ratio test : select the corresponding variable Xn with the smallest ratio of right hand side coefficients of positive Xs coefficient. Put the Xn as a old basic variable which will be replaced by Xs and Xn will become a non-basic variable.
improve the solution by pivoting: Adjust the matrix to fit the new basic variable
is there any positive coefficient in the objective function ？
Select the corresponding variable Xs with the largest positive coefficient in the objective function as the new basic variable
an unbounded solution
is there any other positive coefficient in the column which includes the largest positive coefficient mentioned above？
an optimal solution: The basic variables are equal to zero and the non-basic variables are equal to the right hand side coefficients in the constraints.
yes
no
start pivoting
