Minimize Z = Subject to: 5 XAB +8XAC +6 XAE 0XBB +4XBC +12 XBE + 4 XCB +0 XCC +7XCE 7 XDB +2 XDC +5 XDE + 12 XEB+ 7XEC+ OXEE XAB+XAC+XAE = 750 = 600 XBB + XBC+ +XBE XCB+XCC +XCE= 150 XDB + XDC+XDE = 800 XEB+XEC+XEE = 500 + XBB + XCB XAB XAC + XBC + XAE For all X₁, 20 number of students in sector A number of students in sector B number of students in sector C number of students in sector D number of students in sector E school B capacity school C capacity school E capacity ≤ 1,000 XDB + XEB Xcc + XDC + XEC ≤ 1,000 + XBE + XCE + XDE + XEE $1,000 non negativity condition b) Using a computer software for solving LP, the objective value at the optimal solution achieved is: Minimum number of total miles traveled (objective value) (round your response to a whole number).

Practical Management Science
6th Edition
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Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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Please help me with part b
Minimize Z =
Subject to:
5 XAB +8XAC +6 XAE
0 XBB +4 XBC
+12 XBE
4 XCB +0 XCC +7XCE
7 XDB +2XDC +5 XDE +
12 XEB+7XEC+ OXEE
XAB+XAC+XAE = 750
XBB+XBC+XBE = 600
XCB+XCC +XCE= 150
XDB + XDC + XDE = 800
XEB+XEC+XEE = 500
+
+
+ XDB
XEB $1,000
XAB XBB + XCB
ХАС + XBC Xcc
+ XDC
XEC ≤1,000
XAE+XBE + XCE + XDE + XEE $1,000
For all X₁, 20
number of students in sector A
number of students in sector B
number of students in sector C
number of students in sector D
number of students in sector E
+
b) Using a computer software for solving LP, the objective value at the
Minimum number of total miles traveled (objective value) -
school B capacity
school C capacity
school E capacity
non negativity condition
optimal solution achieved is:
(round your response to a whole number).
Transcribed Image Text:Minimize Z = Subject to: 5 XAB +8XAC +6 XAE 0 XBB +4 XBC +12 XBE 4 XCB +0 XCC +7XCE 7 XDB +2XDC +5 XDE + 12 XEB+7XEC+ OXEE XAB+XAC+XAE = 750 XBB+XBC+XBE = 600 XCB+XCC +XCE= 150 XDB + XDC + XDE = 800 XEB+XEC+XEE = 500 + + + XDB XEB $1,000 XAB XBB + XCB ХАС + XBC Xcc + XDC XEC ≤1,000 XAE+XBE + XCE + XDE + XEE $1,000 For all X₁, 20 number of students in sector A number of students in sector B number of students in sector C number of students in sector D number of students in sector E + b) Using a computer software for solving LP, the objective value at the Minimum number of total miles traveled (objective value) - school B capacity school C capacity school E capacity non negativity condition optimal solution achieved is: (round your response to a whole number).
The Hills County, Michigan, superintendent of education is responsible for assigning students to the three high schools in
his county. He recognizes the need to bus a certain number of students, for several sectors, A-E, of the county are beyond walking distance to a school. The superintendent partitions the county into five geographic sector
he attempts to establish a plan that will minimize the total number of student miles traveled by bus. He also recognizes that if a student happens to live in a certain sector and is assigned to the high school in that sector, the
is no need to bus him because he can walk to school. The three schools are located in sectors B, C, and E.
The accompanying table reflects the number of high-school-age students living in each sector and the distance in miles from each sector to each school:
Distance to School
Sector School in Sector School in Sector School in Sector
B
с
E
A
B
с
с
D
E
Total
5
0
4
7
12
8
4
0
2
7
6
12
7
5
0
Each high school has a capacity of 1,000 students.
You have been asked to develop a linear programming model so as to minimize the total number of student miles traveled by bus.
Decision variable X;;: Number of students living in sector i traveling to school located in sector.
The number of decision variables for the model = 15.
Number of
Students
750
600
150
800
500
2,800
Transcribed Image Text:The Hills County, Michigan, superintendent of education is responsible for assigning students to the three high schools in his county. He recognizes the need to bus a certain number of students, for several sectors, A-E, of the county are beyond walking distance to a school. The superintendent partitions the county into five geographic sector he attempts to establish a plan that will minimize the total number of student miles traveled by bus. He also recognizes that if a student happens to live in a certain sector and is assigned to the high school in that sector, the is no need to bus him because he can walk to school. The three schools are located in sectors B, C, and E. The accompanying table reflects the number of high-school-age students living in each sector and the distance in miles from each sector to each school: Distance to School Sector School in Sector School in Sector School in Sector B с E A B с с D E Total 5 0 4 7 12 8 4 0 2 7 6 12 7 5 0 Each high school has a capacity of 1,000 students. You have been asked to develop a linear programming model so as to minimize the total number of student miles traveled by bus. Decision variable X;;: Number of students living in sector i traveling to school located in sector. The number of decision variables for the model = 15. Number of Students 750 600 150 800 500 2,800
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