Plant A is located at the (X, Y) coordinates of (100, 200) and has a volume of shipping of 500 units a day. Plant B is located at the (X, Y) coordinates of (150, 400) and has a volume of shipping of 200 units a day. Using the centroid method, which of the following is the X coordinate for the new plant location?
A) About 100
B) About 114
C) About 130
D) About 150
E) X coordinate cannot be computed from the data given.

Question

Quizplus · Accepted Answer

The centroid method involves finding the point (X,Y) that represents the average of the X coordinates and the average of the Y coordinates weighted by the volume of shipping for each plant.

Using the formula:
X = [(X1Q1 + X2Q2)/Qtotal]
where X1 and Q1 are the X coordinate and shipment volume of Plant A, X2 and Q2 are the X coordinate and shipment volume of Plant B, and Qtotal is the total shipment volume (500 + 200 = 700).

Plugging in the values:
X = [(100*500 + 150*200)/700]
X = 114.29

Therefore, the new plant location should have an X coordinate of about 114.

Plant a Is Located at the (X, Y) Coordinates of (100