16 The Arden County, Maryland, 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, for several sectors of the counly are beyond walking distance to a school. The superintendent partitions the county into five geognphic sectors as he attempts to establish a plan that will minimize the total number of student miles traveled by bus. He also reeognizes 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 schoot. The three schools are located in sectors B, C, and E. The accompanying table reflects the number of high-school-age students living in each sector and the distance in miles from each sector to each school. Each high school has a capacity or 900 students. a) Set up the objective function and constraints of this problem using linear programming so that the total number of student mites traveted by bus is minimized. b) Solve the problem. its: Call the three schools 1,2 and 3. Variable A1 then means how many students from ighborhood A go to school 1 (which happens to be in neighborhood B); A2 is students from A that go 2 etc, alt the wav to variable F3. Fifteen variablest Eiaht constraints