Which are the basic components of a linear programming problem?

Which are the basic components of a linear programming problem?

• A. Decision variables, nonnegativity, and objective function
• B. Decision variables, objective function, linear constraints, nonnegativity
• C. Only decision variables and constraints
• D. Nonnegativity and constraints

Answer: (B)

Linear programming is about finding the best values for decision variables to optimize an objective within constraints. The four pieces that define a complete LP model are: decision variables that represent the quantities you can choose; the objective function, a linear expression in those variables that you want to maximize or minimize; linear constraints that cap resources or requirements in a linear way; and nonnegativity restrictions ensuring the variables cannot be negative. With all four in place, you have a feasible region defined by the constraints and a objective to guide you to the best point within that region. If any piece is missing, the problem loses essential structure: without linear constraints there’s no defined feasible region; without an objective there’s nothing to optimize; without nonnegativity you could model impossible or nonsensical values; without the decision variables there’s nothing to optimize. Therefore, the complete set includes decision variables, the objective function, linear constraints, and nonnegativity.

Linear programming is about finding the best values for decision variables to optimize an objective within constraints. The four pieces that define a complete LP model are: decision variables that represent the quantities you can choose; the objective function, a linear expression in those variables that you want to maximize or minimize; linear constraints that cap resources or requirements in a linear way; and nonnegativity restrictions ensuring the variables cannot be negative. With all four in place, you have a feasible region defined by the constraints and a objective to guide you to the best point within that region. If any piece is missing, the problem loses essential structure: without linear constraints there’s no defined feasible region; without an objective there’s nothing to optimize; without nonnegativity you could model impossible or nonsensical values; without the decision variables there’s nothing to optimize. Therefore, the complete set includes decision variables, the objective function, linear constraints, and nonnegativity.