Linear Programming Terminology

A constraint is a mathematical expression that represents the objective of a linear programming model.

The problem formulation is the translation of a mathematical model into a verbal statement.

A decision variable is a controllable output for a linear programming model.

Nonnegativity constraints require all variables to be negative.

A linear programming model is a mathematical model with a nonlinear objective function, a set of nonlinear constraints, and negative variables.

A linear function is a mathematical expression in which the variables appear in separate terms and are raised to the second power.

A feasible solution is a solution that does not satisfy all the constraints.

The feasible region is the set of all infeasible solutions.

A slack variable is a variable added to the right-hand side of a less-than-or-equal-to constraint to convert the constraint into an inequality.

The standard form of a linear program is a linear program in which all the constraints are written as inequalities.

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

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

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.

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.

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.