Class 12 Maths - ANDHRA-PRADESH
Linear Programming
The Linear Programming chapter in Class 12 Mathematics for Andhra Pradesh (BSEAP) students deals with optimizing a linear objective function subject to a set of linear inequality constraints. It bridges algebra and real-world decision-making, showing how to maximize profits or minimize costs in business and industry. For the board exams, this chapter is high-scoring and straightforward, typically featuring graphical method problems where you must identify the feasible region, locate corner points, and find the optimal solution. Mastering this chapter ensures secure marks with minimal calculation errors.
Start Learning FreeKey Concepts
Linear Programming Problem (LPP)
A mathematical problem that aims to maximize or minimize a linear function subject to several linear constraints and non-negativity restrictions.
Objective Function
A linear function Z = ax + by whose value needs to be maximized or minimized under given constraints.
Constraints
Linear inequalities or equations representing limitations on resources like time, labor, or raw materials in a given problem.
Feasible Region
The common region determined by all the given constraints, including non-negativity restrictions, representing all valid solutions.
Corner Point Method
A theorem stating that the optimal value of the objective function always occurs at the corner points (vertices) of the feasible region.
Important Formulas
Board Exam Info
In the Andhra Pradesh (BSEAP) Class 12 Mathematics board exams, Linear Programming usually carries around 7 to 8 marks. Questions typically include one very short answer question (2 marks) and one long answer essay question (5 or 6 marks) requiring graph-based step-by-step problem solving.
Frequently Asked Questions
Is it mandatory to draw a graph for LPP questions in the AP Board exam?
Yes, for long answer questions, drawing a neat, properly scaled graph showing the feasible region and corner points is compulsory to get full marks.
How do I know whether to shade towards the origin or away from it?
Test the origin (0,0) in the given inequality. If the inequality becomes true, shade towards the origin; if false, shade away from it.
What if the feasible region is unbounded?
If the feasible region is unbounded, the maximum or minimum value may not exist. We use the half-plane test to check if Z crosses the boundary of the feasible region.
Learn Linear Programming with Your AI Tutor
10 different ways to study this chapter. Free for 3 chapters per day.
Lecture
Key Points
Interactive
Quiz
Flashcards