location for the generator mat cable. Assume rectilinear distance 104 Six housin

Question

location for the generator mat cable. Assume rectilinear distance 104 Six housing subdivisions within a city area are targeted for emergency service by a centralized fire station. Where should the new fire station be located such that the maximum rectilinear travel distance is minimized? The centroid locations (in miles) and total value of the houses in the subdivisions are as follows: Total Value 50 mil. 120 mil. 100 mil. 250 mil. 300 mil. 75 mil. Subdivision X-Coordinate Y-Coordinate 20 25 13 25 15 25 32 14 21 8 18 city council of Fayetteville has decided to locate an emergency response un three maj ow does the answer change if all houses are valued equally? e helow Assume that the weights a

Explanation / Answer

Question 30.4

Here X - coordinate and Y coordinate of fire station is weighted average of X - coordinate of given 6 subdivision

so,

X0 = (50 * 20 + 25 * 120 + 13 * 100 + 25 * 250 + 4 * 300 + 18 * 75)/ (50 + 120 + 100 + 250 + 300 + 75)

= 14100/ 895 = 15.7542

Y0 = (50 * 15 + 25 * 120 + 32 * 100 + 14 * 250 + 21 * 300 + 8 * 75)/ (50 + 120 + 100 + 250 + 300 + 75)

Y0 = 17350/ 895 = 19.3855

so the coordinate is (15.7542, 19.3855)

If the answer change if all houses are valued equally.

X - coordinate = (20 + 25 + 13 + 25 + 4 + 18)/ 6 = 17.5

Y - cordinate = (15 + 25 + 32 + 14 + 21 + 8)/6 = 19.1667

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