Which statement best describes nonnegativity constraints in LP?

• A. They require all decision variables to be nonnegative
• B. They require variables to be integers
• C. They set an upper bound
• D. They are optional

Answer: (A)

Nonnegativity constraints in linear programming require every decision variable to be nonnegative, meaning each x_j must be at least zero. This reflects real-world quantities such as produced units or materials used, which can’t be negative. Because of this, the feasible region lies in the nonnegative quadrant, ensuring solutions are physically meaningful. This constraint is not about integrality—whether a variable must be an integer is a separate consideration handled in integer programming. It also doesn’t by itself set an upper bound; upper limits come from other constraints or explicit bounds like x_j ≤ U_j. In standard LP formulations, nonnegativity is assumed rather than optional, though you can reformulate a variable that could be negative by expressing it as the difference of two nonnegative variables if needed.