A manufacturing concern has five departments (labeled A through E) located in a rectangular building as shown below. All the flow, cost, and distance data are shown below. Fortunately, the symmetry conditions have been satisfied in cost, flow, and distance matrices. B Suppose the flow data, the unit cost data, and the distance matrix are given as follows: Flow-Between Matrix Fro A B C D E A B C D E 3 5 Distance Matrix To A B D E From A 5.5 18 17 11 B 12.5 22.5 14.5 10 6.5 D 8 E m A B D 0 HAFA Unit Cost ($/Unit Dist.) To Fro m A 1 2 02 B 3 2 0 1 2 D 3 E 7 4 0 2 6 3 7 E - Q3-1. Where do you think is the center point of the department E? Please explain why your selected point should be center. (8 points) Q3-2. Using a Distance-based Scoring method, please find the Z value of the layout. (8 points) Q3-3. The manager believes that swapping the locations of departments B and C is beneficial. Q3-3-1. Please find two permutation matrices to swap the departments B and C. (6 points) Q3-3-2. Using a Distance-based Scoring method, please find a Estimated Z score of the updated layout in Q3-3-1. Is the layout better than the current one? (8 points)