The Springfield school board has made the decision to close one of its middle schools (sixth, seventh, and eighth grades) at the end of the school year and reassign all of the 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 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 the other basic data for the next year) , where 0 indicates that bussing is not needed and a dash indicates an infeasible assignments. Area No of students % in 6th grade % in 7th grade % in 8th Grade Bussing Cost per student (lakhs) School1 School2 School3 1 2 3 4 5 6 450 600 550 350 500 450 32 37 30 28 39 34 38 28 32 40 34 28 30 35 38 32 27 38 300 __ 600 200 0 500 0 400 300 500 __ 300 700 500 200 __ 400 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. You have been hired as an operations research consultant to assist the school board in determining how many students in each area should be assigned to each school. (a) Formulate a linear programming model for this problem. (b) What is your resulting recommendation to the school board? (c) Which decision do you think should be made? why?