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4.Feasible Region
Class 12 • Mathematics • NCERT
Feasible Region
[ Embed Your Video Lecture Here ]
This lesson explains the concept of feasible region in Linear Programming, which represents all possible solutions satisfying the given constraints, as prescribed in NCERT Class 12.
Lesson Objectives
- Understand the meaning of feasible region.
- Identify feasible and infeasible solutions.
- Draw feasible region graphically.
- Prepare for NCERT board-level questions.
1. Meaning of Feasible Region
The feasible region is the region in the coordinate plane which represents all possible solutions of a Linear Programming Problem that satisfy all the given constraints simultaneously.
Each point inside this region is a feasible solution.
[ Image Placeholder: Shaded Feasible Region ]
2. Feasible and Infeasible Solutions
A solution that satisfies all the constraints is called a feasible solution.
A solution that violates at least one constraint is called an infeasible solution.
Only feasible solutions are considered for optimization.
[ Image Placeholder: Feasible vs Infeasible Points ]
3. Bounded and Unbounded Feasible Region
The feasible region may be bounded or unbounded depending on the constraints.
• Bounded region: Enclosed within boundaries
• Unbounded region: Extends infinitely
• Unbounded region: Extends infinitely
[ Image Placeholder: Bounded and Unbounded Regions ]
4. Importance of Feasible Region
The feasible region plays a crucial role in solving a Linear Programming Problem.
The optimal solution always lies on a corner point of the feasible region.
[ Image Placeholder: Corner Points of Feasible Region ]
5. Steps to Find Feasible Region (NCERT)
• Plot all constraint lines
• Identify correct half-planes
• Find common region satisfying all constraints
• Apply non-negativity conditions
• Identify correct half-planes
• Find common region satisfying all constraints
• Apply non-negativity conditions
[ Image Placeholder: Steps to Find Feasible Region ]
6. Important NCERT Notes
• Feasible region may be empty
• Only feasible solutions are considered
• Non-negativity conditions are compulsory
• Commonly asked board-exam topic
• Only feasible solutions are considered
• Non-negativity conditions are compulsory
• Commonly asked board-exam topic
Practice Questions (NCERT)
- Define feasible region.
- What is a feasible solution?
- What is an infeasible solution?
- Can feasible region be unbounded?
- Where does the optimal solution lie?
- What happens if feasible region is empty?
- Why non-negativity conditions are important?
- Is every point in the plane a feasible solution?
- Is feasible region always closed?
- Is this topic important for board exams?
✅ Show Answer Key
- Region satisfying all constraints
- Solution satisfying all constraints
- Solution violating at least one constraint
- Yes
- At corner points
- No feasible solution exists
- Restrict variables to first quadrant
- No
- Yes
- Yes
© Aviate Learning – Linear Programming (NCERT Class 12)