Discussion
Which of the following statement(s) is/are true for an LP problem ?
(I) The set of all feasible solutions to an LP problem is a convex set.
(II) Every hyperplane is a convex set.
Answer: A
Both are true.
(I) The feasible region of an LP is the intersection of finitely many half-spaces \(a_{i}^{t}x \le b_{i}\) (and \(x \ge 0\)). Each half-space is convex and an intersection of convex sets is convex, so the feasible set is convex, a fact the simplex method relies on.
(II) A hyperplane \(\{x : a^{t}x = b\}\) is convex: if \(a^{t}x = a^{t}y = b\), then \(a^{t}(\lambda x + (1 - \lambda)y) = b\) for every \(\lambda \in [0, 1]\).
Since both statements hold, the options saying only one is true, or neither, are wrong.
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