At the following lines, we will give a brief and simple explanation about how to use the PHPSimplex tool. Once you had modeled the problem, that is, you have indentified the objetive function to maximize/minimize and its restrictions, you can be sure that the hardest work is done.Let the PHPSimplex work for us.
Let's suppose that the modeled problem is the same that can be found in the section example of Simplex method, wich have 2 basic or decision variables and 3 restrictions. Then only have to indicate to the program, such data, like can be viewed in the screenshot.
Click in continue. You must keep on providing data of the problem, in order to the algorithm be able to resolve it. Facing the cuestion, "Wich is the objetive of the function?", you should choose from the folder if you want Maximize or Minimize, in the event that employs us you would take "Maximize". Fill in adequately the boxes of "Function" with the properly arguments for each decision variable, for this example it will be 3 and 2. Work at the same way to fill the restrictions' boxes, taking special care with the inecuation type for each one, because you can choose from folder "≥", "≤" or "=".
Don't worry about negative values of the decision variables, due to PHPSimplex do it for itself instead you. You should see something like its show in the following figure.
Now, you are facing the problem, type for you, and the problem taken in standard form have been made automatically by the tool. For comfort of those that don't wish to observe each repetition of the Simplex Method (or Two-Phase Simplex Method), has been released an option of "Direct Solution", although you can choose by "Continue" to see the Simplex Method's boards (or Two-Phase Simplex Method).
PHPSimplex will show you each iteration of the method that is being executed. The element wich have green background colour, is the pivot element of the board.
You only have to click on continue, until the method end. At that case, the element with green background colour is the final result, and is given a little text that helps to interprete the final result.
In order to finalize this guide for the tool, we will do mention to the case of that is accomplishing a problem and is necessary to do the Two-Phase Simplex Method. In the step of show the problem in standard form, PHPSimplex will notice you that you are goint into Phase I of the Two-Phase Simplex Method.
When the iterations are made, in the event that the original problem has solution, it is indicated that you will go to Phase II...
... or at the event that the problem has not solution, such information is given.
For the left iterations of the Two-Phase Simplex Method, the way to execute is the same.