Problem 3

A home improvement/building supply company is going to build a new warehouse facility to serve its stores in six North Carolina cities: Charlotte, Winston-Salem, Greensboro, Durham, Raleigh, and Wilmington. The (x , y) coordinates of these cities (in miles), using Columbia, South Carolina as the origin (0,0) of the map, and the annual truckloads that supply each city are shown as follows:

City	Coordinates (x, y)	Number of Truckloads per Year
Charlotte	(15, 85)	160
Winston-Salem	(42, 145)	90
Greensboro	(88, 145)	105
Durham	(125,140)	35
Raleigh	(135, 125)	60
Wilmington	(180,18)	75

1. Determine the coordinates of the best site for the warehouse by the center of gravity method.

2. [Extra Credit] Look at a map of North Carolina and identify the closet town to the grid coordinates developed in (a). Looking at the map, can you suggest a better location in the vicinity? Explain your answer.