This is repeated until it is clear that the current BFS can't be improved for a better objective value. It is clear that one factor is crucial to the method: which variable should replace which.
The variable which is replaced is called the leaving variable and the variable which replaces it is known as the entering variable.
Since the objective function is the same for both models so an optimal solution for the standard model will be optimal for the original model as well.
Therefore we need to bother only about the standard model.
The following table summarizes all the basic solutions to the problem: . This procedure of solving LP models works for any number of variables but is very difficult to employ when there are a large number of constraints and variables.
For example, for m = 10 and n = 20 it is necessary to solve sets of equations, which is clearly a staggering task.
To decide the leaving variable we apply what is sometimes called as the feasibility condition.
That is as follows: we compute the quotient of the solution coordinates (that are 24, 6, 1 and 2) with the constraint coefficients of the entering variable (that are 6, 1, -1 and 0).
Now what are the candidates for the optimal solution?
They are the solutions of the equality constraints.