The Arden County, Maryland, superintendent of education is responsible for assig
ID: 378404 • Letter: T
Question
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 super-intendent 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 that student because he or she can walk to school. The three schools are located in sectors B, C, and E. Each high school has a capacity of 900 students.The following table attached reflects the number of high-school-age students living in each sector and the distance in miles from each sector to each school:
1. Problem statement: Summarize the problem statement and provide data tables as appropriate
2. What is the Linear Programming formulation?(no photos of had written problem formulations allowed here)
DISTANCE TO SCHOOL SCHOOLIN SCHOOL IN SCHOOL IN NUMBER OF SECTOR SECTOR B SECTOR C SECTORE STUDENTS 12 500 100 800 12 0 2,500Explanation / Answer
1) Aim of this problem is to find the number of students that should be assigned to respective school where their travel distance will be minimum. In order to resolve this problem we will analyze distance of student from respective school and then number to students as in one school maximum number of students can be only 900.
For this case for sector B , 500 students are their . We will assign that to school B. Sector c 100 student will be assigned to school c and sector e 400 student will be assigned to school e . From sector a move 400 student to school b. Move sector D 800 student to school C . Rest 300 student of sector A to School E
2)
A + B + C + D + E = 2500.
max students = 5XAB + 8XAC + 6XAE + XBB + 4XBC +12XBE +4XCB + XCC + 7XCE + 7XDB+2XDC +5XDE +12XEB + 7XEC + XEEC.
min miles = 5XAB + 8XAC + 6XAE + 4XBC +12XBE +4XCB + 7XCE + 7XDB +2XDC +5XDE+12XEB + 7XEC
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