Given the following statements with respect to linear programming problem: S1:…
2015
Given the following statements with respect to linear programming problem:
S1: The dual of the dual linear programming problem is again the primal problem
S2: If either the primal or the dual problem has an unbounded objective function value, the other problem has no feasible solution
S3: If either the primal or the dual problem has a finite optimal solution, the other one also possess the same, and the optimal value of the objective functions of the two problems are equal.
Which of the following is true ?
Answer: D. S1, S2 and S3 — Answer: All three statements (S1, S2 and S3) are true. Short justifications: S1: Taking the dual of the dual returns the original primal problem. In standard…
- A.
S1 and S2
- B.
S1 and S3
- C.
S2 and S3
- D.
S1, S2 and S3
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Show answer & explanation
Correct answer: D
Answer: All three statements (S1, S2 and S3) are true. Short justifications:
S1: Taking the dual of the dual returns the original primal problem. In standard finite-dimensional linear programming formulations, dualizing twice restores the original variable and constraint roles, so the dual of the dual is the primal.
S2: If one problem (primal or dual) is unbounded, the other must be infeasible. This follows from weak duality: a feasible solution to one problem provides bounds on the objective of the other, so unboundedness on one side contradicts feasibility on the other.
S3: If either problem has a finite optimal solution, the other also has a finite optimal solution and the optimal objective values are equal. This is the strong duality theorem for linear programming.
Conclusion: All three statements are correct, so the correct choice is the option that includes S1, S2 and S3.