The Hills$$ 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$$ students, for several$$ sectors$,$ A$$E$,$ of the county are beyond walking distance to a school. The superintendent partitions the county into five geographic sectors as he attempts to establish a plan that will minimize the total number of student miles traveled by bus. He also recognizes that if a student happens to live in a certain sector and is assigned to the high school in that$$ 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$.$

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:

Distance to School

Sector

School in Sector B

School in Sector C

School in Sector E

Number of Students

A

B

C

D

E

Total

Each high school has a capacity of students.