Sandbox State University is rearranging the locations of 3 equal-sized academic departments to provide for better faculty communication.

The following tables show the estimated number of person-to-person contacts per month between members of the various faculties, and the distances (in thousands of feet) between available office locations.

interaction English Math History 20 12 English — 14 Distance 2 3 1 3 6 2 — 1 Sandbox State wants to place one department in each location in a way that minimizes total distance traveled for faculty interactions.

(a) Formulate this problem as a quadratic assignment INLP.

(b) Explain why the objective function in this problem must be quadratic rather than linear.

(c) Compute an optimal assignment in your INLP by inspection.