Question

Sylva Warehousing desired to locate a central warehouse to serve five North Carolina markets. Placed on a grid system, its five markets had coordinates and demand as follows: The (X,Y) coordinates, in miles, for the five markets are: M1 = (30,65); M2 = (120,90); M3 = (200,125); M4 = (130,175) and M5 = (185,150). The projected annual demand for each of the markets is: V₁ = 2,800 units, V₂ = 1,5700 units, V₃ = 1,250 units_, V₄ = 900 units and V₅ = 1,750 units.

1. Calculate the X-coordinate of the center-of-gravity location using the center-of-gravity technique. (Round value to nearest integer)
2. Calculate the Y-coordinate of the center-of-gravity location using the center-of-gravity technique. (Round value to nearest integer)

Answer 1

Answer: Using Center of gravity method

X= 117, Y= 108

Explanation:

location	X Coordinate	Y Coordinate	supply demand (lbs)	Rate per Lb	load	weighted X= load* X coordinate	weighted Y= load* Y coordinate
M1	30	65	156	2.5	2800	84000	182000
M2	120	90	60	1.1	1700	204000	153000
M3	200	125	234	1.1	1250	250000	156250
M4	130	175			900	117000	157500
M5	185	150			1750	323750	262500
SUM					8400	978750	911250
						117	108
						X bar= sum of weighted X /total load	Y bar= sum of weighted Y /total load