Class 12 Maths - TELANGANA
Linear Programming
The Linear Programming chapter in Class 12 Mathematics for Telangana (TSBSE) students explores optimization techniques for real-world problems. You will learn how to maximize or minimize a linear objective function subject to several linear inequality constraints. This chapter is vital for board exams as it features in the long-answer section, offering guaranteed scoring opportunities through graphical methods. Mastering this topic helps you understand how businesses allocate resources efficiently, making it both mathematically satisfying and practically useful for future applications in economics and management.
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 raw materials.
Feasible Region
The common region determined by all the given constraints, including non-negative restrictions x >= 0 and y >= 0.
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.
Unbounded Region
A feasible region that extends indefinitely, where a maximum or minimum value may not always exist unless tested with specific inequalities.
Important Formulas
Board Exam Info
In the Telangana (TSBSE) Class 12 Mathematics board exam, Linear Programming typically carries around 7 to 8 marks. Questions usually include one very short answer question (2 marks) and one long-answer question (7 marks) that requires drawing a graph and finding optimal solutions.
Frequently Asked Questions
How do I know whether to shade towards the origin or away from it?
Substitute the origin (0,0) into the inequality. If the resulting statement is true, shade towards the origin; if false, shade away from it.
Is graph paper mandatory for solving LPP questions in the TSBSE board exam?
Yes, graph paper is compulsory for plotting constraints accurately and locating the correct corner points of the feasible region.
What should I do if the feasible region is unbounded?
Plot the inequality ax + by > Z (for maximization) to check if the open half-plane intersects the feasible region. If it does, no maximum value exists; otherwise, the value at tested corner points is valid.
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