In linear programming, what does the constraint X1 ≥ 0 signify?

In linear programming, what does the constraint X1 ≥ 0 signify?

• A. Nonnegativity constraint
• B. Upper bound
• C. Integer constraint
• D. None

Answer: (A)

Nonnegativity constraint. In linear programming, X1 ≥ 0 means X1 cannot take negative values. This mirrors real-world quantities like the number of units produced, amount of a resource used, or money invested, which cannot be negative. By enforcing X1 ≥ 0, the feasible region is restricted to nonnegative values, ensuring the solution makes sense for practical quantities. It’s not an upper bound (that would be X1 ≤ something) and it’s not an integer requirement (that would be something like X1 is an integer).

Nonnegativity constraint. In linear programming, X1 ≥ 0 means X1 cannot take negative values. This mirrors real-world quantities like the number of units produced, amount of a resource used, or money invested, which cannot be negative. By enforcing X1 ≥ 0, the feasible region is restricted to nonnegative values, ensuring the solution makes sense for practical quantities. It’s not an upper bound (that would be X1 ≤ something) and it’s not an integer requirement (that would be something like X1 is an integer).