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The Bayside School District has made the decision to close one of its middle schools (6th, 7th, and 8th grades) at end of this school year and reassign all of next year's middle school students to the three remaining middle schools in the district. The school district provides busing 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 busing cost. The annual cost per student for busing from each of the six residential 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 busing is not needed and a dash indicates an infeasible assignment. The school board also has imposed the restriction that each grade must constitute between 30% and 36% of each school's population. The table below 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. Area 1 2 3 4 5 6 Number of Students 450 600 550 350 500 450 Percentage in 6th Grade 32 37 30 28 39 34 Percentage in 7th Grade 38 28 32 40 34 28 School Capacity: Percentage in 8th Grade 30 35 38 32 27 38 Busing Cost per Student School 1 $300 School 2 School 3 $0 $700 $400 $500 $300 $200 $500 $600 $200 $0 $500 $300 900 $400 0 1,100 1,000

The Bayside School District has made the decision to close one of its middle schools (6th, 7th, and 8th grades) at end of this school year and reassign all of next year's middle school students to the three remaining middle schools in the district. The school district provides busing 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 busing cost. The annual cost per student for busing from each of the six residential 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 busing is not needed and a dash indicates an infeasible assignment. The school board also has imposed the restriction that each grade must constitute between 30% and 36% of each school's population. The table below 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. Area 1 2 3 4 5 6 Number of Students 450 600 550 350 500 450 Percentage in 6th Grade 32 37 30 28 39 34 Percentage in 7th Grade 38 28 32 40 34 28 School Capacity: Percentage in 8th Grade 30 35 38 32 27 38 Busing Cost per Student School 1 $300 School 2 School 3 $0 $700 $400 $500 $300 $200 $500 $600 $200 $0 $500 $300 900 $400 0 1,100 1,000

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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You have been hired as a management science consultant team to assist the school board in determining how many students in each area should be assigned to each school. a) Formulate and solve a linear programming model for this problem. b) What is your resulting recommendation to the school board?
Transcribed Image Text:You have been hired as a management science consultant team to assist the school board in determining how many students in each area should be assigned to each school. a) Formulate and solve a linear programming model for this problem. b) What is your resulting recommendation to the school board?
The Bayside School District has made the decision to close one of its middle schools (6th, 7th, and 8th grades) at end of this school year and reassign all of next year's middle school students to the three remaining middle schools in the district. The school district provides busing 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 busing cost. The annual cost per student for busing from each of the six residential 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 busing is not needed and a dash indicates an infeasible assignment. The school board also has imposed the restriction that each grade must constitute between 30% and 36% of each school's population. The table below 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. Area 1 2 3 4 5 6 Number of Students 450 600 550 350 500 450 Percentage in 6th Grade 32 37 30 28 39 34 Percentage in 7th Grade 38 28 32 40 34 28 School Capacity: Percentage in 8th Grade 30 35 38 32 27 38 Busing Cost per Student School 1 $300 $600 $200 $0 $500 900 School 2 School 3 $0 $700 $400 $500 $300 $200 $500 $400 $300 0 1,100 1,000
Transcribed Image Text:The Bayside School District has made the decision to close one of its middle schools (6th, 7th, and 8th grades) at end of this school year and reassign all of next year's middle school students to the three remaining middle schools in the district. The school district provides busing 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 busing cost. The annual cost per student for busing from each of the six residential 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 busing is not needed and a dash indicates an infeasible assignment. The school board also has imposed the restriction that each grade must constitute between 30% and 36% of each school's population. The table below 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. Area 1 2 3 4 5 6 Number of Students 450 600 550 350 500 450 Percentage in 6th Grade 32 37 30 28 39 34 Percentage in 7th Grade 38 28 32 40 34 28 School Capacity: Percentage in 8th Grade 30 35 38 32 27 38 Busing Cost per Student School 1 $300 $600 $200 $0 $500 900 School 2 School 3 $0 $700 $400 $500 $300 $200 $500 $400 $300 0 1,100 1,000
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