Föreläsningar del 3 Flashcards
(16 cards)
Q: What is the objective of a linear programming problem?
A: The maximization or minimization of a quantity, subject to constraints.
Q: What defines a feasible solution in LP?
A: A solution that satisfies all constraints of the problem.
Q: What is an optimal solution in LP?
A: A feasible solution that provides the best objective function value.
Q: When is a problem considered a linear programming problem?
A: When both the objective function and constraints are linear.
Q: What are the three possible outcomes of an LP problem?
A: Infeasibility, a unique or alternate optimal solution, or an unbounded solution.
Q: What is the objective function coefficient of slack and surplus variables?
zero
Q: What are extreme points in LP?
A: The corner points of the feasible region.
Q: Why are extreme points important in LP?
A: The optimal solution always occurs at an extreme point.
Q: What shapes can the feasible region take?
A: A single point, a line, a polygon, or an unbounded area.
Q: What are the main steps of the simplex method?
A: Formulate the problem, put it in standard form, put it in tableau form, and execute the simplex algorithm.
Q: What is the purpose of an artificial variable in the simplex method?
A: To transform constraints into equalities when there is no natural basic variable.
Q: When should a problem be stopped in the simplex method?
A: If all cj - zj values are ≤ 0, or if an artificial variable remains positive in the final tableau.
Q: What does it mean if all entries in an entering column are non-positive?
A: The LP problem has an unbounded solution.
- Q: What is a linear function?
A: A function where each variable appears in a separate term raised to the first power and is multiplied by a constant.
- Q: What are the three types of constraints in linear programming?
A: “Less than or equal to” (≤), “equal to” (=), and “greater than or equal to” (≥).
- Q: What is problem formulation in linear programming?
A: The process of translating a verbal statement into a mathematical statement.
