one of its middle schools (sixth, seventh and eighth grades) at the
end of this school year and reassign all students in these grades
to the other three middle schools. The school district provides
busing for all middle school students who have to travel more than
about one mile, so the board desires a plan for reassigning
students that minimizes the total cost of busing. The annual cost
per student bused from each of the city's six residential areas to
each of the schools is shown in the following table (along with
other basic data for the coming year), where 0 indicates no
transportation is required and a dash indicates an infeasible
assignment.
Transportation cost per student
- The Springfield School Board Of Trustees Has Decided To Close One Of Its Middle Schools Sixth Seventh And Eighth Grade 1 (30.31 KiB) Viewed 50 times
grade must constitute between 30 and 36% of each school's
population. The table above shows the percentage of each area's
middle school population for the upcoming year that is in each of
the three grades. It is possible to draw area boundaries for school
attendance to divide the given area into more than one school, but
assume that the percentages in the table hold for any partial
assignment of an area to a school.
You are hired as an administrative science consultant to help the
board determine how many students from each area should be assigned
to each school.
a) Formulate and solve a linear programming model for the
problem.
b) What is your recommendation to the school
board?
IMPORTANT NOTE
PLEASE SHOW THE FORMULAS USED IN EXCEL
DON'T FORGET TO SHOW THE FORMULAS USED IN
EXCEL
Area 1 2 3 4 5 1.0 6 Number of students 450 600 550 350 500 450 Percentage in 6th grade 32 37 30 28 39 34 Percentage in 7th grade Percentage School 1 in 8th grade $ 300 - 600 200 0 500 900 38 30 28 35 32 38 40 32 34 27 28 38 School capacity School 2 $0 400 300 500 - 300 1100 School 3 $ 700 500 200 -- 400 0 1000