Question

A toy manufacturer produces toys in five locations throughout the country. Raw materials (primarily barrels of powdered plastic) will be shipped from a new, centralized warehouse whose location is to be determined. The monthly quantities to be shipped to each location are the same. A coordinate system has been established, and the coordinates of each location have been determined as shown. Determine the coordinates of the centralized warehouse. (Round x¯x¯ and y¯y¯ to 1 decimal place.)

Location	(x,y)
A	2,7
B	8,3
C	6,6
D	4,1
E	9,8

x¯x¯  = ________ , y¯y¯ = ._________

Answer 1

Optimal location that will minimize distribution cost is center of gravity.

Center of Gravity approach that seeks to calculate location coordinates for a optimal new facility that will minimize costs.

The monthly quantities to be shipped to each location are the same. Lets assume monthly quantity from each location be "x"

Location	x	y	Weekly demand	x*Weekly demand	y*weekly demand
A	2	7	x	2x	7x
B	8	3	x	8x	3x
C	6	6	x	6x	6x
D	4	1	x	4x	x
E	9	8	x	9x	8x
Sum			5x	29x	25x
Cx= ∑ x*weekly demand/ ∑ weekly demand
=29x/5x	5.80000
Cy= ∑ y*weekly demand/ ∑ weekly demand
=25x/5x	5.00000

Graphical representation:-