GATE-2024-CS1(Forenoon)
February 15, 2025KVS PGT DEC-2013 PART-A
February 16, 2025Duality
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Question 1
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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 optimal solution, then the other problem has no feasible solution at all.
Which of the statements is (are) correct?
(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 optimal solution, then the other problem has no feasible solution at all.
Which of the statements is (are) correct?
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only (a) and (b)
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only (a) and (c)
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only (b) and (c)
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(a), (b) and (c)
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Question 1 Explanation:
Duality in LPP:
TRUE: The final simplex table giving optimal solution of the primal also contains optimal solution of its dual in itself.
TRUE: If either the primal or the dual problem has a finite optimal solution, then the other problem also has a finite optimal solution.
TRUE: If either problem has an unbounded optimal solution, then the other problem has no feasible solution at all.
TRUE: The final simplex table giving optimal solution of the primal also contains optimal solution of its dual in itself.
TRUE: If either the primal or the dual problem has a finite optimal solution, then the other problem also has a finite optimal solution.
TRUE: If either problem has an unbounded optimal solution, then the other problem has no feasible solution at all.
Correct Answer: D
Question 1 Explanation:
Duality in LPP:
TRUE: The final simplex table giving optimal solution of the primal also contains optimal solution of its dual in itself.
TRUE: If either the primal or the dual problem has a finite optimal solution, then the other problem also has a finite optimal solution.
TRUE: If either problem has an unbounded optimal solution, then the other problem has no feasible solution at all.
TRUE: The final simplex table giving optimal solution of the primal also contains optimal solution of its dual in itself.
TRUE: If either the primal or the dual problem has a finite optimal solution, then the other problem also has a finite optimal solution.
TRUE: If either problem has an unbounded optimal solution, then the other problem has no feasible solution at all.
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