What does the nonnegativity constraint mean in linear programming?

What does the nonnegativity constraint mean in linear programming?

• A. Decision variables can take any real value
• B. Decision variables must be greater than or equal to zero
• C. Constraints must be nonnegative
• D. Objective function must be nonnegative

Answer: (B)

Nonnegativity means decision variables must be greater than or equal to zero. In linear programming, these variables represent quantities like production levels or resource amounts, which cannot be negative. This requirement confines the feasible solutions to the portion of the plane where all variables are nonnegative, often called the first-quadrant region, and shapes the feasible set along with any other constraints. It doesn’t say anything about the constraints themselves or the objective function being nonnegative. Saying the variables can take any real value would ignore the nonnegativity restriction. Saying constraints must be nonnegative misstates where the restriction applies, since it’s the variables that are constrained. The objective function being nonnegative is not a requirement; the objective can be negative or positive depending on the problem.

Nonnegativity means decision variables must be greater than or equal to zero. In linear programming, these variables represent quantities like production levels or resource amounts, which cannot be negative. This requirement confines the feasible solutions to the portion of the plane where all variables are nonnegative, often called the first-quadrant region, and shapes the feasible set along with any other constraints. It doesn’t say anything about the constraints themselves or the objective function being nonnegative. Saying the variables can take any real value would ignore the nonnegativity restriction. Saying constraints must be nonnegative misstates where the restriction applies, since it’s the variables that are constrained. The objective function being nonnegative is not a requirement; the objective can be negative or positive depending on the problem.