Class 12 Maths - CBSE
Linear Programming
The Linear Programming chapter in Class 12 CBSE Mathematics deals with optimizing a linear objective function subject to a set of linear inequality constraints. This graphical method of decision-making bridges algebra and real-world resource allocation problems, such as diet planning and manufacturing optimization. For CBSE board exams, this is a high-scoring chapter that consistently features a long-answer question carrying 5 or 6 marks, making graphical accuracy and correct constraint formulation essential for securing top grades.
Start Learning FreeKey Concepts
Objective Function
A linear function Z = ax + by that needs to be maximized or minimized based on given conditions.
Constraints
Linear inequalities or equations representing limitations on resources like time, labor, or material, usually including non-negativity restrictions (x ≥ 0, y ≥ 0).
Feasible Region
The common region determined by all the given constraints, including the non-negativity restrictions, representing all valid solutions.
Optimal Solution
A point in the feasible region that produces the maximum or minimum value of the objective function.
Corner Point Method
A theorem stating that the optimal value of a linear programming problem always occurs at the corner points (vertices) of the feasible region.
Important Formulas
Board Exam Info
In the CBSE Class 12 Mathematics exam, Linear Programming typically carries around 5 to 6 marks. The section usually features one mandatory 5-mark long-answer question where students must translate a real-world word problem into mathematical constraints, draw an accurate graph, identify the feasible region, and use the corner point method to find the optimal solution.
Frequently Asked Questions
Do I need to shade the feasible region or the unwanted region in the CBSE exam?
It is best practice to shade or lightly indicate the feasible region (the region that satisfies all constraints simultaneously) and clearly label it, as this is what the examiner looks for.
Can the optimal solution occur anywhere inside the feasible region?
No, according to the corner point theorem, the optimal value of the objective function always occurs at one of the corner points (vertices) of the feasible region.
What should I do if the feasible region is unbounded?
If the feasible region is unbounded, check if a maximum or minimum value actually exists using the half-plane test. Sometimes, an optimal value may not exist for unbounded regions.
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