In Spring there were 4 high schools, and the Spring school board made the decision to close one of its high schools (7th, 8th, and 9th) at the end of this school year and reassign all students to the remaining three high schools. The school district provides transportation to all high school students who must travel more than approximately one mile, so the school board wants to plan for student reassignment to minimize the total cost of transportation. The annual cost per student of transportation 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 the next year), where 0 indicates that the transport and a dash indicates an infeasible assignment. Area # Of Students 650 1100 800 900 800 1000 1 2 3 4 5 6 Data % in Seventh 32 37 34 30 28 39 % in % in Eight Ninth 38 30 28 35 28 38 32 38 40 32 34 27 High School capacity Transportation cost per student High High High School 1 School 2 School 3 $300 $0 $700 $400 $500 $500 $300 $600 $300 $200 $200 $500 $0 $400 1600 1920 1760 0 ---- The school board has also imposed the restriction that each grade (7, 8 and 9) must be between 30 and 36 percent of the population of each school. The table above shows the percentage of the student population in all three grades for each area for the upcoming year. The school attendance zone percentages shown in the table are valid for any partial assignment of an area to a school. You have been hired as an operations research consultant to help the school board determine how many students in each area should be assigned to each school. Ka) Formulate a linear programming model for this problem. In Spring there were 4 high schools, and the Spring school board made the decision to close one of its high schools (7th, 8th, and 9th) at the end of this school year and reassign all students to the remaining three high schools. The school district provides transportation to all high school students who must travel more than approximately one mile, so the school board wants to plan for student reassignment to minimize the total cost of transportation. The annual cost per student of transportation 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 the next year), where 0 indicates that the transport and a dash indicates an infeasible assignment. Area # Of Students 650 1100 800 900 800 1000 1 2 3 4 5 6 Data % in Seventh 32 37 34 30 28 39 % in % in Eight Ninth 38 30 28 35 28 38 32 38 40 32 34 27 High School capacity Transportation cost per student High High High School 1 School 2 School 3 $300 $0 $700 $400 $500 $500 $300 $600 $300 $200 $200 $500 $0 $400 1600 1920 1760 0 ---- The school board has also imposed the restriction that each grade (7, 8 and 9) must be between 30 and 36 percent of the population of each school. The table above shows the percentage of the student population in all three grades for each area for the upcoming year. The school attendance zone percentages shown in the table are valid for any partial assignment of an area to a school. You have been hired as an operations research consultant to help the school board determine how many students in each area should be assigned to each school. Ka) Formulate a linear programming model for this