The department of engineering at a university in New Jersey must assign six faculty members to their new offices. The following closeness matrix indicates the expected number of contacts per day between professors. The available office Spaces (1€”6) for the six faculty members are shown in Figure. Assume equal-sized offices. The distance between offices I and 2 (and between offices 1 and 3) is I unit, whereas the distance between offices 1 and 4 is 2 units.

a. Because of their academic positions, Professor A must be assigned to office 1, Professor C must be assigned to office 2, and Professor D must be assigned to office 6. Which faculty members should be assigned to offices 3, 4, and 5, respectively to minimize the total weighted- distance score (assuming rectilinear distance)?
b. What is the weighted-distance score of yoursolution?

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6. 2.