The simplex method demonstrated in the previous section consists of the following steps.
1.
Transform the model constraint inequalities into equations.
2.
Set up the initial tableau for the basic feasible solution at the origin and compute the z _{ j } and c _{ j } z _{ j } row values.
3.
Determine the pivot column (entering nonbasic solution variable) by selecting the column with the highest positive value in the c _{ j } z _{ j } row.
4.
Determine the pivot row (leaving basic solution variable) by dividing the quantity column values by the pivot column values and selecting the row with the minimum nonnegative quotient .
5.
Compute the new pivot row values using the formula
6.
Compute all other row values using the formula
7.
Compute the new z _{ j } and c _{ j } z _{ j } rows.
8.
Determine whether or not the new solution is optimal by checking the c _{ j } z _{ j } row. If all c _{ j } z _{ j } row values are zero or negative, the solution is optimal. If a positive value exists, return to step 3 and repeat the simplex steps.