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August 21, 2024UGC NET June-2019 CS Paper-2
August 22, 2024Duality
| Question 1 |
Given the following statements with respect to linear programming problem:
S 1 : The dual of the dual linear programming problem is again the primal problem
S 2 : If either the primal or the dual problem has an unbounded objective function value, the other problem has no feasible solution.
S 3 : 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?
S 1 : The dual of the dual linear programming problem is again the primal problem
S 2 : If either the primal or the dual problem has an unbounded objective function value, the other problem has no feasible solution.
S 3 : 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?
| S 1 and S 2 | |
| S 1 and S 3 | |
| S 2 and S 3 | |
| S 1 , S 2 and S 3 |
Question 1 Explanation:
S 1 : TRUE: The dual of the dual linear programming problem is again the primal problem
S 2 : TRUE: If either the primal or the dual problem has an unbounded objective function value, the other problem has no feasible solution.
S 3 : TRUE: 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.
S 2 : TRUE: If either the primal or the dual problem has an unbounded objective function value, the other problem has no feasible solution.
S 3 : TRUE: 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 Answer: D
Question 1 Explanation:
S 1 : TRUE: The dual of the dual linear programming problem is again the primal problem
S 2 : TRUE: If either the primal or the dual problem has an unbounded objective function value, the other problem has no feasible solution.
S 3 : TRUE: 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.
S 2 : TRUE: If either the primal or the dual problem has an unbounded objective function value, the other problem has no feasible solution.
S 3 : TRUE: 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.
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