Currently Empty: $0.00
5.Optimization Problems
Class 12 • Mathematics • NCERT
Optimization Problems
[ Embed Your Video Lecture Here ]
This lesson explains optimization problems in Linear Programming, where the objective function is maximized or minimized subject to given constraints, as prescribed in NCERT Class 12.
Lesson Objectives
- Understand optimization in Linear Programming.
- Solve maximization and minimization problems.
- Apply corner point method.
- Prepare for NCERT board-level questions.
1. Meaning of Optimization
Optimization refers to finding the best possible solution (maximum or minimum value) of an objective function under given constraints.
In Linear Programming, optimization is done graphically.
[ Image Placeholder: Objective Function Optimization ]
2. Maximization Problems
A maximization problem is one in which the objective function is to be maximized.
Example: Maximize Z = ax + by
[ Image Placeholder: Maximization Problem Graph ]
3. Minimization Problems
A minimization problem is one in which the objective function is to be minimized.
Example: Minimize Z = ax + by
[ Image Placeholder: Minimization Problem Graph ]
4. Corner Point Method
According to the corner point method, the optimal value of the objective function occurs at one of the corner points of the feasible region.
Evaluate the objective function at all corner points.
[ Image Placeholder: Corner Point Method ]
5. Steps to Solve Optimization Problems (NCERT)
• Formulate the LPP
• Draw graphs of constraints
• Identify feasible region
• Find corner points
• Evaluate objective function
• Select optimal value
• Draw graphs of constraints
• Identify feasible region
• Find corner points
• Evaluate objective function
• Select optimal value
[ Image Placeholder: Steps of Optimization ]
6. Important NCERT Notes
• Optimal solution lies at corner points
• Feasible region may be bounded or unbounded
• Only feasible solutions are considered
• Graphical accuracy is important in exams
• Feasible region may be bounded or unbounded
• Only feasible solutions are considered
• Graphical accuracy is important in exams
Practice Questions (NCERT)
- What is optimization?
- Define maximization problem.
- Define minimization problem.
- What is corner point method?
- Where does optimal solution lie?
- Can optimal solution lie inside feasible region?
- Is optimization possible without constraints?
- Which method is used in Class 12?
- Is graphical accuracy important?
- Is this chapter high-weightage?
✅ Show Answer Key
- Finding best value
- Maximize objective function
- Minimize objective function
- Method using corner points
- At corner points
- No
- No
- Graphical method
- Yes
- Yes
© Aviate Learning – Linear Programming (NCERT Class 12)