Question

1. A local supermarket in Macau wants to set up a new distribution center. The following table shows the locations of the existing branches (in terms of coordinates) and the corresponding weekly delivery. What is the location of the new distribution center which can minimize the overall delivery cost?

Branch	X	Y	Weekly delivery
A	1	5	6
B	4	3	14
C	5	4	14
D	10	1	10
E	8	5	8
F	6	9	12
G	4	1	14

Answer 1

The lowest shipping cost location can be found using Center of Gravity Method.

Location x-coordinate will be = sum total of x-coordinate of branch*weekly delivery for all branched divided by sum total of weekly delivery of each branch

Location y-coordinate will be = sum total of y-coordinate of branch*weekly delivery for all branched divided by sum total of weekly delivery of each branch

Cx = (1*6 + 4*14 + 5*14 + 10*10 + 8*8 + 6*12 + 4*14)/(6 + 14 + 14 + 10 + 8 + 12 + 14)

= 424/78

= 5.44

Cy = (5*6 + 3*14 + 4*14 + 1*10 + 5*8 + 9*12 + 1*14)/(6 + 14 + 14 + 10 + 8 + 12 + 14)

= 300/78

= 3.85

***Generally the coordinates should be rounded to the nearest whole number. Please consider any rounding approach mentioned with the question. If nothing has been provided, round it to the nearest whole number as mentioned below.

The location should be: (X = 5, Y = 4) (rounded to the nearest whole number)

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