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?

Question

Chelsea Kent

Mathematics

10 September, 22:27

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?

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Answers (1)

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Rishi Eaton · Answer 1

X = 87.5

Y = 137.5

Step-by-step 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