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. $$\begin{array} { l l }
\text { Location } & ( \mathrm { x } , \mathrm { y } ) \
\hline 1 & 2,3 \
2 & 3,7 \
3 & 5,5 \
4 & 7,3 \
5 & 8,7
\end{array}$$ If weekly shipments to each warehouse will be approximately equal, what is the optimal location for the distribution center?

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. $$\begin{array} { l l } 
\text { Location } & ( \mathrm { x } , \mathrm { y } ) \
\hline 1 & 2,3 \
2 & 3,7 \
3 & 5,5 \
4 & 7,3 \
5 & 8,7
\end{array}$$ If weekly shipments to each warehouse will be approximately equal, what is the optimal location for the distribution center?

Quizplus · Accepted Answer

The optimal location for the distribution center is the centroid of the five warehouses, which is (5, 5). This location minimizes the total distance that goods must be shipped to each warehouse.

A Hardware Distributor Has Regional Warehouses at the Locations Shown