Linear Programming Terminology

Linear Programming Terminology

• A constraint is an equation or inequality that rules out certain combinations of decision variables as feasible solutions.

Problem Formulation

• Problem formulation is the process of translating a verbal statement of a problem into a mathematical statement, resulting in a mathematical model.

Decision Variables and Nonnegativity Constraints

• A decision variable is a controllable input for a linear programming model.
• Nonnegativity constraints require all variables to be nonnegative.

Linear Programming Models

• A linear programming model is a mathematical model with a linear objective function, a set of linear constraints, and nonnegative variables.
• A linear function is a mathematical expression where variables appear in separate terms and are raised to the first power.
• A linear program is another term for a linear programming model.

Feasible Solutions and Regions

• A feasible solution is a solution that satisfies all the constraints.
• The feasible region is the set of all feasible solutions.

Slack Variables and Standard Form

• A slack variable is added to the left-hand side of a less-than-or-equal-to constraint to convert it into an equality, representing the amount of unused resource.
• Standard form is a linear program where all constraints are written as equalities, with the optimal solution being the same as the original linear program.

Redundant Constraints and Extreme Points

• A redundant constraint does not affect the feasible region and can be removed without affecting the feasible region.
• An extreme point is a feasible solution point occurring at the vertices or “corners” of the feasible region, determined by the intersection of the constraint lines in two-variable problems.