| Area | Fraction Minority | Number of Students |
|---|---|---|
| 1 | .20 | 1,200 |
| 2 | .10 | 900 |
| 3 | .85 | 1,700 |
| 4 | .60 | 2,000 |
| 5 | .90 | 2,500 |
The ruling handed down for Greenville is that a school can have neither more than 75 percent nor less than 30 percent minority enrollment. There are three schools in Greenville with the following capacities:
| School | Capacity |
|---|---|
| Bond | 3,900 |
| Washington | 3,100 |
| Pierron | 2,100 |
The objective is to design an assignment of students to schools so as to stay within the capacity of each school and satisfy the composition constraints while minimizing the distance traveled by students. The distances in kilometers between areas and schools are:
| School | Area | ||||
|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |
| Bond | 2.7 | 1.4 | 2.4 | 1.1 | 0.5 |
| Washington | 0.5 | 0.7 | 2.9 | 0.8 | 1.9 |
| Pierron | 1.6 | 2.0 | 0.1 | 1.3 | 2.2 |
There is an additional condition that no student can be transported more than 2.6 kilometers. Find the number of students which should be assigned to each school from each area. Assume that any group of students from an area have the same ethnic mix as the whole area.