Examples:
 
--------------------------------------------------------------
Ex1:  Min:  18 x 1 + 22 x 2 + 14 x 3 + 36 x 4 + 17 x 5 + 14 x 6 + 18 x 7 
            + 24 x 8 + 14 x 9 + 7 x 10 .

          x 3 + x 5 = 1 ,
          x 4 + x 5 + x 6 = 1 ,
          x 2 + x 4 + x 8 + x 9 = 1 ,
          x 3 + x 4 + x 8 + x 10 = 1 ,
          x 1 + x 2 + x 7 + x 9 = 1 ,
          x 1 + x 2 + x 4 + x 6 + x 8 = 1 .

RGB size=10
 feasiable solution:
x1=0, x2=0, x3=0, x4=0, x5=1, x6=0, x7=1, x8=1, x9=0, x10=0
 the optimal solution:
x1=0, x2=0, x3=1, x4=0, x5=0, x6=1, x7=0, x8=0, x9=1, x10=0

--------------------------------------------------------------
E2: Min: 23 x 1 + 15 x 2 + 6 x 3 + 7 x 4 + x 5 + 53 x 6 + 4 x 7 .


          3 x 1 + x 2 + 11 x 3 + 2 x 4 + 3 x 5 + 5 x 6 + 3 x 7 = 31 ,
          4 x 1 + 5 x 2 + x 4 + 7 x 5 + 4 x 6 + 6 x 7 = 27 ,
          5 x 1 + 6 x 2 + x 3 + 9 x 4 + 2 x 5 + 3 x 6 + 3 x 7 = 38 .

RGB size=17

the feasible solution:  x1=5, x2=0, x3=1, x4=1, x5=0, x6=0, x7=1

the optimal solution:   x1=0, x2=4, x3=2, x4=1, x5=0, x6=0, x7=1

-----------------------------------------------------------------------------
Ex3: Min: x 1 + 8 x 2 + 8 x 3 + 16 x 4 + 2 x 5 + 2 x 6  + 2 x 7 + 2 x 8 .

19 x 1 + 20 x 2 + 21 x 3 + 22 x 4 + 18 x 5 + 19 x 6 + 22 x 7 + 23 x 8 = 752 ,
21 x 1 + 22 x 2 + 23 x 3 + 20 x 4 + 20 x 5 + 23 x 6 + 24 x 7 + 19 x 8 = 772 ,
23 x 1 + 24 x 2 + 21 x 3 + 22 x 4 + 24 x 5 + 25 x 6 + 20 x 7 + 21 x 8 = 800 ,
25 x 1 + 22 x 2 + 23 x 3 + 24 x 4 + 26 x 5 + 21 x 6 + 22 x 7 + 25 x 8 = 844 .

RGB size=9

the feasible solution:  x1=1, x2=2, x3=3, x4=4, x5=5, x6=6, x7=7, x8=8

the optimal solution:   x1=6, x2=2, x3=0, x4=0, x5=2, x6=7, x7=8, x8=11

-----------------------------------------------------------------------------
Ex4: Min: x 1 +  8 x 3 + 2 x 5 + 2 x 6  + 2 x 7 + 2 x 8 .

x 1 + 2 x 2 + 3 x 3 + 4 x 4 + 2 x 5 + x 6 + 4 x 7 + 4 x 8 + 
3 x 9 + 4 x 10 = 173 ,
3 x 1 + 4 x 2 + 4 x 3 + 2 x 4 + 2 x 5 + 4 x 6 + 3 x 7 + x 8 + 
4 x 9 + 3 x 10 = 160 ,
4 x 1 + 3 x 2 + 3 x 3 + 4 x 4 + 4 x 5 + 4 x 6 + 2 x 7 + 3 x 8 + 
4 x 9 + x 10 = 163 ,
4 x 1 + 4 x 2 + 2 x 3 + 2 x 4 + 4 x 5 + 3 x 6 + 4 x 7 + 4 x 8 + 
3 x 9 + 4 x 10 = 191 ,
4 x 1 + 3 x 2 + 4 x 3 + 4 x 4 + 4 x 5 + 4 x 6 + 3 x 7 + 4 x 8 + 
2 x 9 + 4 x 10 = 193 .


RGB size=85
feasible solution: x1=1,x2=2,x3=3,x4=4,x5=5,x6=6,x7=7,x8=8,x9=9,x10=10
optimal solution: x1=2,x2=17,x3=0,x4=12,x5=1,x6=0,x7=0,x8=7,x9=5,x10=11

-----------------------------------------------------------------------------
Ex5:  Min:  18 x 1 + 22 x 2 + 14 x 3 + 36 x 4 + 17 x 5 + 14 x 6 + 18 x 7 
            + 24 x 8 + 14 x 9 + 7 x 10 .
            
          x 3 + x 5 = 1 ,
          x 4 + x 5 + x 6 = 1 ,
          x 2 + x 4 + x 8 + x 9 = 1 ,
          x 3 + x 4 + x 8 + x 10 = 1 ,
          x 1 + x 2 + x 7 + x 9 = 1 ,
          x 1 + x 2 + x 4 + x 6 + x 8 = 1 ,
          x 1 + x 2 + x 4 + x 5 + x 7 + x 8 + x 10 + x 11 + x 13 + x
          15 = 1 ,
          x 1 + x 2 + x 4 + x 5 + x 8 + x 10 + x 11 + x 12 + x 13 + x
          14 + x 16 = 1 .
 

RGB size=11

feasible solution : x3,x6,x9,x11=1, others =0
optimal solution : x3,x6,x9,x15,x16=1, others =0

-----------------------------------------------------------------------------

Ex6:  Min:  18 x 1 + 22 x 2 + 14 x 3 + 36 x 4 + 17 x 5 + 14 x 6 + 18 x 7 
            + 24 x 8 + 14 x 9 + 7 x 10 .
            
          x 3 + x 5 + x 7 + x 9 + x 10 + x 12 = 1 ,
          x 4 + x 5 + x 6 + x 9 + x 11 + x 13 + x 14 + x 16 = 1 ,
          x 2 + x 7 + x 8 + x 9 + x 12 + x 13 + x 15 = 1 ,
          x 3 + x 4 + x 6 + x 8 + x 10 + x 14 + x 15 + x 16 = 1 ,
          x 1 + x 2 + x 6 + x 7 + x 9 + x 11 + x 12 + x 13 + x 15 = 1 ,
          x 1 + x 3 + x 4 + x 6 + x 8 + x 14 + x 16 = 1 ,
          x 1 + x 2 + x 5 + x 7 + x 8 + x 10 + x 11 + x 13 + x 15 = 1 ,
          x 1 + x 2 + x 3 + x 4 + x 5 + x 10 + x 11 + x 12 + x 14 + x 16 = 1 .
 
RGB size=19
feasible solution: x7,x16=1,others=0
optimal solution: x3,x13=1,others=0

-----------------------------------------------------------------------------



















