The Simplex Method

The simplex method is used to allocate to provide an optimal allocation of resources to maximise a function called the 'objective function;. To start the simplex method, we require an initial basic feasible solution. The simplex algorithm proceeds according to the following rules.
1. Find the largest negative entry in the objective row and choose that labelled column.
2. Compute the ratios of the solution values to the corresponding elements in the labelled column. Choose the row with the minimum ratio and pivot on that member for the rest of the column.
3. Repeat step 1 on the resulting tableau.

The algorithm stops according to the following rules.
a) If there are no negative entries in the objective row then the finite optimal solution exists and the algorithm stops.
b) If all the entries in the pivotal column are negative, then no finite optimal solution exists and the algorithm stops.
We can draw the flowchart below.