Operations research
Guess first
Unbounded region = no solution? Guess first
Most students get this LP special case wrong. Commit before I explain.
Quick check · tap an answer to continue
Lesson notes
Recognise infeasible, unbounded, multiple-optimum and redundant-constraint problems
Key points
- When you minimise cost, the corner closest to the origin wins, so an open region can still have a finite optimum.
- So justify it in the exam: unboundedness is about the objective improving forever, not just the region being open.
Definitions
- Unbounded solution
- The objective can improve without limit within the feasible region; in simplex, no positive ratio exists
Takeaway: An open feasible region does not guarantee an unbounded solution.
Quick check: A mine minimises haulage cost: 2x+3y, x+y≥6, x,y≥0. The region is open. Result?
- Unbounded solution
- Infeasible problem
- Finite optimum at a corner
Open region plus minimisation usually still gives a finite corner optimum.
infeasibilityunboundednessalternative optimaMinimisationUnboundedness
Lessons like this, for your syllabus.
Short narrated study videos written for your course, level and exam. Free to start.
Get lessons for your own syllabus