constraints needed - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-06-20T06:24:35Z http://mathoverflow.net/feeds/question/85666 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/85666/constraints-needed constraints needed Hasan 2012-01-14T14:22:45Z 2012-01-14T14:22:45Z <p>Hi , i want to kno what are the constraints for this case for the point in which it is mentioned that each grade shld be between 30-36 percent of total population..</p> <p>The Springfield school board has made the decision to close one of its middle schools (sixth, seventh, and eighth grades) at the end of this school year and reassign all of next year’s middle school students to the three remaining middle schools. 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 (along with other basic data for next year), where 0 indicates that bussing is not needed and a dash indicates an infeasible assignment. CASE 4.3 ASSIGNING STUDENTS TO SCHOOLS Percentage Percentage Percentage No. of in 6th in 7th in 8th Bussing Cost per Student Area Students Grade Grade Grade School 1 School 2 School 3 1 450 32 38 30 3000700 2 600 37 28 35 — 400500 3 550 30 32 38 600300 2004350284032200 500—55003934270—400 6 450 34 28 38 500300 0 School capacity: 900 1,100 1,000 The school board also has imposed the restriction that each grade must constitute between 30 and 36 percent of each school’s population. The above 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.</p>