A company is deciding where to locate a new warehouse that will receive shipments from three suppliers: 1, 2, and 3. The locations of the suppliers (xi, yi) and the annual number of shipments from supplier i (Wi) are provided below: The coordinates for the new warehouse suggested by the center of gravity method are
A) x = 311.4 and y = 309.4
B) x = 309.4 and y = 311.4
C) x = 291.2 and y =198.9
D) x = 193.2 and y = 219.4

Question

A company is deciding where to locate a new warehouse that will receive shipments from three suppliers: 1, 2, and 3. The locations of the suppliers (xi, yi) and the annual number of shipments from supplier i (Wi) are provided below:  The coordinates for the new warehouse suggested by the center of gravity method are
A) x = 311.4 and y = 309.4 
B) x = 309.4 and y = 311.4 
C) x = 291.2 and y =198.9 
D) x = 193.2 and y = 219.4

Quizplus · Accepted Answer

The center of gravity method suggests that the new warehouse should be located at the point (x, y), where:

x = (ΣWi * xi) / ΣWi 
y = (ΣWi * yi) / ΣWi

Using the values given in the table, we can calculate:

x = (300*200 + 500*300 + 200*400) / (300 + 500 + 200) = 309.4
y = (300*300 + 500*200 + 200*100) / (300 + 500 + 200) = 311.4

Therefore, the coordinates for the new warehouse suggested by the center of gravity method are (309.4, 311.4). The answer is B.

A Company Is Deciding Where to Locate a New Warehouse