The Springfield School Board has made the decision to close one of its middle schools (sixth, seventh, and eighth grades) at the end of this school year and reassign all of next year's middle school students to the three remaining middle schools. 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. Area 1 2 3 4 5 6 Number of Students 450 600 550 350 500 450 Percentage in 6th Percentage in 7th Percentage in Grade Grade 8th Grade 32 38 37 28 30 32 28 40 34 28 39 34 30 35 38 32 27 38 School Capacity School 1 $ 300 600 200 0 500 900 Busing Cost per Student School 2 $0 400 300 500 300 1,100 School 3 $ 700 500 200 400 0 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 a management science consultant to assist the school board in determining how many students in each area should be assigned to each school.
The Springfield School Board has made the decision to close one of its middle schools (sixth, seventh, and eighth grades) at the end of this school year and reassign all of next year's middle school students to the three remaining middle schools. 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. Area 1 2 3 4 5 6 Number of Students 450 600 550 350 500 450 Percentage in 6th Percentage in 7th Percentage in Grade Grade 8th Grade 32 38 37 28 30 32 28 40 34 28 39 34 30 35 38 32 27 38 School Capacity School 1 $ 300 600 200 0 500 900 Busing Cost per Student School 2 $0 400 300 500 300 1,100 School 3 $ 700 500 200 400 0 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 a management science consultant to assist the school board in determining how many students in each area should be assigned to each school.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section12.5: Analytic Steady-state Queueing Models
Problem 35P
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DO ONLY PART 3 AND THE QUESTIONS PROVIDED. I WILL UPVOTE ALL THANK YOU. BETTER IF EXCEL SOLVER WITH FORMULAS. MUCH APPRECIATED
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