Problem 1. (30 POINTS) Tech offers a number of off-campus courses in its professional and executive Master of Information Technology (MIT) programs at various locations around the state. The courses are taught by a group of regular Tech information technology faculty and adjuncts they hire from around the state. There are 2 main considerations in assigning individual faculty to courses: 1. The travel distance 2. The average course teaching evaluation scores from past years The college would like to minimize the mileage for teaching the courses not only for each faculty member's benefit but also to reduce program expenses. It would also like to have the faculty member who does the best job with a particular course teach that course. The following table shows the mileage for each faculty member to each course location and his or her average teaching evaluation scores (on a 5 scale where 5 is outstanding and 1 is poor) for the fall semester: Table 1 Distance Course TEACHER TEACHER TEACHER TEACHER TEACHER TEACHER (MILEAGE/SCORE) | 1 2 3 4 5 6 MIT001 101 168 160 137 210 203 MIT002 135 100 230 62 119 199 MIT003 153 107 93 188 188 54 MIT004 39 225 176 102 184 61 MIT005 100 41 122 52 60 147 MIT006 220 205 35 225 226 31 Table 2 Scores Course TEACHER TEACHER TEACHER TEACHER TEACHER TEACHER (MILEAGE/SCORE) | 1 2 3 4 5 6 MIT001 3.92 5.45 2.83 2.05 4.95 5.85 MIT002 3.79 5.61 4.53 5 3.56 2.65 MIT003 2.84 4.93 3.11 2.49 4.99 2.19 MIT004 4.34 4.02 3.7 4.23 4.71 2.81 MIT005 5.11 3.04 2.47 5.31 5.81 5.38 MIT006 2.22 5.29 5.65 3.1 4.47 5.14 1. Formulate a linear programming model that will assign all the faculty members with that all course are covered and each faculty member teaches at least one, but no more than 2 courses. 2. Solve the linear programming model 3. Explain your solution