Linear programming - Simplex Method - Stuck with picking the right 'generator'

[Eni]

Dear All,

Thank you for reading my post. I'm stuck with picking the correct 'generator' element in the attached example (Simplex method). As you can see, the solution keeps picking the yellow elements as 'generators', but I don’t understand why we can't choose the purple ones.
Can somebody please explain?

View attachment 9042

 

[jvicens]

Dear [Forum User],

Thank you for reaching out with your question. As a scientist with expertise in mathematical optimization, I would be happy to provide some insight into your query.

In the attached example, the Simplex method is being used to solve a linear programming problem. The purpose of this method is to find the optimal solution to a problem by iteratively pivoting between different "basic feasible solutions" or "bases". In this context, the term "generator" refers to the basic variable that is used to create the next basic feasible solution.

In the Simplex method, the choice of generator is crucial as it determines the direction in which the algorithm moves towards the optimal solution. In this particular example, the yellow elements have been chosen as generators because they are the most restrictive variables in the current basic feasible solution. This means that they have the most impact on the objective function and therefore need to be adjusted in order to reach the optimal solution.

On the other hand, the purple elements are not as restrictive and do not have as much impact on the objective function. Therefore, choosing them as generators would not lead to an optimal solution.

I hope this explanation helps to clarify why the yellow elements are chosen as generators in this example. Please let me know if you have any further questions or need additional clarification.