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When we fill in the table, why do we need to add both a Surplus variable (S) and an Artificial variable (A) when we have a less than or equal constraint? Couldn't we just use one of them to balance the equation?

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Actually, for a less-than-or-equal (≤) constraint, you normally do not need both a surplus and an artificial variable. You only add a slack variable (S) with a positive sign to convert the inequality into an equation. For example, \(2x+y\le10\) becomes \(2x+y+S=10\). Surplus and artificial variables are generally needed for ≥ or = constraints, where a surplus variable alone cannot provide the initial basic variable required by the Simplex method.

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