As part of a course ‘linear programming’ I have to solve the following question. I understand the issue of the question, but I can’t succeed in setting up a mathematical model. (it’s an example from the book ‘introduction to operation research’)

- The Springfield school board has to close one of its middle schools (6th, 7th and 8th grades) at the end of this school year and reassign all of next year’s middle school students to the three remaining middle schools (school 1, school 2 and school 3)
- The school district provides bussing for all middle school students who must travel more than approximately a mile, so the school board wants a plan for reassigning the students that will minimize the total bussing cost.
- The annual cost per student of bussing from each of the six residential areas of the city to each of the schools is shown in the following table
- The school board also has imposed the restriction that each grade must constitute between 30 and 36 percent of each school’s population.
- The following table shows the percentage of each area’s middle school population for next year that falls into each of the three grades.
- The school attendance zone boundaries can be drawn so as to split any given area among more than one school, but assume that the percentages shown in the table will continue to hold for any partial assignment of an area to a school

The final question is ‘how many students in each area should be assigned to each school?’

Thx for your help!