The Hils County, Michigan, superintendent of education is responsible for assigning students to the three high schools in his county. He recognizes the need to bus a certain number of students, because several sectors, AE, of the county are beyond walking distance to a school. The superintendent partitions the county into five geographic sectors as he attempts to establish a plan that will minimize the total number of student miles traveled by bus. He also recognizes that if a student happens to live in a certain sector and is assigned to the high school in that sector, there is no need to bus him because he can walk to school. The three schools are located in sectors B,C, and E. Each high school has a capacity of 900 students. a) Set up the objective function and constraints of this problem using linear programming so that the total number of student miles traveled by bus is minimized. b) Solve the probiem. Distance Sector \begin{tabular}{|r|r|r|r|} \hline Sehool in B & SchoolinC & School in E & \multicolumn{2}{r|}{ Number of itudents } \\ \hline 5 & 8 & 5 & 700 \\ \hline 0 & 4 & 12 & 500 \\ \hline 4 & 0 & 7 & 100 \\ \hline 7 & 2 & 5 & 500 \\ \hline 12 & 7 & 0 & 400 \\ \hline \end{tabular}