Slack and surplus variables are required to be non-negative because they represent unused resources or excess amounts, and these values cannot be less than zero.

Non-negativity constraints are used because decision variables usually represent quantities that cannot be negative, such as products produced, money invested, or resources allocated.

Slack and surplus variables must have non-negativity constraints because they represent unused or excess amounts, which cannot be negative.

Both slack and surplus variables must be non-negative because they represent physical or logical quantities—specifically, unused resource capacity and excess achievement over a minimum requirement—that cannot be less than zero. If they were allowed to be negative, it would imply that resources were over-consumed or minimum requirements were unmet, contradicting the original inequality constraints. Furthermore, standard linear programming algorithms like the Simplex method require all variables to be non-negative to properly define the boundaries of the feasible region and ensure valid mathematical operations.