Simplex Method Iteration Calculator

About this calculator

Dantzig's simplex method solves linear programming problems by walking along the vertices of the feasible region's polytope, improving the objective value at each step until no further improvement is possible. One pivot iteration on the tableau consists of picking the entering variable (usually the column with the most negative coefficient in the objective row, for a maximization problem) and the leaving variable (found via the minimum-ratio test on the RHS column, to keep all values feasible), then performing Gauss-Jordan elimination around that pivot element.

This calculator takes a simplex tableau — with the objective in the last row and the right-hand-side values in the last column — and executes exactly one pivot step, returning the updated tableau so you can see the entering/leaving variable choice and the arithmetic explicitly. Operations research and linear programming students use it to check a single hand-worked iteration of a larger simplex problem, rather than a solver that jumps straight to the optimal solution.