A College is considering building on-campus dorms to house 40 students. In order to maximize student satisfaction, a survey consisting of 6 questions has been developed and administered to the students who will be staying in the dorms. The questions pertain to issues such as sleep time, noise, smoking, etc. The following questions along with the potential response are reported below.

1. What time do you go to bed at night? 6pm = 6, Midnight = 12, 2am = 14, etc.

2. What time do you get up in the morning? 6am = 6, noon = 12, 2pm = 14, etc.

3. How neat are you? 1 - Messy, 2 - Moderate, 3 - Very neat

4. Do you smoke? 0 - no, 10 - yes

5. How much noise do you like in your environment? 1 - Little noise, 2 - moderate noise, 3 - lots of noise

6. How many guests do you like having over? 1 - No guests, 2 - some guests, 3 - lots of guests

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 10 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 10 3 8 9 1 2 10 107 82 10 1 10 0 1