 8 + 2 ).P = ( 6x2 + 7x 5 + 16x4 + 10x 9 + 8x4 + 4x5 + 14 x 8 + 1x 2)
Or, 39.P = 12 + 35 + 64 +90 + 32 + 20 + 112 + 2 = 367
Or, P = 367/39 = 9.41 ( 9 rounded to nearest whole number )
Sum of round trips per day x Q = Sum of all ( X coordinate x round trip per day )
( 2 + 5 + 4 + 9 + 4 + 5 + 8 + 2 ).Q = ( 9x2 + 10x 5 + 8x4 + 7x 9 + 17x4 + 3x5 + 5 x 8 + 18x 2)
Or, 39.Q = 18 + 50 + 32 + 63 + 68 + 15 + 40 + 36 = 322
Or , Q = 322/39 = 8.25 ( 8 rounded to nearest whole number )
THE CENTER OF GRAVITY X COORDINATE = 9
THE CENTER OF GRAVITY Y COORDINATE = 8
THE CENTER OF GRAVITY X COORDINATE = 9
THE CENTER OF GRAVITY Y COORDINATE = 8
Explanation / Answer
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 Werk, 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 Round trips per day x, y, Coordinates (miles) (6,9) (7, 10 (16, 8) (10, 7) (8,17) (4, 3) (14, 5) a. Calculate the center of gravity as a possible location for the new facility. (Enter your responses rounded to the nearest whole number) The center of gravity "X" coordinate The center of gravity "Y" coordinate-
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