Question

PRO-GYM has several establishments throughout Puerto Rico. The general manager understands that it will be desirable to have a distribution center from which to send products to different gyms.

Using the data in the following table, calculate the location of the new distribution center.

Do not forget to present the graph that shows the location of the gyms and the distribution center. City 
Coordinates Number of deliveries per week  

City	Coordinates	Number of deliveries per week
	(X,Y)
A	(4, 1)	2
B	(2, 10)	3
C	(6, 15)	4
D	(7, 9)	6
E	(8, 20)	2
F	(15, 10)	5
G	(12, 4)	3
H	(1, 18)	4

Answer 1

Solution:

Using the center-of-gravity method, the location of the new distribution center is calculated as below:

X = Sum of (Xi x Number of deliveries per week) / Total number of deliveries per week

Y = Sum of (Yi x Number of deliveries per week) / Total number of deliveries per week

Total number of deliveries per week = 2 + 3 + 4 + 6 + 2 + 5 + 3 + 4 = 29

X = [(4 x 2) + (2 x 3) + (6 x 4) + (7 x 6) + (8 x 2) + (15 x 5) + (12 x 3) + (1 x 4)] / 29

X = 7.28

Y = [(1 x 2) + (10 x 3) + (15 x 4) + (9 x 6) + (20 x 2) + (10 x 5) + (4 x 3) + (18 x 4)] / 29

Y = 11.03

A​​​​​​​nswer: Coordinates of the location of the new distribution Center = (7.28, 11.03)

The location of the gyms and the distribution center is shown in the graph below: