princeallstar
New Member
The Gotham City School has three high schools that serve the needs of five neighborhood areas. The capacities of the various schools are:
School
Capacity (maximum enrollment)
A
4,000
B
3,000
C
2,000
Total
9,000
The size (number of high school students) and ethnic mix of each neighborhood are as shown:
Neighborhood
Number of Students
Percent Minority Students
1
2,100
30
2
2,400
80
3
1,300
20
4
800
10
5
1,600
20
Total
8,200
The distances (in miles) from each neighborhood to each school are shown:
Neighborhood
School
1
2
3
4
5
A
1.2
0.4
2.6
1.4
2.4
B
0.8
2
0.5
0.7
3
C
1.3
2.2
1.6
2
0.2
A federal judge has ruled that no high school in the city can have more than 50 percent nor less than a 30 percent minority enrollment. Assume that students bused from each neighborhood have the same ethnic mix as the whole neighborhood. You wish to devise a busing plan that will minimize the total number of student-miles bused while meeting the judge’s integration requirements, and at the same time guarantee that no student is bused more than 2.5 miles.
Be sure to indicate the objective function and all of the constraints.
Formulate and solve the above in an excel spreadsheet.
School
Capacity (maximum enrollment)
A
4,000
B
3,000
C
2,000
Total
9,000
The size (number of high school students) and ethnic mix of each neighborhood are as shown:
Neighborhood
Number of Students
Percent Minority Students
1
2,100
30
2
2,400
80
3
1,300
20
4
800
10
5
1,600
20
Total
8,200
The distances (in miles) from each neighborhood to each school are shown:
Neighborhood
School
1
2
3
4
5
A
1.2
0.4
2.6
1.4
2.4
B
0.8
2
0.5
0.7
3
C
1.3
2.2
1.6
2
0.2
A federal judge has ruled that no high school in the city can have more than 50 percent nor less than a 30 percent minority enrollment. Assume that students bused from each neighborhood have the same ethnic mix as the whole neighborhood. You wish to devise a busing plan that will minimize the total number of student-miles bused while meeting the judge’s integration requirements, and at the same time guarantee that no student is bused more than 2.5 miles.
Be sure to indicate the objective function and all of the constraints.
Formulate and solve the above in an excel spreadsheet.
