Discussion
The problem :
Max. : \(Z = 3x_{1} + 2x_{2}\)
Subject to :
\(x_{1} - x_{2} \le 1\),
\(x_{1} + x_{2} \ge 3\)
\(x_{1}, x_{2} \ge 0\)
has :
Answer: D
The problem has an unbounded solution.
The feasible region is not empty: (2, 1) satisfies \(2 - 1 \le 1\) and \(2 + 1 \ge 3\). But it is not bounded. Take \(x_{1} = 0\) and let \(x_{2}\) grow: \(0 - x_{2} \le 1\) and \(0 + x_{2} \ge 3\) hold for every \(x_{2} \ge 3\), while \(Z = 2x_{2}\) increases without limit. So Z has no finite maximum.
An LP is classified by what happens to its optimum. Feasible points exist, but 'feasible solution' does not describe the outcome; 'optimum solution' and 'feasible but not optimum' do not fit either, since there is no maximum to attain. The standard classification of this problem is unbounded.
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