Use the Sensitivity Report to answer the next two questions.

3. The school board can add portable classrooms to increase capacity in one or more schools, if doing so results in lower costs. Each portable classroom can hold 20 students, and has a leasing cost of $2500 per year. (The board assumes area 6 construction can be ignored for analyzing this option.) Determine the best combination of portable classrooms (how many in which school) that can be added without changing any shadow price, to minimize annual total (busing plus leasing) cost. Calculate the resulting total cost/year.

The school board in a large city has decided to close one of its middle schools (grades 6,7,8 ) at the end of this school year, and reassign all of next year's middle school students to the remaining three middle schools. The school district provides busing for all middle school students who must travel more than 1.5 km, so the school board wants a plan for reassigning the students that will minimize the total busing cost. The annual cost of busing a student from each of the six residential areas of the city to each school is shown below, along with other basic data. A cost of 0 indicates that busing is not needed, and a dash indicates an infeasible assignment. The schoolboard has added a restriction that each grade must constitute between 27% and 37% of each school's enrolment. You are a member of the management consulting team advising the school board on how many students from each of the six areas to assign to each of the three schools. Students within a residential area can be divided up among the three schools in any numbers desired. Your client (the school board) has asked you to assume that the percentages shown above will continue to hold even if only some of the students in a residential area are assigned to a school. Thus, for example, if half the students in area 1 are assigned to school 1 , and the remaining half are split between schools 2 and 3 , the percentage of area 1 students in grades 6/7/8 in each school will be 32/38/30. Formulate an LP to minimize the total busing cost. Solve the linear programming problem using Excel Solver and report your findings. The written report should include: 1. Your LP, with carefully defined decision variables, objective function and all constraints written out using Word's equation editor. Include brief explanations of your constraints. (15 marks) 2. A table showing your recommended optimal number of students from each residential area assigned to each school j and the resulting total cost