The Cold Lake, Alberta, superintendent of education is responsible for assigning students to the three high schools in his jurisdiction. He recognizes the need to bus a certain number of students, because several sectors, A€“E, of the region are beyond walking distance to a school. The superintendent partitions the district into five geographic sectors as he attempts to establish a plan that will minimize the total number of student kilometres travelled 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.
The accompanying table reflects the number of high-school age students living in each sector and the distance in kilometers from each sector to each school:

a) Set up the objective function and constraints of this problem using linear programming so that the total number of student kilometres travelled by bus is minimized.

b) Solve the problem.

Transcribed Image Text:

Distance to School School in School in School in Number of Sector Sector B Sector C Sector E Students A 5 700 B 4 12 500 100 D 800 12 400 2500 Each high school has a capacity of 900 students.