% 
% Written by:
% -- 
% John L. Weatherwax                2007-07-01
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

clc; 
%%%format rat; 

tab = [ 2, -3, 1, -1, 1, 0, 0, 6 ; 1, 2, -1, 2, 0, 1, 0, 4; -3, 2, 1, -1, 0, 0, 1, 0 ]

% the first column is the pivot column; the first row is the pivot row: 
tab(1,:) = tab(1,:)/2;
tab(2,:) = -tab(1,:) + tab(2,:);
tab(3,:) = 3*tab(1,:) + tab(3,:);
tab

% the second column is the pivot column; the second row is the pivot row:
tab(2,:) = (2/7) * tab(2,:);
tab(1,:) = (3/2) * tab(2,:) + tab(1,:);
tab(3,:) = (5/2) * tab(2,:) + tab(3,:);
tab

% the fourth column is the pivot column; the second row is the row: 
[ 24/7, 2/7 ] ./ [ 4/7, 5/7 ] 

tab(2,:) = (7/5) * tab(2,:);
tab(1,:) = -(4/7) * tab(2,:) + tab(1,:);
tab(3,:) = (5/7) * tab(2,:) + tab(3,:);
tab

% this gives the solution: x_1 = 3.2; x_2 = 0; x_3 = 0; x_4 = 0.4; x_5 = 0; x_6 = 0; z = 10