The Burger Doodle restaurant chain purchases ingredients from four different food suppliers. The company wants to construct a new central distribution center to process and package the ingredients it uses in its menu items before shipping them to their various restaurants. The suppliers

transport the food items in 40-foot tractor-trailer trucks. The coordinates of the four suppliers and the annual number of truckloads that will be transported to the distribution center are as follows:

Coordinates

Supplier x y Annual Truckloads

A 200 200 65

B 100 500 120

C 250 600 90

D 500 300 75

Determine the set of coordinates for the new distribution center that will minimize the total miles traveled from the suppliers

Answer :

Given Information:

Site 1: x1 = 360 , y1 = 180

Site 2: x2 = 420 , y2 = 450

Site 3: x3 = 250 , y3 = 400

Solution:

Xa = 200, Ya = 200, Wa = 75

Xb = 100, Yb = 500, Wb = 105

Xc = 250, Yc = 600, Wc = 135

Xd = 500, Yd = 300, Wd = 60

If centre of gravity is (x,y)

then x = (200*75+100*105+250*135+500*60)/(75+105+135+60)        

x = 238

then y = (200*75+500*105+600*135+300*60)/(75+105+135+60)        

 y = 444

Using centre-of-gravity method, location of distribution centre = (238,444) Using rectilinear distance,

Load distance score of Site 1: 75*(abs(360-200)+abs(180-200))+105*(abs(360-100)+abs(180-500))+135*(abs(360-250)+abs(180-600))+60*(abs(360-500)+abs(180-300)) = 161550

Load distance score of Site 2: 75*(abs(420-200)+abs(450-200))+105*(abs(420-100)+abs(450-500))+135*(abs(420-250)+abs(450-600))+60*(abs(420-500)+abs(450-300)) = 131100

Load distance score of Site 3: 75*(abs(250-200)+abs(400-200))+105*(abs(250-100)+abs(400-500))+135*(abs(250-250)+abs(400-600))+60*(abs(250-500)+abs(400-300)) = 93000

Site 3 tends to be optimal as it offers a lower distance ranking.

I HOPE THIS IS RIGHT AND IT HELPS