Discussion
For the LPP
Min : 4x + 6y + 18z
s.t. x + 3y ≥ 3;
y + 2z ≥ 5;
x, y, z ≥ 0,
which of the following is not a constraint in the corresponding dual ?
Answer: C
The inequality that is not a dual constraint is \(3u + v \ge 6\).
The primal is a minimisation with \(\ge\) constraints and non-negative variables, so the dual is: maximise \(3u + 5v\) subject to
\[ \begin{aligned} u &\le 4 \quad (\text{column of } x) \\ 3u + v &\le 6 \quad (\text{column of } y) \\ 2v &\le 18,\ \text{i.e. } v \le 9 \quad (\text{column of } z) \\ u, v &\ge 0 \end{aligned} \]
The y-column constraint is \(3u + v \le 6\); option C reverses the inequality, so it is not a dual constraint. Options A, B and D appear in the dual exactly as written.
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development