The responses for each of the 40 students are reported in Table 1. Formulate the problem as an optimization model and determine what is the optimal (or near optimal) arrangement for students staying four to a room. As a hint, this problem should be formulated as a TSP and the All different constraint will be used. The objective function should consist of a total variance between 10 different sets of four roommates. (Hint take the variance across four people for each question, add these variances together to get a variance measure for each dorm. Then, sum all of the variances for each room and minimize this result. Remember, the variance is essentially just a Sum of Squares measure, the whole foundation of statistics.)

Question Question Question Question Question Question 1 2 1 10 5 1 11 / / 1 1 2 12 2 - NO TTTTTTTTT - 119 3 8 9 1 2 10 107 82 10 1 10 0 1 Question Question Question Question Question Question 1 2 1 10 5 1 11 / / 1 1 2 12 2 - NO TTTTTTTTT - 119 3 8 9 1 2 10 107 82 10 1 10 0 1