Linear Programming Problem — Chapter Summary
CBSE · Class 12 · Applied Mathematics
Summary of Linear Programming Problem for CBSE Class 12 Applied Mathematics. Part of the CBSE Class 12 Applied Mathematics syllabus.
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Overview
Linear Programming Problem (LPP) is a mathematical technique used to optimize (maximize or minimize) a linear objective function subject to linear constraints. This chapter introduces students to the fundamental concepts of LPP, its mathematical formulation, and graphical methods to solve optimizati
Key Concepts
A mathematical optimization technique that deals
A mathematical optimization technique that deals with maximizing or minimizing a linear objective function subject to linear constraints. It consists
Variables (usually x
Variables (usually x, y) that represent the quantities to be determined in the problem. They are non-negative, continuous, and controllable variables
A linear function Z = ax
A linear function Z = ax + by that needs to be optimized (maximized for profit or minimized for cost). The coefficients 'a' and 'b' represent the cont
Linear inequalities or equations that represent
Linear inequalities or equations that represent limitations on resources or requirements. Include structural constraints (resource limitations) and no
The common region on the graph
The common region on the graph that satisfies all constraints including non-negativity conditions. Every point in this region represents a feasible so
Learning Objectives
- Understand the concept and components of Linear Programming Problem
- Learn mathematical formulation of LPP with decision variables, objective function, and constraints
- Distinguish between feasible and infeasible regions, bounded and unbounded regions
- Differentiate between feasible solution and optimal solution
- Master the graphical method for solving LPP using Corner-Point Method
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Sources & Official References
- NCERT Official — ncert.nic.in
- CBSE Academic — cbseacademic.nic.in
- CBSE Official — cbse.gov.in
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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