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

• MHB
• Eni
In summary: Your Name]In summary, the Simplex method is being used to solve a linear programming problem by pivoting between different "basic feasible solutions" or "bases". The choice of generator is crucial as it determines the direction towards the optimal solution. In this example, the yellow elements are chosen as generators because they are the most restrictive and have the most impact on the objective function. Choosing the purple elements as generators would not lead to an optimal solution.
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.

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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.

## 1. What is linear programming?

Linear programming is a mathematical method used to optimize a linear objective function, subject to a set of linear constraints. It is commonly used to find the best possible solution to a problem with multiple variables and constraints.

## 2. What is the simplex method?

The simplex method is an algorithm used to solve linear programming problems. It involves systematically moving from one feasible solution to another, with the goal of finding the optimal solution.

## 3. How does the simplex method work?

The simplex method works by starting at a feasible solution and then moving to adjacent feasible solutions that improve the objective function until the optimal solution is reached. This process continues until no further improvement can be made.

## 4. How do I choose the right generator for the simplex method?

The choice of generator for the simplex method depends on the specific problem being solved. Generally, the most commonly used generators are the two-phase method, the Big M method, and the revised simplex method. It is important to carefully consider the constraints and objective function of the problem to determine which generator will be most effective.

## 5. What should I do if I am stuck with picking the right generator?

If you are having trouble selecting the right generator for your linear programming problem, it is best to consult with a mathematical expert or utilize a software program that can help guide you in the decision-making process. It is important to carefully consider the constraints and objective function of the problem to determine the most suitable generator.

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