Linear Programming — Chapter Summary
Jammu & Kashmir Board · Class 12 · Mathematics
Summary of Linear Programming for Jammu & Kashmir Board Class 12 Mathematics. Part of the Jammu & Kashmir Board Class 12 Mathematics syllabus.
Interactive on Super Tutor
Studying Linear Programming? Get the full interactive chapter.
Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for chapter summary and more.
Free trial, no card needed.

One of 7 illustrations for Linear Programming in Super Tutor — alongside flashcards, concept maps and practice questions.
Overview
Linear programming is a special type of optimisation problem. It deals with finding the maximum or minimum value of a linear objective function subject to linear constraints and non-negative restrictions on the variables. The chapter develops the graphical method for two-variable problems and shows
Key Concepts
A linear function of the form
A linear function of the form Z = ax + by that is to be maximised or minimised. In the furniture example, the objective function is Z = 250x + 75y, wh
Linear inequalities or equations that restrict
Linear inequalities or equations that restrict the values of the variables. In the furniture example, the constraints are 5x + y ≤ 100, x + y ≤ 60, x
The variables whose values are
The variables whose values are to be decided, such as x and y in the furniture example.
The common region determined by all
The common region determined by all constraints, including the non-negative constraints. It is always a convex region.
Any point within or on
Any point within or on the boundary of the feasible region.
Learning Objectives
- Understand the meaning of a linear programming problem and its mathematical formulation.
- Identify decision variables, constraints, objective function, feasible region, and feasible solution.
- Use the graphical method to solve two-variable linear programming problems.
- Apply the corner point method to find maximum or minimum values of the objective function.
- Recognise bounded and unbounded feasible regions and their effect on optimal solutions.
Frequently Asked Questions
What are the important topics in Linear Programming for Jammu & Kashmir Board Class 12 Mathematics?
How should I revise Linear Programming for the Jammu & Kashmir Board Class 12 board exam?
Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
More resources for Linear Programming
Practice Quiz
Test yourself with a quick quiz
Important Questions
Exam-style questions with answers
Revision Notes
Key points for last-minute revision
Formula Sheet
The chapter's formulas in one place
Concept Maps
See how topics connect
Study Plan
Step-by-step plan for this chapter
Flashcards
Quick-fire cards for active recall
Syllabus
What topics to cover
NCERT Solutions
Every textbook question solved step by step
For serious students
Get the full Linear Programming chapter — start free.
Quizzes, flashcards, an AI doubt solver and a study plan for Jammu & Kashmir Board Class 12 Mathematics. Free to start, no card needed.