A new storage area needs to be located within a facility. The centroids of the departments that will be served by this new storage area are located at (0,10), (20,90), (30,20), (30,80), (50,50) and (80,10). Deliveries to each one of these locations have the same weight. a) (12 points) Find the location for a new storage area that minimizes the total weighted rectilinear distance to all departments that will be served. Is it a feasible location? b) (3 points) Evaluate the total weighted rectilinear distance for the optimal location found in part a) when 10 unit loads per day are delivered from the new storage area to each one of the six existing departments