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 involves taking the weighted average of the coordinates of the suppliers, where the weights are the annual number of shipments. Using the formula for the x-coordinate, we have:

x = (W1x1 + W2x2 + W3x3) / (W1 + W2 + W3)
  = (500(300) + 300(320) + 200(280)) / (500 + 300 + 200)
  = 309.4

Similarly, for the y-coordinate, we have:

y = (W1y1 + W2y2 + W3y3) / (W1 + W2 + W3)
  = (500(300) + 300(280) + 200(200)) / (500 + 300 + 200)
  = 311.4

Therefore, the suggested coordinates for the new warehouse are (309.4,311.4) and the best choice is B.

A Company Is Deciding Where to Locate a New Warehouse