optimization methods question

(a) Formulate a linear programming model for this problem. (b) Solve the model using LINGO. (c) What is your resulting recommendation to the school board? The Springfield School Board still has the policy of providing bussing for all middle school students who must travel more than approximately 1 mile. Another current policy is to allow splitting residential areas among multiple schools if this will reduce the total bussing cost. However, before adopting a bussing plan based on parts (a) and (b), the school board now wants to conduct some postoptimality analysis. (d) Generate a sensitivity analysis report with the same software package as used in part (a). 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. (e) Use the report from part (d) to check how much the bussing cost from area 6 to school 1 can increase (assuming no change in the costs for the other schools) before the current optimal solution would no longer be optimal. If the allowable increase is less than 10 percent, re-solve to find the new optimal solution with a 10 percent increase. (f) Repeat part (e) for school 2 (assuming no change in the costs for the other schools). (g) Now assume that the bussing cost from area 6 would increase by the same percentage for all the schools. Use the report from part (d) to determine how large this percentage can be before the current optimal solution might no longer be optimal. If the allowable increase