Question: consider the facility location problem where there are four facilities...

Consider the facility location problem where there are four facilities are located at the following coordinates: (3,0)𝑇,(0,−3)𝑇,(2,1)𝑇, and (1,4)𝑇. Formulate an LP of finding the optimal location for a new facility (𝑥1,𝑥2)𝑇so 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 (𝑥1,𝑥2)𝑇 and the facility at (3,0)𝑇 is |𝑥1 − 3| + |𝑥2|. Note 2: Clearly define decision variables and state the objective function and constraints.