Question

A Major Waste Management Company in the country wants to minimize the transportation cost for their trucks to disposal center from five receiving stations with coordinates in the table 1 below. Assume a leaner relationship between volumes transported and the transportation costs (no premium charges).

Location of waste (x,      y)	Volume of waste (tons per day)
10,     5	26
4,      1	9
4,     7	25
2,     6	30
8,     7	40

(a) Using the center of gravity method and the information displayed in the table 1 above, determine the location for siting the disposal center.

(b) Assume that the estimated volume of waste (tons per day) transported from five receiving stations are the same; determine the location for siting the disposal center.

Answer 1

Answer to question a :

Let, location of the disposal center = ( P, Q )

Sum of volume per day x P = Sum ( Location of X x Corresponding volume )

Or, ( 26 +9 + 25 + 30 + 40 ) x P = sum ( 10 x26 + 4 x 9 + 4 x 25 + 2 x 30 + 8 x 40 )

Or, 130 x P = 260 + 36 + 100 + 60 + 320

Or, 130 x P = 776

Or, P = 776/130

Or, P = 5.97 ( rounded to 2 decimal places )

Sum of volume per day x Q = Sum ( Location of Y x Corresponding volume )

Or , ( 26 + 9 + 25 + 30 + 40 )x Q = 5x 26 + 1x 9 + 7 x 25 + 6 x 30 + 7 x 40

Or, 130 x Q = 130 + 9 + 175 + 180 + 280

Or, 130 x Q = 774

Or, Q = 774/130

Or, Q = 5.95 ( rounded to 2 decimal places )

LOCATION FOR SITTING THE DISPOSAL CENTER = ( 5.97, 5.95 )

Answer to question b :

When volume of waste transported from 5 receiving stations are same ,

X axis for location of sitting the disposal center = Sum ofX axis of all locations /5 = ( 10 + 4 + 4 + 2 + 8 ) / 5 = 28/5 = 5.6

Y axis for location of sitting the disposal center = sum of Y axis of all locations/ 5 = ( 5 + 1+7+6+7 )/5 = 26/5 = 5.2

Location for sitting the disposal center = ( 5.6, 5.2 )