Simplex Method Questions

Simplex Method Questions

• What are the key steps involved in formulating a linear programming problem?
• How do you identify the objective function and constraints in a word problem?
• What are the different types of constraints in linear programming (e.g., equality, inequality)?
• Explain how to express a linear programming problem in standard form.
• Describe the concept of slack variables and their role in the simplex method.
• What are artificial variables and when are they used in the simplex method?
• How do you determine the pivot column and row in the simplex method?
• Explain the concept of the simplex tableau and its components.
• How do you interpret the optimal solution from the final simplex tableau?
• Describe the concept of unbounded solutions in linear programming and how the simplex method detects them.

Formulating Linear Programs

• Linear programming problems consist of an objective function, decision variables, and constraints.
• The objective function defines the quantity to be maximized or minimized.
• Decision variables represent the choices that need to be made.
• Constraints represent the limitations or restrictions on the decision variables.
• Constraints are expressed as linear inequalities or equalities.
• Formulation involves identifying the objective, decision variables, and constraints from a word problem.
• It's crucial to carefully define the variables to ensure the problem is accurately represented.
• The problem can be solved using the simplex method.

Revised Simplex Method

• The revised simplex method is an alternative algorithm for solving linear programs.
• It maintains a triangular matrix of the constraint coefficients.
• Updating the basis involves factorizations, maintaining sparsity.
• This contrasts with the standard simplex method's pivotal operations.
• It involves updating the inverse basis and calculation of current variables rather than whole tableaus.
• The revised simplex is numerically stable.
• The revised simplex method is, in many cases, preferred to the standard method, especially with large-scale problems.
• The method avoids creating entire tableaus and focusing on just the essentials.
• Improved numerica stability is a primary benefit.