Question 117
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?
Answer : 4. (a), (b) and (c) (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?
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All 3 statements are correct as they all are properties of dual and primal
Duality in LPP follows all given properties.
So, option 4 is correct answer
Duality in LPP:
Weak duality (Unboundedness Property)
If the primal (dual) problem has an unbounded solution, then the dual (primal) problem is infeasible. In particular, if the primal is unbounded (from above) then the dual has no feasible solution, and if the dual is unbounded (from below) then the primal has no feasible solution.
Strong Duality Property If the primal (dual) problem has a finite optimal solution, then so does the dual (primal) problem, and these two values are equal. The strong duality theorem says that if one of the two problems has an optimal solution, so does the other one and that the bounds given by the weak duality theorem are tight
Reference 1 : Duality in Linear Programming
Reference 2 : The duality theorems