A hardware distributor has regional warehouses at the locations shown below. The company wants to locate a new central distribution center to serve this warehouse network. $$\begin{array} { c c }
\text { Location } & ( \mathrm { x } , \mathrm { y } ) \
\hline \mathrm { A } & 2,3 \
\mathrm {~B} & 3,7 \
\mathrm { C } & 5,5 \
\mathrm { D } & 7,3 \
\mathrm { E } & 8,7
\end{array}$$
If weekly shipments to each warehouse will be approximately equal, what is the optimal location for the distribution center?
A) 5, 5
B) 5, 4
C) 4, 5
D) 5, 6
E) 6, 5

Question

A hardware distributor has regional warehouses at the locations shown below. The company wants to locate a new central distribution center to serve this warehouse network. $$\begin{array} { c c } 
\text { Location } & ( \mathrm { x } , \mathrm { y } ) \
\hline \mathrm { A } & 2,3 \
\mathrm {~B} & 3,7 \
\mathrm { C } & 5,5 \
\mathrm { D } & 7,3 \
\mathrm { E } & 8,7
\end{array}$$
If weekly shipments to each warehouse will be approximately equal, what is the optimal location for the distribution center?
A) 5, 5
B) 5, 4
C) 4, 5
D) 5, 6
E) 6, 5

Quizplus · Accepted Answer

One way to approach this problem is to use the centroid of the given locations as a starting point for the optimal location of the distribution center. The centroid is the point that represents the average of the locations, and is given by:

$(\bar{x}, \bar{y}) = \left(\frac{2+3+5+7+8}{5}, \frac{3+7+5+3+7}{5}\right) = (5, 5)$

Intuitively, this means that a distribution center located at (5, 5) would be equidistant from all the regional warehouses, and would minimize the total distance traveled for all shipments. Therefore, the optimal location for the distribution center is A) 5, 5.

A Hardware Distributor Has Regional Warehouses at the Locations Shown