The Winston School Board has made a 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 years middle school students to the three remaining middle schools. The school district provides bussing for all middle school students who must travel more than one mile, so the school board wants a plan for reassigning students that will minimize the total bussing cost. The annual cost per student for bussing from each of the six residential areas of the city to each of the schools is shown in the table in the file Winston data.xlsx (along with other basic data for next year), where 0 indicates that bussing is not needed and a dash indicates an infeasible assignment. The school board has also imposed the restriction that each grade must constitute between 30 and 36 percent of each schools population. The table shows the percentage of each areas middle school population 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 (i.e. if 100 students are sent from area 1 to school 1, then 32 of them are 6th graders, 38 of them are 7th graders and 30 of them are 8th graders). You have been hired as a consultant to assist the school board in determining how many students in each area should be assigned to each school

One concern of the school board is the ongoing road construction in area 6. These construction projects have been delaying traffic considerably and are likely to affect the cost of bussing students from area 6, perhaps increasing them as much as 10 percent. Use a solver table (500 to 550 by 5s) to check how much the bussing cost from area 6 to school 1 can increase (assuming no change in costs for the other schools) before the bussing plan would change. Then do the same for area 6 to school 2 (300 to 330 by 5s) (assuming no change in costs for the other schools)