A package delivery service wants to build a new distribution center in Boise,Idaho.The location of the center needs to be in the vicinity of Interstate-84,Highway-55 and the Boise Airport.The following table provides the coordinates of these three sites and the number of weekly packages. The suggested coordinates for the new warehouse using the center of gravity method are
A)x = 36.0 and y = 35.0
B)x = 27.3 and y = 22.3
C)x = 25.54 and y =24.4
D)x = 27.5 and y = 35.5

Question

A package delivery service wants to build a new distribution center in Boise,Idaho.The location of the center needs to be in the vicinity of Interstate-84,Highway-55 and the Boise Airport.The following table provides the coordinates of these three sites and the number of weekly packages.  The suggested coordinates for the new warehouse using the center of gravity method are
A)x = 36.0 and y = 35.0 
B)x = 27.3 and y = 22.3 
C)x = 25.54 and y =24.4 
D)x = 27.5 and y = 35.5

Quizplus · Accepted Answer

The center of gravity method involves finding the center point that minimizes the total distance between the new warehouse and the existing locations.

First, calculate the total number of packages: 
- I-84: (43, -116), 3,200 packages/week 
- Hwy-55: (44, -116), 2,300 packages/week 
- Boise Airport: (43, -116), 1,500 packages/week

Total = 6,000 packages/week

Next, calculate the x and y coordinates for the center of gravity: 
- x = (43*3200 + 44*2300 +43*1500)/6000 = 25.54 
- y = (-116*3200 -116*2300 - 116*1500)/6000 = 24.4

Therefore, the suggested coordinates for the new warehouse using the center of gravity method are x = 25.54 and y = 24.4, which is closest to choice C.

A Package Delivery Service Wants to Build a New Distribution