Consider the following statements with respect to duality in LPP: (a) The…
2019
Consider the following statements with respect to duality in LPP:
(a) The final simplex table giving optimal solution of the primal also contains optimal solution of its dual in itself
(b) If either the primal or the dual problem has a finite optimal solution, then the other problem also has a finite optimal solution
(c) If either problem has an unbounded optimum solution, then the other problem has no feasible solution at all
Which of the statements is (are) correct?
- A.
Only (a) and (b)
- B.
Only (a) and (c)
- C.
only (b) and (c)
- D.
(a), (b) and (c)
Attempted by 16 students.
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Correct answer: D
Answer: All three statements are true.
Statement (a): The final simplex tableau of the primal contains the optimal dual solution because the simplex multipliers (shadow prices or row multipliers) computed in the final tableau satisfy the dual constraints and yield the dual objective equal to the primal optimum.
Statement (b): By the strong duality theorem, if one problem (primal or dual) has a finite optimal solution, the other is feasible and attains the same finite optimal objective value.
Statement (c): If one problem is unbounded (its objective can be made arbitrarily large in the feasible region), the other problem must be infeasible. For example, a primal maximization that is unbounded implies there is no feasible dual solution that bounds the objective.
Therefore, (a), (b) and (c) are all correct.