disp('initial data')
initial data
A=[3 2 1 1 0 0

A =

     3     2     1     1     0     0
     1     1     2     0     1     0
     2     1     1     0     0     1

1 1 2 0 1 0
2 1 1 0 0 1]
[m,n]=size(A)

m =

     3


n =

     6

b=[36; 32; 22]

b =

    36
    32
    22

c=[10 7 6 0 0 0 ]'

c =.


    10
     7
     6
     0
     0
     0

pause
disp('optimal basis - nonbasic variables')
optimal basis - nonbasic variables
B=[2 5 3]

B =

     2     5     3

N=[1 4 6]

N =

     1     4     6

[x isort]=sort([B N]);
pause
disp('optimal basis matrix')
optimal basis matrix
A_B=A(:,B)

A_B =

     2     0     1
     1     1     2
     1     0     1

pause
disp('inverse of optimal basis matrix')
inverse of optimal basis matrix
A_Bi=inv(A_B)

A_Bi =

     1     0    -1
     1     1    -3
    -1     0     2

pause
disp('optimal primal solution x')
optimal primal solution x
x_B=A_Bi*b

x_B =

    14
     2
     8

x_N=zeros(n-m,1);x=[x_B;x_N]; x=x(isort)     % sorted true x

x =

     0
    14
     8
     0
     2
     0

pause
disp('c_B and dual vrbles y')
c_B and dual vrbles y
c_B=c(B)

c_B =

     7
     0
     6

y=(c_B'*A_Bi)'

y =

     1
     0
     5

pause
disp('verify dual feasibility and complementary slackness')
verify dual feasibility and complementary slackness
[A'*y-c   x]

ans =

     3     0
     0    14
     0     8
     1     0
     0     2
     5     0

pause
disp('reduced costs')
reduced costs
c'-y'*A

ans =

    -3     0     0    -1     0    -5

pause
disp('row 1 of current tableau for ratio test for basic c_2 change')
row 1 of current tableau for ratio test for basic c_2 change
Abar=A_Bi*A;
Abar(1,N)

ans =

     1     1    -1

pause
disp('row 2 of current tableau for ratio test for basic c_5 change')
row 2 of current tableau for ratio test for basic c_5 change
Abar=A_Bi*A;
Abar(2,N)

ans =

    -2     1    -3

pause
disp('row 3 of current tableau for ratio test for basic c_3 change')
row 3 of current tableau for ratio test for basic c_3 change
Abar=A_Bi*A;
Abar(3,N)

ans =

     1    -1     2

pause

echo off