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Non-negativity constraints in a Linear Programming problem is represented as :

  • A.X \(\geq\) 0 and Y \(\leq\) 0
  • B.X \(\leq\) 0 and Y \(\geq\) 0
  • C.X \(\leq\) 0 and Y \(\leq\) 0
  • D.X \(\geq\) 0 and Y \(\geq\) 0

Answer: D

The non-negativity constraints are X \(\geq\) 0 and Y \(\geq\) 0.

In a linear programming problem the decision variables represent physical quantities, such as units of two products to be made, which cannot be negative. Every LP formulation therefore adds the constraints that each variable is greater than or equal to zero, which confines the feasible region to the first quadrant.

The other options require one or both variables to be zero or negative, which would describe meaningless negative production levels.

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