A clothing manufacturer produces clothing in five locations in the United States. In a move to vertical integration, the company is planning a new fabric production plant that will supply fabric to all five clothing plants. The clothing plants have been located on a coordinate system as follows: $$\begin{array} { c c }
\text { Location } & ( \mathrm { x } , \mathrm { y } ) \
\hline \mathrm { A } & 7,2 \
\mathrm {~B} & 4,7 \
\mathrm { C } & 5,5 \
\mathrm { D } & 6,2 \
\mathrm { E } & 8,4
\end{array}$$
If the amount of fabric shipped to each plant is equal, what is the optimal location for the fabric plant?

Question

A clothing manufacturer produces clothing in five locations in the United States. In a move to vertical integration, the company is planning a new fabric production plant that will supply fabric to all five clothing plants. The clothing plants have been located on a coordinate system as follows: $$\begin{array} { c c } 
\text { Location } & ( \mathrm { x } , \mathrm { y } ) \
\hline \mathrm { A } & 7,2 \
\mathrm {~B} & 4,7 \
\mathrm { C } & 5,5 \
\mathrm { D } & 6,2 \
\mathrm { E } & 8,4
\end{array}$$
If the amount of fabric shipped to each plant is equal, what is the optimal location for the fabric plant?

Quizplus · Accepted Answer

The optimal location for the fabric plant is the centroid of the locations, which minimizes the total distance to all points when the amount shipped is equal. The centroid (average of x-coordinates, average of y-coordinates) is approximately (6, 4).

A Clothing Manufacturer Produces Clothing in Five Locations in the United