Q: explain the role of artificial variable in linear programming

A: In linear programming, a slack variable is required to turn an inequality into an equality where a linear combination of variables is less than or equal to a given constant in the former. [ As with the other variables in the augmented constraints, the slack variable cannot take on negative values, as the Simplex algorithm requires them to be positive or zero.
- If the slack variable associated

with a constraint is zero in a given state, the constraint is binding, as the constraint restricts the possible changes of the point.
- If a slack variable is positive in a given state, the constraint is non-binding, as the constraint does not restrict the possible changes of the point.
- If a slack variable is negative in a given state, the point is infeasible, and not allowed, as it does not satisfy the constraint.
]

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