B. Find the optimal solution of the PL model! Use the same variable name (consistent) as you used in No. 1. The order of constraints corresponds to the order of constraints in No.1. Include evidence in the form of PL MODELS AND SOLUTIONS C. Based on the solution obtained in No. 2, write a recommendation for the City of Busville School Board! Show that your recommendation meets all the requirements and that all students in the 3 districts get a school. D. Currently the maximum number of students that can be admitted to Walt Whitman High (call it bwwmax) is 500 people. What is the allowable bwwmax value so that the current base remains optimal? Explain with evidence.

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1. The city of Busville contains three school districts. The number of
minority and nonminority students in each district is given in Table 1.
Of all students, 25% (200/800) are minority students.
The local court has decided that both of the town's two high schools
(Cooley High and Walt Whitman High) must have approximately the
same percentage of minority students (within + 5%) as the entire town.
The distances (in miles) between the school districts and the high
schools are given in Table 2. Each high school must have an enrolment
of 300 – 500 students. The city school board needs to determine an
assignment of students to schools that minimizes the total distance
students must travel to schools.
Table 1. Number of students
Table 2. Distances (in miles)
Minority Nonminority
District Students
Cooley
District High Whitman
Walt
Students
High
1.
50
200
1.8
2.9
50
250
2
2.8
1.9
100
150
3
1.8
1.9
(Adapted from Winston 2004)
PL = Program Linear or Linear Program ( LP)
%3D
2.
3.
Transcribed Image Text:1. The city of Busville contains three school districts. The number of minority and nonminority students in each district is given in Table 1. Of all students, 25% (200/800) are minority students. The local court has decided that both of the town's two high schools (Cooley High and Walt Whitman High) must have approximately the same percentage of minority students (within + 5%) as the entire town. The distances (in miles) between the school districts and the high schools are given in Table 2. Each high school must have an enrolment of 300 – 500 students. The city school board needs to determine an assignment of students to schools that minimizes the total distance students must travel to schools. Table 1. Number of students Table 2. Distances (in miles) Minority Nonminority District Students Cooley District High Whitman Walt Students High 1. 50 200 1.8 2.9 50 250 2 2.8 1.9 100 150 3 1.8 1.9 (Adapted from Winston 2004) PL = Program Linear or Linear Program ( LP) %3D 2. 3.
A. Formulate the problem into the OT model! Define the decision
variables clearly. Give information about the objective function and
constraints.
B. Find the optimal solution of the PL model! Use the same variable
name (consistent) as you used in No. 1. The order of constraints
corresponds to the order of constraints in No.1. Include evidence in the
form of PL MODELS AND SOLUTIONS
C. Based on the solution obtained in No. 2, write a recommendation for
the City of Busville School Board! Show that your recommendation
meets all the requirements and that all students in the 3 districts get a
school.
D. Currently the maximum number of students that can be admitted to
Walt Whitman High (call it bwWma) is 500 people. What is the
allowable bwwmax value so that the current base remains optimal?
Explain with evidence.
Transcribed Image Text:A. Formulate the problem into the OT model! Define the decision variables clearly. Give information about the objective function and constraints. B. Find the optimal solution of the PL model! Use the same variable name (consistent) as you used in No. 1. The order of constraints corresponds to the order of constraints in No.1. Include evidence in the form of PL MODELS AND SOLUTIONS C. Based on the solution obtained in No. 2, write a recommendation for the City of Busville School Board! Show that your recommendation meets all the requirements and that all students in the 3 districts get a school. D. Currently the maximum number of students that can be admitted to Walt Whitman High (call it bwWma) is 500 people. What is the allowable bwwmax value so that the current base remains optimal? Explain with evidence.
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