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The fundamental goal in solving such linear programming problems is to maximize or minimize the objective function given the linear constraints on the solution.
It may even happen that some tableau is repeated in a sequence of degenerate pivot steps.
It may even happen that some tableau is repeated in a sequence of degenerate pivot steps, and so the algorithm might pass through an infinite sequence of tableau without any progress. A pivot rule is a rule for selecting the entering variable if there are several possibilities, which is usually the case(in our algorithm determine this element).
The Simplex Method starts at some point within the feasible region, and then with each iteration of the algorithm maps from one adjacent corner (representing a possible solution to the problem) of the convex polytope to another, such that each step gives a better or equivalent solution than the one in the previous step.
This is hardly a satisfactory description of the Simplex Method, so if the reader wants a more insightful intuition into the method, I recommend visiting this article, or watching the first two short videos on the Simplex Method video series by Patrick JMT, which give a good introduction into the kinds of problems the Method solves and how it works.
In the previous part we implemented and tested the simplex method on a simple example, and it has executed without any problems. In the first part, we have seen an example of the unbounded linear program.
What will happen if we apply the simplex algorithm for it?
In the following embedded Jupyter Notebook, I implement a version of the Simplex Method that uses matrix operations in Num Py instead of the tableau method to solve linear constrained optimization problems.
As such, we obtain a far more efficient, concise, and natural implementation of the Simplex Method.
Upon taking classes in operations research or optimization (particularly at the undergraduate level) and reviewing the resources available online that cover the Simplex Method, one will almost certainly be introduced to the method for solving linear programming problems with the Simplex method.
Some examples of solving linear programming problems with the tableau method are given here and here.