# UGC-NET | UGC NET CS 2015 Jun – III | Question 69

• Last Updated : 18 Jun, 2018

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 dual problem has a finite optimal solution, the other one also possesses the same, and the optimal value of the objective functions of the two problems are equal.
Which of the following is true?
(A) S1 and S2
(B) S1 and S3
(C) S2 and S2
(D) S1 , S2 and S3

Explanation:

• The dual of the dual linear programming problem is again the primal problem. Correct
• If either the primal or the dual problem has an unbounded objective function value, the other problem has no feasible solution. Correct
• If either the primal or dual problem has a finite optimal solution, the other one also possesses the same, and the optimal value of the objective functions of the two problems are equal.Correct

All statement are correct.
So, option (D) is correct.

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