Question

A company wants to determine where they should locate a new warehouse. They have two existing production plants (i.e., Plant A and Plant B) that will ship units of a product to this warehouse. Plant A is located at the (X, Y) coordinates of (50, 100) and will have volume of shipping of 250 units a day. Plant B is located at the (X, Y) coordinates of (150, 200) and will have a volume of shipping of 150 units a day. Using the centroid method, which of the following are the X and Y coordinates for the new plant location?

Answer 1

X = 87.5

Y = 137.5

Explanation:

Let's X and Y be the xy-coordinates of the center warehouse.

We know that X is in between the x coordinates or the 2 plants:

50 < X < 150

Similarly Y is in between the y coordinates or the 2 plants:

100 < Y < 200

Using centroid method with the shipping units being weight we can have the following equations

250*50 + 150*150 = X*(250 + 150)

Hence X = (250*50 + 150*150)/(250+150) = 87.5

Similarly 250*100 + 150*200 = Y*(250 + 150)

Hence Y = (250*100 + 150*200)/(250+150) = 137.5