A Generalized Single-Row Facility Layout Problem Recall that the single-row facility layout problem we discussed in the class. Now let us consider a generalized problem. There are n departments, from department 1 to department n. Let be the amount of loads between department i and department j. Let the cost of moving one unit load through one unit distance between department i and department j be 1. So, the cost of moving all the loads between department i and department j equals times the distance between the center of department i and the center of department j. This is exactly same as the single-row facility layout problem we discussed in the class. However, each department, from 1 to department n, has 3 options for the length, and different lengths correspond to different revenue. For example, department i has 3 candidates of potential lengths: 1 , 2 , and 3 ; the corresponding revenue is 1 , 2, and 3. Now, we aim to find an optimal facility layout such that (1) for each department, only one option among 3 length candidates is selected; (2) there is no overlap between any pair of departments, and (3) the net benefit, which equals the total revenue minus the total cost, is maximized. You are asked to formulate this optimization problem. It is OK to have nonlinear terms in the model.