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. $$\begin{array} { c c }
\text { Location } & ( \mathrm { x } , \mathrm { y } ) \
\hline \mathrm { A } & 2,3 \
\mathrm {~B} & 3,7 \
\mathrm { C } & 5,5 \
\mathrm { D } & 7,3 \
\mathrm { E } & 8,7
\end{array}$$ Weekly shipments to each warehouse will be: WH1, 100; WH2, 150; WH3, 120; WH4, 150; and WH5, 120. What is the optimal location of the distribution center?
A) 5.1, 4.2
B) 5.2, 4.0
C) 5.1, 5.1
D) 4.2, 5.1
E) 4.9, 5.2

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. $$\begin{array} { c c } 
\text { Location } & ( \mathrm { x } , \mathrm { y } ) \
\hline \mathrm { A } & 2,3 \
\mathrm {~B} & 3,7 \
\mathrm { C } & 5,5 \
\mathrm { D } & 7,3 \
\mathrm { E } & 8,7
\end{array}$$ Weekly shipments to each warehouse will be: WH1, 100; WH2, 150; WH3, 120; WH4, 150; and WH5, 120. What is the optimal location of the distribution center?
A) 5.1, 4.2
B) 5.2, 4.0
C) 5.1, 5.1
D) 4.2, 5.1
E) 4.9, 5.2

Quizplus · Accepted Answer

To find the optimal location for the distribution center, we need to minimize the total distance traveled by all the shipments from the center to the warehouses. This is known as the "sum of distances" problem and can be solved by finding the geometric center of the warehouse locations. This point is known as the centroid, which is the average of the x-coordinates and y-coordinates of the warehouse locations.

Using the given coordinates, we calculate the centroid as:

x-coordinate of centroid = (2 + 3 + 5 + 7 + 8)/5 = 5
y-coordinate of centroid = (3 + 7 + 5 + 3 + 7)/5 = 5

The centroid is located at (5, 5), which is answer choice C. Therefore, the optimal location for the distribution center is at (5, 5).

A Hardware Distributor Has Regional Warehouses at the Locations Shown