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. $$\begin{array} { l l }
\text { Location } & ( \mathrm { x } , \mathrm { y } ) \
\hline 1 & 2,3 \
2 & 3,7 \
3 & 5,5 \
4 & 7,3 \
5 & 8,7
\end{array}$$ 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. $$\begin{array} { l l } 
\text { Location } & ( \mathrm { x } , \mathrm { y } ) \
\hline 1 & 2,3 \
2 & 3,7 \
3 & 5,5 \
4 & 7,3 \
5 & 8,7
\end{array}$$ 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

We can use the centroid method to determine the optimal location of the distribution center.

To do this, we calculate the coordinates of the centroid of the warehouse locations, weighted by their weekly shipments. Let (x,y) be the coordinates of the distribution center, then:

x = (2*100 + 3*150 + 5*120 + 7*150 + 8*120)/(100+150+120+150+120) = 5.1
y = (3*100 + 7*150 + 5*120 + 3*150 + 7*120)/(100+150+120+150+120) = 5.1

Therefore, the optimal location of the distribution center is (5.1,5.1), which is choice C.

A Hardware Distributor Has Regional Warehouses at the Locations Shown