Discuss the following:
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 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 a certain high school in that sector, there is no need to bus that student because he or she 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.
Sector School in School in School in # of Students
Sector B Sector C Sector E
A 5 8 6 700
B 0 4 12 500
C 4 0 7 100
D 7 2 5 800
E 12 7 0 400
Each high school has a capacity of 900 students.
"Each high school has a capacity of 900 students." Would this statement be a consideration for one of this problem's constraints?
A. YES
B. NO
What is the mathematical representation for the objective function of this problem?
A. minimize A + B + C + D + E = 2500
B. max students = 5XAB + 8XAC + 6XAE + XBB + 4XBC +12XBE +4XCB + XCC + 7XCE + 7XDB +2XDC +5XDE +12XEB + 7XEC + XEE
C. min miles = 5XAB + 8XAC + 6XAE + 4XBC +12XBE +4XCB + 7XCE + 7XDB +2XDC +5XDE +12XEB + 7XEC
Would XA,B + XA,C + XA,E = 700 mathematically represent one of the constraints?
A. YES
B. NO
How many students can be sent by bus to the school in sector C?
A. 800
B. 300
C. 900
D. 100