Problem 2 A city wishes to locate a police station in an attempt to reduce the crime rate of the five most dangerous zones of the city. The following table presents the position of a central location within each zone, as well as a measure of its danger level. The more dangerous the area, the closer the police station must be located. Zone Index a bi Danger Level (W) 1 4 12 4 2 8 2 2 3 14 10 2 4 3 8 5 14 4 2-1. Suppose that instead of driving, the police officers will patrol the zones using a helicopter (i.e.assume Euclidean distances). For an initial guess, find the solution to the centroid problem. 9 2-2. Using the answer from 2-1, find the optimal location of the station and show your process. You can apply Weiszfelds algorithm until the decrease in the objective values less than 0.01. 2-3. Find the optimal solution of the minimax location problem assuming rectilinear distances. 2.4. Find the optimal solution of the minimax location problem assuming Euclidean distances. In this sub problem, all weight values (Danger Level) are assumed to be I. Problem 3 Problem 2 A city wishes to locate a police station in an attempt to reduce the crime rate of the five most dangerous zones of the city. The following table presents the position of a central location within each zone, as well as a measure of its danger level. The more dangerous the area, the closer the police station must be located. Zone Index a bi Danger Level (W) 1 4 12 4 2 8 2 2 3 14 10 2 4 3 8 5 14 4 2-1. Suppose that instead of driving, the police officers will patrol the zones using a helicopter (i.e.assume Euclidean distances). For an initial guess, find the solution to the centroid problem. 9 2-2. Using the answer from 2-1, find the optimal location of the station and show your process. You can apply Weiszfelds algorithm until the decrease in the objective values less than 0.01. 2-3. Find the optimal solution of the minimax location problem assuming rectilinear distances. 2.4. Find the optimal solution of the minimax location problem assuming Euclidean distances. In this sub problem, all weight values (Danger Level) are assumed to be I. Problem 3