Class 12 Maths - TAMILNADU
Linear Programming
The Linear Programming chapter in Class 12 Mathematics under the Tamil Nadu Samacheer Kalvi syllabus introduces students to optimization techniques used in real-world decision-making. You will learn how to mathematically model business and resource allocation problems by maximizing or minimizing a linear objective function subject to several linear constraints. This chapter carries significant weight in the board examinations, usually featuring in the 5-mark or 10-mark section. Mastery of graphical solutions and corner point methods is essential to score high marks and secure your overall mathematics percentage.
Start Learning FreeKey Concepts
Objective Function
A linear function Z = ax + by that needs to be maximized or minimized based on the given constraints.
Constraints
Linear inequalities or equations representing the limitations on resources such as time, labor, and raw materials.
Feasible Region
The common region determined by all the given constraints, including the non-negative constraints x >= 0 and y >= 0.
Corner Point Method
A method to find the optimal solution by evaluating the objective function at every vertex (corner point) of the feasible region.
Unbounded Region
A feasible region that extends indefinitely, where optimal solutions may or may not exist depending on the constraints.
Important Formulas
Board Exam Info
In the Tamil Nadu (Samacheer Kalvi) Class 12 Mathematics board examination, Linear Programming typically carries around 5 to 10 marks. Questions usually include a compulsory long-answer problem where students must formulate a word problem into a linear programming problem and solve it graphically to find the maximum or minimum value.
Frequently Asked Questions
How do I know whether to shade towards the origin or away from the origin?
Test the origin (0,0) in the inequality. If the statement is true, shade towards the origin; if false, shade away from the origin.
What is the difference between a bounded and an unbounded feasible region?
A bounded region is enclosed completely with a finite area, whereas an unbounded region extends infinitely in one or more directions.
Are non-negative constraints (x >= 0, y >= 0) mandatory in every LPP problem?
Yes, in most practical applications, quantities of items produced or resources used cannot be negative, so they must be included.
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