Question

A textile manufacturer produces children clothes at five different location in Nevada. Weekly quantities to be shipped to each location are shown in the table below. Determine the coordinates of the location that will minimize distribution costs.

       Location(x,y)   Weekly Quantity

A(5,7)   15

B(6,9)   20

C (3,9) 25

D(9,4)   30

E(3,5) 35

Answer 1

As per center of gravity method, we will calculate x and y coordinates of the location to minimize distribution cost.

x - coordinate, X = Summation (x-coordinate of each location * Quantity for each location)/ Sum (Quantity for all locations)

x - coordinate, X = Summation (xi*Qi)/ Sum (Qi)

x - coordinate, X = (5*15+6*20+3*25+9*30+3*35)/(15+20+25+30+35) = 5.16

Similarly we will calculate

y - coordinate, Y = Summation (y-coordinate of each location * Quantity for each location)/ Sum (Quantity for all locations)

y - coordinate, Y = Summation (yi*Qi)/ Sum (Qi)

y - coordinate, Y = (7*15+9*20+9*25+4*30+5*35)/(15+20+25+30+35) = 6.44

Hence, the location coordinates are (5.16, 6.44).

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