Consider the following problem. You have five faculty members in your department and you wish to allocate them to five offices so that a single faculty member occupies each office. Due to their research areas, some faculty members have close collaborations. Let fij denote the measure of research collaboration between faculty members i and j, i = 1,...,5; j = 1,...,5; ij. Larger values of fij indicate a higher level of collaboration. The distance between office k and office l is given by dkl, where k = 1,...,5; l = 1,...,5; kl. All the offices are located next to one another in a row so that dkl = |kl|, k = 1,...,5; l = 1,...,5; kl. If faculty member i is located in office k and faculty member j is in office l, then the cost of this assignment is fij.dkl, i = 1,...,5; j = 1,...,5; ij, k = 1,...,5; l = 1,...,5; kl.

How can I solve this problem? This question is already on chegg, but the aswer/explanation is not correct or even near to cover this question.