Question

Question:A small manufacturing facility is being planned that will feed parts to three heavy manufacturing facilities. The locations of the current plants with their coordinates and volume requirements are given in the following table:

Plant Location	Coordinates (x,y)	Volume (parts per year)
Peoria	300,320	4,000
Decatur	375,470	6,000
Joliet	470,180	3,000

Use the centroid method to determine a location for this new facility.

Short answer

Answer

The new warehouse would be located at (373.84,356.92).

Step-by-step solution

Formula to calculate the coordinates

$C_x=\frac{\sum _{}{X}_i{Y}_i}{\sum _{}{V}_i},C_y=\frac{\sum _{}{Y}_{i}Vi}{\sum _{}{V}_i},$

Prepare the chart to get the coordinates

The chart is shown below:

Put the calculated values in the above formula

$$\begin{gathered} C_{xi}=\frac{4860000}{13000} \\ =373.84 \end{gathered}$$

X coordinate is 373.84.

$$\begin{gathered} C_{yi}=\frac{4640000}{13000} \\ =356.92 \end{gathered}$$

Y coordinate is 356.92.