Question

Explanation of the problem chapter 3.12 problem 18 of the book operations research 4th edition

We classify that:
                               Cooley High School = 1
                               Walt High School = 2
Where:
       Mij ​​= # of minority students living in district i to be assigned to school j
       Nij = # of majority students living in district i to be assigned to school j
                                                               i = 1, 2.3 j = 1.2
Objective function: Step # 2

The goal is to minimize the total distance that students must travel to school.
(M11, NM11) = is the distance between district 1 and Cooley High.
(M12, NM12) = is the distance between district 1 and Walt Whitman High.
(M21, NM21) = is the distance between district 2 and Cooley High.
(M22, NM22) = is the distance between district 2 and Walt Whitman High.
(M31, NM31) = is the distance between District 3 and Cooley High.
(M32, NM32) = is the distance between District 3 and Walt Whitman High.
Therefore the objective function is:
Minimize Z = (M11 + NM11) + 2 (M12 + NM12) + 2 (M21 + NM21) +
                               (M22 + NM22) + (M31 + NM31) + (M32 + NM32)


Step 3:
Restriction 1
There are 50 minority students in district 1 and 200 majority students in district 1.

M11 + M12 = 50
NM11 + NM12 = 200
Restriction 2
There are 50 minority students in district 2 and 250 majority students in district 2.

M21 + M22 = 50
NM21 + NM22 = 250
Restriction 3
There are 100 minority students in District 3 and 150 Majority students in District 3.

M31 + M32 = 100
NM31 + NM32 = 150
Restriction 4
For school 1, the following mixing restriction is obtained:
0.20  0
0.7 M11 + 0.7 M21 + 0.7 M31 - 0.3 NM11 - 0.3 NM21 - 0.3 NM31 <0

Restriction 5
For school 2, the following mixing restriction is obtained:
0.20  0
0.7 M12 + 0.7 M22 + 0.7 M32 - 0.3 NM12 - 0.3 NM22 - 0.3 NM32 <0
Restriction 6
Each school must have an enrollment between 300 and 500 students.
                  300 

What I need is the explanation itself of the problem as it was to get the data

Answer 1