Use The Simplex Method To Solve The Linear Programming Problem

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There is one very big problem with that line of reasoning, however.

If we move any more than 8, we're leaving the feasible region.

When we placed the objective function into the tableau, we moved the decision variables and their coefficients to the left hand side and made them negative.

Therefore, the most negative number in the bottom row corresponds to the most positive coefficient in the objective function and indicates the direction we should head.

Therefore, we have to move the smallest distance possible to stay within the feasible region.

The pivot row is the row that has the smallest non-negative ratio.We are moving off of the line corresponding to the non-basic variable in the pivot column.That means that variable is exiting the set of basic variables and becoming non-basic. Now that we have a direction picked, we need to determine how far we should move in that direction.A positive value in the bottom row of the tableau would correspond to a negative coefficient in the objective function, which means heading in that direction would actually decrease the value of the objective.That's not what we want to do if we want a maximum value, so we stop when there are no more negatives in the bottom row of the objective function.Note that you can resize the problem using the menu "Add Row" and "Delete Row" To begin the calculations click on one of these two actions: 1) Step by Step Execution: This option will run the Simplex algorithm showing each iteration: A window opens showing how the algorithm pivoting matrix at each step, the solutions and some statistics, such as phase, number of steps of the simplex, the indexes on the base ...Within this option, select 1a) for the calculation mode "Fraction Mode" or "numeric mode" 1b) Next step: This option will Avanze a new step in the simplex algorithm 1c) Back to Menu: Closes the current window and returns to the original with the simplex algorithm.At the same time the maximum processing time for a linear programming problem is 20 second, after that time any execution on the simplex algorithm will stop if no solution is found.As the independent terms of all restrictions are positive no further action is required.Form the ratios between the non-negative entries in the right hand side and the positive entries in the pivot column for each of the problem constraints. Do not find the ratio if the element in the pivot column is negative or zero, but do find the ratio if the right hand side is zero. We can also tell which line we'll be moving to by looking at the variable that is basic for that row. Your first thought might be that since we're gaining for every unit we move, we should move as many units as we can.If we move 8 units, we gain ×8 = 320, if we move 9 units, we gain ×9 = 360, and if we move 16 units, we gain ×16 = 640.


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