4. A new warehouse is targeted to serve seven zip codes in the Hamilton County,

Question

4. A new warehouse is targeted to serve seven zip codes in the Hamilton County, Ohio. The table given below shows the coordinates for the center of each zip code, along with the projected volume of demand (measured in 100 thousands) Customers in these seven zip codes will be served from this planned warehouse. Details of the seven zip codes, coordinate distances along with the demand volume for each zip are given below. Find the center of gravity for the proposed new warehouse that minimizes the weighted distance ip emand volume Z1 Z2 Z4 Z5 Z6 Z7 (2.5, 4.5)3 (3.5, 3.5) 6 (5.5, 4.0)12 (2,5) 8 (8, 6) 0 (7,2) 7 (9,3) 20

Explanation / Answer

As per the formula

Xi = Xn*Wn/Wn

Xi=(2.5*3 +3.5*6 +5.5*12+2*8+8*10+7*7+9*20)/(3+6+12+8+10+7+20) =6.36

Yi = Yn*Wn/Wn

Yi=(4.5*3 +3.5*6 +4*12+5*8+6*10+2*7+3*20)/(3+6+12+8+10+7+20) =3.88

So the location coordinates will be (Xi, Yi) = (6.36,3.88)

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