Why are nonnegative constraints included in a factory production linear programming model?

In a factory production linear programming model, nonnegative constraints (e.g., $x_1\ge 0$ and $x_2\ge 0$) are included because it is physically impossible to produce a negative quantity of a commodity.12

These constraints are fundamental to defining the set of feasible solutions. By requiring that production variables remain greater than or equal to zero, the model ensures that the solution space is restricted to realistic, achievable outcomes. In graphical representations, these constraints confine the feasible region to the first quadrant of the coordinate plane, lying on or above the axes. Furthermore, in algebraic methods like the simplex method, these restrictions are essential for maintaining valid solutions, as increasing variables beyond certain limits would otherwise result in negative values for other variables, such as slack variables, which would violate the problem's constraints.123