An Elementary School Board (ESB) has made the decision to close one of its elementary schools (1st Grade, 2nd Grade, and 3rd Grade) at the end of this school year and re-assign all of next year's students to the three remaining schools. The school district provides transportation services for all students who must travel more than approximately one Kilometer, so the ESB wants a plan for re assigning the students that will minimize the total transportation cost. The annual transportation cost per student of transportation from each of the six areas to each of the schools is shown in the following table (along with other basic data for next year), where 0 indicates that bussing is not needed and a dash (-) indicates an infeasible assignment.

Area	Number of Students In each area	Percentage of students :in eacb grade (%)
					Transportation cost/student in USD
		1'1Grade,	2nd Grade,	3n1 Grade,	School A	School B	School C
1	450	32%	38%	30%	30	0	70
2	600	37%	28%	35%	-	40	50
3	550	30%	32%	38%	60	30	20
4	350	28%	40%	32%	20	50	-
5	500	39%	34%	27%	0	-	40
6	450	34%	28%	38%	50	30	0
School Capacity (students)					900	1000	1000

The ESD 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 elementary 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.

As a consultant, assist the ESB in finding how many students in each area should be assigned to each school.

Part A:

1 - Formulate a mathematical linear model for the above problem and solve the model using any software. What is your recommendation to the ESB?

2. The school board is considering eliminating some bussing to reduce costs. Option a: is to eliminate bussing only for students traveling 1 to 1.5 Kilometers, where the cost per student is given in the table as $20. Option b: is to also eliminate bussing for students traveling

1.5 to 2 Kilometers, where the estimated cost per student is $30. Revise the model from part (J)

to fit Option a, and solve it.

3- Compare these results with those from part (J), including the reduction in total bussing cost. 4- Repeat part (2) for Option b.

Part B:

5 - After seeing your recommendation in question (1), the ESB expresses concern about all the splitting of residential areas among multiple schools. They indicate that they "would like to keep each neighborhood together." Adjust your recommendation as well as you can to enable each area to be assigned to just one school. (Adding this restriction may force you to fudge on some other constraints.). Determine how much the total bussing cost changes because of the decision to prohibit the splitting of residential areas among multiple schools. (Hint: develop a binary integer programming model).

6- Repeat question (2 & 4) of part A under the new school board decision to prohibit splitting residential areas among multiple schools