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Consider the facility location problem where there are four facilities are located at the following coordinates:...

Consider the facility location problem where there are four facilities are located at the following coordinates: (3,0)?,(0,−3)?,(2,1)?, and (1,4)?. Formulate an LP of finding the optimal location for a new facility (?1,?2)?so that the sum of distances from the new facility to the four existing facilities can be minimized. Note 1: Use the “street distance” (rectilinear norm). For instance, the street distance between the new facility (?1,?2)? and the facility at (3,0)? is |?1 − 3| + |?2|. Note 2: Clearly define decision variables and state the objective function and constraints.  

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