A hardware distributor has regional warehouses at the locations shown below.The company wants to locate a new central distribution centre to serve this warehouse network. 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 centre?
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 centre to serve this warehouse network.  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 centre?
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, we need to calculate the weighted centroid of the warehouses. The coordinates for the centroid are (x,y), where x is the average of the x-coordinates of the warehouses weighted by their weekly shipments, and y is the average of the y-coordinates of the warehouses weighted by their weekly shipments. Using this formula, we get:

x = (1100*3 + 150*5 + 120*6 + 150*4 + 120*2)/(1100+150+120+150+120) = 5.1
y = (1100*2 + 150*2 + 120*7 + 150*3 + 120*1)/(1100+150+120+150+120) = 5.1

Therefore, the optimal location for the distribution center is at (5.1, 5.1). Choice C is the only option that has this coordinate pair.

A Hardware Distributor Has Regional Warehouses at the Locations Shown