What is the purpose of adding a slack variable to a constraint such as 2x + 3y ≤ 12?
Correct answer: C. To convert the inequality into an equality
- A. To remove the non-negativity requirement
- B. To change a maximization problem into minimization
- C. To convert the inequality into an equality
- D. To make the objective function nonlinear
Explanation
A non-negative slack variable s converts the constraint into 2x + 3y + s = 12. The slack represents unused capacity, not a change in the objective or in the variable sign restrictions.
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Linear programming models the maximum or minimum of an objective function subject to linear constraints. Questions involve translating word conditions into inequalities, drawing the feasible region, identifying corner points and evaluating the objective function, including cases involving non-negativity restrictions and redundant constraints.
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