Given the difficulty and the major role played by the process of reaching the optimal solution in addressing the systems of facilities, laboratories, or government institutions, by making the appropriate decision or the optimal alternative from among the group of alternatives or scientific decisions available using various economic, administrative, and statistical sciences, it has therefore become necessary to find ways that facilitate the owners of Factories, factories, etc. The process of making decisions that fit the vision of these companies. Scientists have found many methods of linear programming, and one of these methods is the simplex method or (the method of tables).

A mathematical approach for calculating a linear function's maximum or minimum value under specific constraints is known as Linear program (LP).

 LP is a mathematical technique for determining how to achieve the best outcome (such as the highest profit or the lowest cost) in a specific mathematical model for a set of needs defined by linear relationships. LP is a technique for profit maximization that also guarantees the optimization of a linear objective function. This is accomplished by applying linear equality or linear inequality constraints to the objective function.

To solve problems with more than two variables and to increase profits or decrease losses in companies, sectors, and other economic endeavors, the simplex method (SM), also known as table method, is regarded as one of the key techniques in linear programming. In 1947, the British mathematician Dantizg G. developed this technique. Using this approach, he started by identifying a potential basic starting solution and then progressed to a potential basic solution that would be superior to the original solution by swapping out one of the non-basic variables with the basic variables.

The simplex method (SM) goes through predictable processes. The process begins with a basic initial solution (corner point), moves to an adjacent solution (adjacent corner point), and repeats this process whenever the new solution is better than the previous one and better than any adjacent corner point (the objective function improves in every step - every table).

The results of the optimization test indicated that we have not yet found the best option (it can be made better).

Steps to solve linear programming using the simplex method:

1-     Converting linear programming from the usual form to the standard form by adding variables

2-    Design the table based on the constraints coefficients and the objective function.

3-    Determine the internal variable and the pivot column

4-    Define the external variable and the pivot row.

5-    Determine the pivot element, which is the element resulting from the intersection of the column of the input variable and the row of the output variable.

6-    Obtaining the pivot equation by dividing the values in the row of the output variable by the pivot element.

7-    The optimal solution to this maximization problem can be obtained when all parameters of the new objective function in the solution table are greater than or equal to zero. However, if a negative number is found, this means that the optimal solution has not been reached, and the steps from step 3 are repeated and we continue until we obtain the optimum solution.