UGC NET CSE | December 2019 | Part 2 | Question: 67

Question

Consider the following statements with respect to duality in $\text{LPP}$:

1. The final simplex table giving optimal solution of the primal also contains optimal solution of its dual in itself
2. If either the primal or the dual problem has a finite optimal solution, then the other problem also has a finite optimal solution
3. 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?

• A. Only (i) and (ii)
• B. Only (i) and (iii)
• C. only (ii) and (iii)
• D. (i), (ii) and (iii)

Answer 1

Concept:
Duality in Linear programming problem (LPP) : It means a linear programming problem has another
LPP which is derived from it. Original LPP is known as primal and derived LPP is known as Dual.
Explanation:
Some points about dual LPP:
1) The final simplex table giving optimal solution of the primal also contains optimal solution of its
dual in itself.
2) If either the primal or the dual problem has a finite optimal solution, then the other problem also
has a finite optimal solution.
3) If either problem has an unbounded optimum solution, then the other problem has no feasible
solution at all
Example:
We have a set of equations as:
Maximize z = 10x1 + 20 x2
Subject to:
3x1 + 4x2 < =100
5x1 + 6x2 < = 150
Get Started
X1, x2 >= 0
Dual of this will be:
Minimize z = 100 y1 + 150 y2
Subject to:
3y1 + 4y2 >=10
5y1 + 6y2 > = 20
y1, y2 <= 0