Can anyone please help me solve part d e and f manually?

The Springfield school board has made the decision to close schools. The school district provides bussing for all middle one of its middle schools (sixth, seventh, and eighth grades) school students who must travel more than approximately a at the end of this school year and reassign all of next year's mile, so the school board wants a plan for reassigning the middle school students to the three remaining middle students that will minimize the total bussing cost. The CASE 4.3 ASSIGNING STUDENTS TO SCHOOLS annual cost per student of bussing from each of the six res- idential 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. Bussing Cost per Student No. of Area Students Percentage Percentage Percentage in 6th in 7th in 8th Grade Grade Grade School 1 School 2 School 3 $300 1 2 3 4 5 6 $700 $500 $200 450 600 550 350 500 450 32 37 30 28 39 34 38 28 32 40 34 28 30 35 38 32 27 38 0 $400 $300 $500 $600 $200 0 $500 $400 0 $300 School capacity: 900 1,100 1,000 The school board also has imposed the restriction that for students traveling 1 to 1.5 miles, where the cost per stu- each grade must constitute between 30 and 36 percent of dent is given in the table as $200. Option 2 is to also elim- each school's population. The above table shows the per- inate bussing for students traveling 1.5 to 2 miles, where the centage of each area's middle school population for next estimated cost per student is $300. year that falls into each of the three grades. The school at- (e) Revise the model from part (a) to fit Option 1, and solve. Com- tendance zone boundaries can be drawn so as to split any pare these results with those from part (c), including the re- given area among more than one school, but assume that the duction in total bussing cost. percentages shown in the table will continue to hold for any (f) Repeat part (e) for Option 2. partial assignment of an area to a school. You have been hired as an operations research consul- The school board now needs to choose among the three tant to assist the school board in determining how many stu- alternative bussing plans (the current one or Option 1 or Op- dents in each area should be assigned to each school. tion 2). One important factor is bussing costs. However, the school board also wants to place equal weight on a second (a) Formulate a linear programming model for this problem. factor: the inconvenience and safety problems caused by (b) Solve the model. forcing students to travel by foot or bicycle a substantial dis- (c) What is your resulting recommendation to the school board? tance (more than a mile, and especially more than 1.5 miles). After seeing your recommendation, the school board ex- Therefore, they want to choose a plan that provides the best presses concern about all the splitting of residential areas trade-off between these two factors. among multiple schools. They indicate that they would like (g) Use your results from parts (c), (e), and () to summarize the to keep each neighborhood together." key information related to these two factors that the school (d) Adjust your recommendation as well as you can to enable each board needs to make this decision. area to be assigned to just one school. (Adding this restriction (h) Which decision do you think should be made? Why? may force you to fudge on some other constraints.) How much Note: A data file for this case is included on this website does this increase the total bussing cost? (This line of analysis for your convenience. Also note that this case will be con- will be pursued more rigorously in Case 12.4.) tinued in later chapters (Cases 7.3 and 12.4), so we suggest The school board is considering eliminating some that you save your analysis, including your basic model. bussing to reduce costs. Option 1 is to eliminate bussing only