A company wants to determine where they should locate a new warehouse.They have two existing production plants 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?
A)(81,117)
B)(88, 138)
C)(117,102)
D)(76,123)
E)X and Y coordinates cannot be computed from the data given

Question

Quizplus · Accepted Answer

According to the centroid method, the X and Y coordinates for the new plant location can be calculated as follows:
X coordinate = (X1*A1 + X2*A2 + X3*A3)/Total Volume
Y coordinate = (Y1*A1 + Y2*A2 + Y3*A3)/Total Volume

Where X1 and Y1 are the coordinates of the first plant, A1 is its volume of shipping, X2 and Y2 are the coordinates of the second plant, A2 is its volume of shipping, and X3 and Y3 are the coordinates of the new plant.

Calculating for X:
X = (0*A1 + 150*150 + X3*250)/(A1 + 150 + 250)
X = (22500 + 250X3)/550
X3 = (550X - 22500)/250

Calculating for Y:
Y = (0*A1 + 200*150 + Y3*250)/(A1 + 150 + 250)
Y = (30000 + 250Y3)/550
Y3 = (550Y - 30000)/250

Using the given information, we can substitute the values and calculate:

X3 = (550*150 - 22500)/250 = 88
Y3 = (550*200 - 30000)/250 = 138

Therefore, the coordinates for the new plant location are (88, 138), which is answer choice B.

A Company Wants to Determine Where They Should Locate a New