Problem (1) - (50 points): Consider the following data for the locations of the existing facilities: Facility (a, b) mts 1 (5.4) 3 0 2 (9.12) 5 4 3 (12,5) 2 3 4 (4.9) 1 0 5 6 (2.10) (10,12) 4 2 2 0 7 (3,6) 8 5 8 (8.2) 0 4 w g mts Find the location of the new facility which minimizes the following criteria: a) The total weighted rectilinear distance by applying the median rule. b) The total weighted Sq. Euclidean distance by applying he weighted average rule. Then, solve it using any solver such as LINGO/GAMS / AMPL. c) Minimizing the maximum rectilinear distance between the new facility and the existing facilities. c) The total weighted Euclidean distance by using any solve only: LINGO/GAMS/ AMPL. d) The maximum of weighted Euclidean distance using any solver only: LINGO/GAMS/ AMPL Problem (1) - (50 points): Consider the following data for the locations of the existing facilities: Facility (a, b) mts 1 (5.4) 3 0 2 (9.12) 5 4 3 (12,5) 2 3 4 (4.9) 1 0 5 6 (2.10) (10,12) 4 2 2 0 7 (3,6) 8 5 8 (8.2) 0 4 w g mts Find the location of the new facility which minimizes the following criteria: a) The total weighted rectilinear distance by applying the median rule. b) The total weighted Sq. Euclidean distance by applying he weighted average rule. Then, solve it using any solver such as LINGO/GAMS / AMPL. c) Minimizing the maximum rectilinear distance between the new facility and the existing facilities. c) The total weighted Euclidean distance by using any solve only: LINGO/GAMS/ AMPL. d) The maximum of weighted Euclidean distance using any solver only: LINGO/GAMS/ AMPL