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A mathematical method for determining a way to achieve the best outcome in a given mathematical model for some list of requirements represented as linear relationships.

Restrictions or conditions expressed as linear inequalities or equations that define the feasible region within which the linear programming problem must be solved.

A situation in linear programming where multiple basic feasible solutions correspond to the same corner point of the feasible region, which may cause the simplex algorithm to stall.

The amount by which an objective function coefficient must improve before it would be possible for the corresponding variable to assume a positive value in the optimal solution.

A linear function that is optimized (maximized or minimized) subject to the constraints of the linear programming problem.

An approach used in linear programming to find a basic feasible solution by incorporating artificial variables with a very large positive or negative coefficient (M) into the objective function.

In the context of the simplex method, a basis is a set of linearly independent vectors equal to the number of constraints. A basic feasible solution is a solution obtained by setting non-basis variables to zero and solving for the basis variables.

An additional variable introduced into a linear programming problem to turn an inequality constraint into an equality, facilitating the use of the simplex method.

The change in the optimal value of the objective function of a linear programming problem per unit increase in the right-hand side of a constraint, assuming all other data remains constant.

A set of constraints in linear programming problems that require all the decision variables to be non-negative, ensuring that the solutions make practical sense in real-world scenarios.

The set of all possible points that satisfy all the given constraints of a linear programming problem, typically visualized graphically as a polygon or polyhedron.

In linear programming, the dual problem involves the maximization of a linear function subject to linear inequalities, and is associated with the minimization problem of the primal by a relationship known as duality.

An algorithm for solving linear programming problems by systematically testing vertices of the feasible region to find the optimal value of the objective function.

A concept in linear programming where every linear programming problem (the primal) has a corresponding dual problem, with a strong connection between their solutions.