运筹学运输问题

Exam2

model:
sets:
Warehouse/1..3/:a;
Customer/1..4/:b;
Routes(Warehouse,Customer):c,x;
endsets
data:
a=7,5,7;
b=2,3,4,6;
c=2,11,3,4,10,3,5,9,7,8,1,2;
enddata
[obj]min=@sum(Routes:c*x);
@for(Warehouse(i):[SUP]
@sum(Customer(j):x(i,j))<=a(i));
@for(Customer(j):[DEM]
@sum(Warehouse(i):x(i,j))=b(j));
end




  Global optimal solution found.
  Objective value:                              35.00000
  Infeasibilities:                              0.000000
  Total solver iterations:                             5


                       Variable           Value        Reduced Cost
                          A( 1)        7.000000            0.000000
                          A( 2)        5.000000            0.000000
                          A( 3)        7.000000            0.000000
                          B( 1)        2.000000            0.000000
                          B( 2)        3.000000            0.000000
                          B( 3)        4.000000            0.000000
                          B( 4)        6.000000            0.000000
                       C( 1, 1)        2.000000            0.000000
                       C( 1, 2)        11.00000            0.000000
                       C( 1, 3)        3.000000            0.000000
                       C( 1, 4)        4.000000            0.000000
                       C( 2, 1)        10.00000            0.000000
                       C( 2, 2)        3.000000            0.000000
                       C( 2, 3)        5.000000            0.000000
                       C( 2, 4)        9.000000            0.000000
                       C( 3, 1)        7.000000            0.000000
                       C( 3, 2)        8.000000            0.000000
                       C( 3, 3)        1.000000            0.000000
                       C( 3, 4)        2.000000            0.000000
                       X( 1, 1)        2.000000            0.000000
                       X( 1, 2)        0.000000            8.000000
                       X( 1, 3)        0.000000            0.000000
                       X( 1, 4)        3.000000            0.000000
                       X( 2, 1)        0.000000            8.000000
                       X( 2, 2)        3.000000            0.000000
                       X( 2, 3)        0.000000            2.000000
                       X( 2, 4)        0.000000            5.000000
                       X( 3, 1)        0.000000            7.000000
                       X( 3, 2)        0.000000            7.000000
                       X( 3, 3)        4.000000            0.000000
                       X( 3, 4)        3.000000            0.000000

                            Row    Slack or Surplus      Dual Price
                            OBJ        35.00000           -1.000000
                        SUP( 1)        2.000000            0.000000
                        SUP( 2)        2.000000            0.000000
                        SUP( 3)        0.000000            2.000000
                        DEM( 1)        0.000000           -2.000000
                        DEM( 2)        0.000000           -3.000000
                        DEM( 3)        0.000000           -3.000000
                        DEM( 4)        0.000000           -4.000000


Exam3
model:
sets:
Warehouse/1..3/:a;
Customer/1..4/:b,D;
Routes(Warehouse,Customer):c,x;
endsets
data:
a=50,60,50;
b=30,70,0,10;
d=50,70,30,1000000;
c=16,13,22,17,14,13,19,15,19,20,23,1000000;
enddata
[obj]min=@sum(Routes:c*x);
@for(Warehouse(i):[SUP]
@sum(Customer(j):x(i,j))<=a(i));
@for(Customer(j):[DEM]
@sum(Warehouse(i):x(i,j))>=b(j));
@for(Customer(j):[FHS]
@sum(Warehouse(i):x(i,j))<=d(j));
end



  Global optimal solution found.
  Objective value:                              1480.000
  Infeasibilities:                              0.000000
  Total solver iterations:                             4


                       Variable           Value        Reduced Cost
                          A( 1)        50.00000            0.000000
                          A( 2)        60.00000            0.000000
                          A( 3)        50.00000            0.000000
                          B( 1)        30.00000            0.000000
                          B( 2)        70.00000            0.000000
                          B( 3)        0.000000            0.000000
                          B( 4)        10.00000            0.000000
                          D( 1)        50.00000            0.000000
                          D( 2)        70.00000            0.000000
                          D( 3)        30.00000            0.000000
                          D( 4)        1000000.            0.000000
                       C( 1, 1)        16.00000            0.000000
                       C( 1, 2)        13.00000            0.000000
                       C( 1, 3)        22.00000            0.000000
                       C( 1, 4)        17.00000            0.000000
                       C( 2, 1)        14.00000            0.000000
                       C( 2, 2)        13.00000            0.000000
                       C( 2, 3)        19.00000            0.000000
                       C( 2, 4)        15.00000            0.000000
                       C( 3, 1)        19.00000            0.000000
                       C( 3, 2)        20.00000            0.000000
                       C( 3, 3)        23.00000            0.000000
                       C( 3, 4)        1000000.            0.000000
                       X( 1, 1)        0.000000            2.000000
                       X( 1, 2)        50.00000            0.000000
                       X( 1, 3)        0.000000            22.00000
                       X( 1, 4)        0.000000            2.000000
                       X( 2, 1)        30.00000            0.000000
                       X( 2, 2)        20.00000            0.000000
                       X( 2, 3)        0.000000            19.00000
                       X( 2, 4)        10.00000            0.000000
                       X( 3, 1)        0.000000            5.000000
                       X( 3, 2)        0.000000            7.000000
                       X( 3, 3)        0.000000            23.00000
                       X( 3, 4)        0.000000            999985.0

                            Row    Slack or Surplus      Dual Price
                            OBJ        1480.000           -1.000000
                        SUP( 1)        0.000000            0.000000
                        SUP( 2)        0.000000            0.000000
                        SUP( 3)        50.00000            0.000000
                        DEM( 1)        0.000000           -14.00000
                        DEM( 2)        0.000000           -13.00000
                        DEM( 3)        0.000000            0.000000
                        DEM( 4)        0.000000           -15.00000
                        FHS( 1)        20.00000            0.000000
                        FHS( 2)        0.000000            0.000000
                        FHS( 3)        30.00000            0.000000
                        FHS( 4)        999990.0            0.000000

Exam4
model:
sets:
Warehouse/1..11/:a;
Customer/1..11/:b;
Routes(Warehouse,Customer):c,x;
endsets
data:
a=27,24,29,20,20,20,20,20,20,20,20;
b=20,20,20,20,20,20,20,23,26,25,26;
c=0,1,3,2,1,4,3,3,11,3,10,1,0,1000000000,3,5,100000000,2,1,9,2,8,3,100000000,0,1,10000000,2,3,7,4,10,5,2,3,1,0,1,3,2,2,8,4,6,1,5,10000000,1,0,1,1,4,5,2,7,4,10000,2,3,1,0,2,1,8,2,4,3,2,3,2,1,2,0,1,100000,2,6,3,1,7,2,4,1,1,0,1,4,2,11,9,4,8,5,8,10000,1,0,2,1,3,2,10,4,2,2,2,4,2,0,8,10,8,5,6,7,4,6,2,1,8,0;
enddata
[obj]min=@sum(Routes:c*x);
@for(Warehouse(i):[SUP]
@sum(Customer(j):x(i,j))<=a(i));
@for(Customer(j):[DEM]
@sum(Warehouse(i):x(i,j))=b(j));
end

  Global optimal solution found.
  Objective value:                              68.00000
  Infeasibilities:                              0.000000
  Total solver iterations:                            22


                       Variable           Value        Reduced Cost
                          A( 1)        27.00000            0.000000
                          A( 2)        24.00000            0.000000
                          A( 3)        29.00000            0.000000
                          A( 4)        20.00000            0.000000
                          A( 5)        20.00000            0.000000
                          A( 6)        20.00000            0.000000
                          A( 7)        20.00000            0.000000
                          A( 8)        20.00000            0.000000
                          A( 9)        20.00000            0.000000
                         A( 10)        20.00000            0.000000
                         A( 11)        20.00000            0.000000
                          B( 1)        20.00000            0.000000
                          B( 2)        20.00000            0.000000
                          B( 3)        20.00000            0.000000
                          B( 4)        20.00000            0.000000
                          B( 5)        20.00000            0.000000
                          B( 6)        20.00000            0.000000
                          B( 7)        20.00000            0.000000
                          B( 8)        23.00000            0.000000
                          B( 9)        26.00000            0.000000
                         B( 10)        25.00000            0.000000
                         B( 11)        26.00000            0.000000
                       C( 1, 1)        0.000000            0.000000
                       C( 1, 2)        1.000000            0.000000
                       C( 1, 3)        3.000000            0.000000
                       C( 1, 4)        2.000000            0.000000
                       C( 1, 5)        1.000000            0.000000
                       C( 1, 6)        4.000000            0.000000
                       C( 1, 7)        3.000000            0.000000
                       C( 1, 8)        3.000000            0.000000
                       C( 1, 9)        11.00000            0.000000
                      C( 1, 10)        3.000000            0.000000
                      C( 1, 11)        10.00000            0.000000
                       C( 2, 1)        1.000000            0.000000
                       C( 2, 2)        0.000000            0.000000
                       C( 2, 3)       0.1000000E+10        0.000000
                       C( 2, 4)        3.000000            0.000000
                       C( 2, 5)        5.000000            0.000000
                       C( 2, 6)       0.1000000E+09        0.000000
                       C( 2, 7)        2.000000            0.000000
                       C( 2, 8)        1.000000            0.000000
                       C( 2, 9)        9.000000            0.000000
                      C( 2, 10)        2.000000            0.000000
                      C( 2, 11)        8.000000            0.000000
                       C( 3, 1)        3.000000            0.000000
                       C( 3, 2)       0.1000000E+09        0.000000
                       C( 3, 3)        0.000000            0.000000
                       C( 3, 4)        1.000000            0.000000
                       C( 3, 5)       0.1000000E+08        0.000000
                       C( 3, 6)        2.000000            0.000000
                       C( 3, 7)        3.000000            0.000000
                       C( 3, 8)        7.000000            0.000000
                       C( 3, 9)        4.000000            0.000000
                      C( 3, 10)        10.00000            0.000000
                      C( 3, 11)        5.000000            0.000000
                       C( 4, 1)        2.000000            0.000000
                       C( 4, 2)        3.000000            0.000000
                       C( 4, 3)        1.000000            0.000000
                       C( 4, 4)        0.000000            0.000000
                       C( 4, 5)        1.000000            0.000000
                       C( 4, 6)        3.000000            0.000000
                       C( 4, 7)        2.000000            0.000000
                       C( 4, 8)        2.000000            0.000000
                       C( 4, 9)        8.000000            0.000000
                      C( 4, 10)        4.000000            0.000000
                      C( 4, 11)        6.000000            0.000000
                       C( 5, 1)        1.000000            0.000000
                       C( 5, 2)        5.000000            0.000000
                       C( 5, 3)       0.1000000E+08        0.000000
                       C( 5, 4)        1.000000            0.000000
                       C( 5, 5)        0.000000            0.000000
                       C( 5, 6)        1.000000            0.000000
                       C( 5, 7)        1.000000            0.000000
                       C( 5, 8)        4.000000            0.000000
                       C( 5, 9)        5.000000            0.000000
                      C( 5, 10)        2.000000            0.000000
                      C( 5, 11)        7.000000            0.000000
                       C( 6, 1)        4.000000            0.000000
                       C( 6, 2)        10000.00            0.000000
                       C( 6, 3)        2.000000            0.000000
                       C( 6, 4)        3.000000            0.000000
                       C( 6, 5)        1.000000            0.000000
                       C( 6, 6)        0.000000            0.000000
                       C( 6, 7)        2.000000            0.000000
                       C( 6, 8)        1.000000            0.000000
                       C( 6, 9)        8.000000            0.000000
                      C( 6, 10)        2.000000            0.000000
                      C( 6, 11)        4.000000            0.000000
                       C( 7, 1)        3.000000            0.000000
                       C( 7, 2)        2.000000            0.000000
                       C( 7, 3)        3.000000            0.000000
                       C( 7, 4)        2.000000            0.000000
                       C( 7, 5)        1.000000            0.000000
                       C( 7, 6)        2.000000            0.000000
                       C( 7, 7)        0.000000            0.000000
                       C( 7, 8)        1.000000            0.000000
                       C( 7, 9)        100000.0            0.000000
                      C( 7, 10)        2.000000            0.000000
                      C( 7, 11)        6.000000            0.000000
                       C( 8, 1)        3.000000            0.000000
                       C( 8, 2)        1.000000            0.000000
                       C( 8, 3)        7.000000            0.000000
                       C( 8, 4)        2.000000            0.000000
                       C( 8, 5)        4.000000            0.000000
                       C( 8, 6)        1.000000            0.000000
                       C( 8, 7)        1.000000            0.000000
                       C( 8, 8)        0.000000            0.000000
                       C( 8, 9)        1.000000            0.000000
                      C( 8, 10)        4.000000            0.000000
                      C( 8, 11)        2.000000            0.000000
                       C( 9, 1)        11.00000            0.000000
                       C( 9, 2)        9.000000            0.000000
                       C( 9, 3)        4.000000            0.000000
                       C( 9, 4)        8.000000            0.000000
                       C( 9, 5)        5.000000            0.000000
                       C( 9, 6)        8.000000            0.000000
                       C( 9, 7)        10000.00            0.000000
                       C( 9, 8)        1.000000            0.000000
                       C( 9, 9)        0.000000            0.000000
                      C( 9, 10)        2.000000            0.000000
                      C( 9, 11)        1.000000            0.000000
                      C( 10, 1)        3.000000            0.000000
                      C( 10, 2)        2.000000            0.000000
                      C( 10, 3)        10.00000            0.000000
                      C( 10, 4)        4.000000            0.000000
                      C( 10, 5)        2.000000            0.000000
                      C( 10, 6)        2.000000            0.000000
                      C( 10, 7)        2.000000            0.000000
                      C( 10, 8)        4.000000            0.000000
                      C( 10, 9)        2.000000            0.000000
                     C( 10, 10)        0.000000            0.000000
                     C( 10, 11)        8.000000            0.000000
                      C( 11, 1)        10.00000            0.000000
                      C( 11, 2)        8.000000            0.000000
                      C( 11, 3)        5.000000            0.000000
                      C( 11, 4)        6.000000            0.000000
                      C( 11, 5)        7.000000            0.000000
                      C( 11, 6)        4.000000            0.000000
                      C( 11, 7)        6.000000            0.000000
                      C( 11, 8)        2.000000            0.000000
                      C( 11, 9)        1.000000            0.000000
                     C( 11, 10)        8.000000            0.000000
                     C( 11, 11)        0.000000            0.000000
                       X( 1, 1)        20.00000            0.000000
                       X( 1, 2)        7.000000            0.000000
                       X( 1, 3)        0.000000            4.000000
                       X( 1, 4)        0.000000            2.000000
                       X( 1, 5)        0.000000            0.000000
                       X( 1, 6)        0.000000            3.000000
                       X( 1, 7)        0.000000            2.000000
                       X( 1, 8)        0.000000            1.000000
                       X( 1, 9)        0.000000            8.000000
                      X( 1, 10)        0.000000            0.000000
                      X( 1, 11)        0.000000            6.000000
                       X( 2, 1)        0.000000            2.000000
                       X( 2, 2)        13.00000            0.000000
                       X( 2, 3)        0.000000           0.1000000E+10
                       X( 2, 4)        0.000000            4.000000
                       X( 2, 5)        0.000000            5.000000
                       X( 2, 6)        0.000000           0.1000000E+09
                       X( 2, 7)        0.000000            2.000000
                       X( 2, 8)        6.000000            0.000000
                       X( 2, 9)        0.000000            7.000000
                      X( 2, 10)        5.000000            0.000000
                      X( 2, 11)        0.000000            5.000000
                       X( 3, 1)        0.000000            2.000000
                       X( 3, 2)        0.000000           0.1000000E+09
                       X( 3, 3)        20.00000            0.000000
                       X( 3, 4)        0.000000            0.000000
                       X( 3, 5)        0.000000            9999998.
                       X( 3, 6)        0.000000            0.000000
                       X( 3, 7)        0.000000            1.000000
                       X( 3, 8)        0.000000            4.000000
                       X( 3, 9)        9.000000            0.000000
                      X( 3, 10)        0.000000            6.000000
                      X( 3, 11)        0.000000            0.000000
                       X( 4, 1)        0.000000            2.000000
                       X( 4, 2)        0.000000            2.000000
                       X( 4, 3)        0.000000            2.000000
                       X( 4, 4)        20.00000            0.000000
                       X( 4, 5)        0.000000            0.000000
                       X( 4, 6)        0.000000            2.000000
                       X( 4, 7)        0.000000            1.000000
                       X( 4, 8)        0.000000            0.000000
                       X( 4, 9)        0.000000            5.000000
                      X( 4, 10)        0.000000            1.000000
                      X( 4, 11)        0.000000            2.000000
                       X( 5, 1)        0.000000            2.000000
                       X( 5, 2)        0.000000            5.000000
                       X( 5, 3)        0.000000           0.1000000E+08
                       X( 5, 4)        0.000000            2.000000
                       X( 5, 5)        20.00000            0.000000
                       X( 5, 6)        0.000000            1.000000
                       X( 5, 7)        0.000000            1.000000
                       X( 5, 8)        0.000000            3.000000
                       X( 5, 9)        0.000000            3.000000
                      X( 5, 10)        0.000000            0.000000
                      X( 5, 11)        0.000000            4.000000
                       X( 6, 1)        0.000000            5.000000
                       X( 6, 2)        0.000000            10000.00
                       X( 6, 3)        0.000000            4.000000
                       X( 6, 4)        0.000000            4.000000
                       X( 6, 5)        0.000000            1.000000
                       X( 6, 6)        20.00000            0.000000
                       X( 6, 7)        0.000000            2.000000
                       X( 6, 8)        0.000000            0.000000
                       X( 6, 9)        0.000000            6.000000
                      X( 6, 10)        0.000000            0.000000
                      X( 6, 11)        0.000000            1.000000
                       X( 7, 1)        0.000000            4.000000
                       X( 7, 2)        0.000000            2.000000
                       X( 7, 3)        0.000000            5.000000
                       X( 7, 4)        0.000000            3.000000
                       X( 7, 5)        0.000000            1.000000
                       X( 7, 6)        0.000000            2.000000
                       X( 7, 7)        20.00000            0.000000
                       X( 7, 8)        0.000000            0.000000
                       X( 7, 9)        0.000000            99998.00
                      X( 7, 10)        0.000000            0.000000
                      X( 7, 11)        0.000000            3.000000
                       X( 8, 1)        0.000000            5.000000
                       X( 8, 2)        0.000000            2.000000
                       X( 8, 3)        0.000000            10.00000
                       X( 8, 4)        0.000000            4.000000
                       X( 8, 5)        0.000000            5.000000
                       X( 8, 6)        0.000000            2.000000
                       X( 8, 7)        0.000000            2.000000
                       X( 8, 8)        17.00000            0.000000
                       X( 8, 9)        3.000000            0.000000
                      X( 8, 10)        0.000000            3.000000
                      X( 8, 11)        0.000000            0.000000
                       X( 9, 1)        0.000000            14.00000
                       X( 9, 2)        0.000000            11.00000
                       X( 9, 3)        0.000000            8.000000
                       X( 9, 4)        0.000000            11.00000
                       X( 9, 5)        0.000000            7.000000
                       X( 9, 6)        0.000000            10.00000
                       X( 9, 7)        0.000000            10002.00
                       X( 9, 8)        0.000000            2.000000
                       X( 9, 9)        14.00000            0.000000
                      X( 9, 10)        0.000000            2.000000
                      X( 9, 11)        6.000000            0.000000
                      X( 10, 1)        0.000000            6.000000
                      X( 10, 2)        0.000000            4.000000
                      X( 10, 3)        0.000000            14.00000
                      X( 10, 4)        0.000000            7.000000
                      X( 10, 5)        0.000000            4.000000
                      X( 10, 6)        0.000000            4.000000
                      X( 10, 7)        0.000000            4.000000
                      X( 10, 8)        0.000000            5.000000
                      X( 10, 9)        0.000000            2.000000
                     X( 10, 10)        20.00000            0.000000
                     X( 10, 11)        0.000000            7.000000
                      X( 11, 1)        0.000000            14.00000
                      X( 11, 2)        0.000000            11.00000
                      X( 11, 3)        0.000000            10.00000
                      X( 11, 4)        0.000000            10.00000
                      X( 11, 5)        0.000000            10.00000
                      X( 11, 6)        0.000000            7.000000
                      X( 11, 7)        0.000000            9.000000
                      X( 11, 8)        0.000000            4.000000
                      X( 11, 9)        0.000000            2.000000
                     X( 11, 10)        0.000000            9.000000
                     X( 11, 11)        20.00000            0.000000

                            Row    Slack or Surplus      Dual Price
                            OBJ        68.00000           -1.000000
                        SUP( 1)        0.000000            1.000000
                        SUP( 2)        0.000000            2.000000
                        SUP( 3)        0.000000            0.000000
                        SUP( 4)        0.000000            1.000000
                        SUP( 5)        0.000000            2.000000
                        SUP( 6)        0.000000            2.000000
                        SUP( 7)        0.000000            2.000000
                        SUP( 8)        0.000000            3.000000
                        SUP( 9)        0.000000            4.000000
                       SUP( 10)        0.000000            4.000000
                       SUP( 11)        0.000000            5.000000
                        DEM( 1)        0.000000           -1.000000
                        DEM( 2)        0.000000           -2.000000
                        DEM( 3)        0.000000            0.000000
                        DEM( 4)        0.000000           -1.000000
                        DEM( 5)        0.000000           -2.000000
                        DEM( 6)        0.000000           -2.000000
                        DEM( 7)        0.000000           -2.000000
                        DEM( 8)        0.000000           -3.000000
                        DEM( 9)        0.000000           -4.000000
                       DEM( 10)        0.000000           -4.000000
                       DEM( 11)        0.000000           -5.000000





a.
model:
sets:
Warehouse/1..3/:a;
Customer/1..4/:b;
Routes(Warehouse,Customer):c,x;
endsets
data:
a=15,25,5;
b=5,15,15,10;
c=10,2,20,11,12,7,9,20,2,14,16,18;
enddata
[obj]min=@sum(Routes:c*x);
@for(Warehouse(i):[SUP]
@sum(Customer(j):x(i,j))<=a(i));
@for(Customer(j):[DEM]
@sum(Warehouse(i):x(i,j))=b(j));
end



  Global optimal solution found.
  Objective value:                              335.0000
  Infeasibilities:                              0.000000
  Total solver iterations:                             5


                       Variable           Value        Reduced Cost
                          A( 1)        15.00000            0.000000
                          A( 2)        25.00000            0.000000
                          A( 3)        5.000000            0.000000
                          B( 1)        5.000000            0.000000
                          B( 2)        15.00000            0.000000
                          B( 3)        15.00000            0.000000
                          B( 4)        10.00000            0.000000
                       C( 1, 1)        10.00000            0.000000
                       C( 1, 2)        2.000000            0.000000
                       C( 1, 3)        20.00000            0.000000
                       C( 1, 4)        11.00000            0.000000
                       C( 2, 1)        12.00000            0.000000
                       C( 2, 2)        7.000000            0.000000
                       C( 2, 3)        9.000000            0.000000
                       C( 2, 4)        20.00000            0.000000
                       C( 3, 1)        2.000000            0.000000
                       C( 3, 2)        14.00000            0.000000
                       C( 3, 3)        16.00000            0.000000
                       C( 3, 4)        18.00000            0.000000
                       X( 1, 1)        0.000000            13.00000
                       X( 1, 2)        5.000000            0.000000
                       X( 1, 3)        0.000000            16.00000
                       X( 1, 4)        10.00000            0.000000
                       X( 2, 1)        0.000000            10.00000
                       X( 2, 2)        10.00000            0.000000
                       X( 2, 3)        15.00000            0.000000
                       X( 2, 4)        0.000000            4.000000
                       X( 3, 1)        5.000000            0.000000
                       X( 3, 2)        0.000000            7.000000
                       X( 3, 3)        0.000000            7.000000
                       X( 3, 4)        0.000000            2.000000

                            Row    Slack or Surplus      Dual Price
                            OBJ        335.0000           -1.000000
                        SUP( 1)        0.000000            5.000000
                        SUP( 2)        0.000000            0.000000
                        SUP( 3)        0.000000            0.000000
                        DEM( 1)        0.000000           -2.000000
                        DEM( 2)        0.000000           -7.000000
                        DEM( 3)        0.000000           -9.000000
                        DEM( 4)        0.000000           -16.00000


b.
model:
sets:
Warehouse/1..3/:a;
Customer/1..4/:b;
Routes(Warehouse,Customer):c,x;
endsets
data:
a=7,25,26;
b=10,10,20,15;
c=8,4,1,2,6,9,4,7,5,3,4,3;
enddata
[obj]min=@sum(Routes:c*x);
@for(Warehouse(i):[SUP]
@sum(Customer(j):x(i,j))<=a(i));
@for(Customer(j):[DEM]
@sum(Warehouse(i):x(i,j))=b(j));
end
  Global optimal solution found.
  Objective value:                              193.0000
  Infeasibilities:                              0.000000
  Total solver iterations:                             7


                       Variable           Value        Reduced Cost
                          A( 1)        7.000000            0.000000
                          A( 2)        25.00000            0.000000
                          A( 3)        26.00000            0.000000
                          B( 1)        10.00000            0.000000
                          B( 2)        10.00000            0.000000
                          B( 3)        20.00000            0.000000
                          B( 4)        15.00000            0.000000
                       C( 1, 1)        8.000000            0.000000
                       C( 1, 2)        4.000000            0.000000
                       C( 1, 3)        1.000000            0.000000
                       C( 1, 4)        2.000000            0.000000
                       C( 2, 1)        6.000000            0.000000
                       C( 2, 2)        9.000000            0.000000
                       C( 2, 3)        4.000000            0.000000
                       C( 2, 4)        7.000000            0.000000
                       C( 3, 1)        5.000000            0.000000
                       C( 3, 2)        3.000000            0.000000
                       C( 3, 3)        4.000000            0.000000
                       C( 3, 4)        3.000000            0.000000
                       X( 1, 1)        0.000000            5.000000
                       X( 1, 2)        0.000000            3.000000
                       X( 1, 3)        7.000000            0.000000
                       X( 1, 4)        0.000000            1.000000
                       X( 2, 1)        9.000000            0.000000
                       X( 2, 2)        0.000000            5.000000
                       X( 2, 3)        13.00000            0.000000
                       X( 2, 4)        0.000000            3.000000
                       X( 3, 1)        1.000000            0.000000
                       X( 3, 2)        10.00000            0.000000
                       X( 3, 3)        0.000000            1.000000
                       X( 3, 4)        15.00000            0.000000

                            Row    Slack or Surplus      Dual Price
                            OBJ        193.0000           -1.000000
                        SUP( 1)        0.000000            3.000000
                        SUP( 2)        3.000000            0.000000
                        SUP( 3)        0.000000            1.000000
                        DEM( 1)        0.000000           -6.000000
                        DEM( 2)        0.000000           -4.000000
                        DEM( 3)        0.000000           -4.000000
                        DEM( 4)        0.000000           -4.000000