Class 12 Maths - KERALA
Linear Programming
The chapter 'Linear Programming' in Class 12 Mathematics for Kerala SCERT introduces students to optimization techniques used in real-world decision-making. You will learn how to maximize or minimize a linear objective function subject to several linear inequalities, known as constraints. The region formed by these constraints is the feasible region, and the optimal solution always occurs at one of its corner points. This chapter is vital for board exams as it consistently features a straightforward, high-scoring long-answer question where you must draw graphs and evaluate corner points to find the optimal solution.
Start Learning FreeKey Concepts
Linear Programming Problem (LPP)
A problem that aims to maximize or minimize a linear function subject to a set of linear constraints.
Objective Function
The linear function Z = ax + by whose value needs to be maximized or minimized.
Constraints
Linear inequalities or equations representing limitations on resources, usually including non-negativity restrictions like x ≥ 0 and y ≥ 0.
Feasible Region
The common region determined by all the given constraints, including the non-negativity restrictions, representing all valid solutions.
Corner Point Method
A graphical method to solve LPPs by evaluating the objective function at the vertices (corner points) of the feasible region.
Important Formulas
Board Exam Info
In the Kerala (SCERT) Class 12 Mathematics board examination, Linear Programming usually carries around 6 marks. Questions typically appear as a compulsory long-answer problem where students are required to graph the constraints, identify the feasible region, and use the corner point method to find the optimal value.
Frequently Asked Questions
Do I always need to shade the feasible region towards the origin or away from it?
Not always. You should test a point (like the origin 0,0) in the given inequality. If the inequality is true, shade towards that point; if false, shade away from it.
What is the difference between bounded and unbounded feasible regions?
A bounded region is enclosed on all sides, meaning the optimal value is guaranteed to exist. An unbounded region extends infinitely, and testing the corner points requires checking specific rules to see if a maximum or minimum actually exists.
Why are non-negativity constraints (x ≥ 0, y ≥ 0) important?
In most practical, real-world scenarios, quantities like items produced, time spent, or distance cannot be negative, so the solution must lie in the first quadrant.
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