CBSE 12 Math · U5
Linear Programming
Linear constraints, objective functions, feasible regions, graphical solution, corner-point optimization, and applied LPP problems.
Test yourself
A focused, distraction-free run through 25 multiple-choice questions. Hints if you need them; your score at the end.
Difficulty guide
The label describes the problem, not your ability.
1/5 - Foundational
Warm-up setup; checks one basic idea.
2/5 - Routine exam skill
Normal syllabus skill; usually one main rule or interpretation.
3/5 - Standard multi-step
Exam-style problem with multiple steps or a common trap.
4/5 - Hard exam skill
High-end exam problem; combines methods carefully.
5/5 - Challenge
Stretch problem beyond normal exam pressure.
Topic 5.1
Linear Programming Terminology
Decision variables, objective function, constraints, feasible solutions, and non-negativity conditions
Item 1
Open
Item 2
Open
Item 3
Open
Item 4
Open
Item 5
Open
Item 6
Open
Item 7
Open
Item 8
Open
Item 9
Open
Item 10
Open
Topic 5.2
Graphical Method and Feasible Regions
Graphing constraints, selecting the feasible side, bounded regions, vertices, and infeasible points
Item 1
Open
Item 2
Open
Item 3
Open
Item 4
Open
Item 5
Open
Item 6
Open
Item 7
Open
Item 8
Open
Item 9
Open
Item 10
Open
Topic 5.3
Corner Point Method
Evaluating objective functions at vertices to find maximum and minimum values
Item 1
Open
Item 2
Open
Item 3
Open
Item 4
Open
Item 5
Open
Item 6
Open
Item 7
Open
Item 8
Open
Item 9
Open
Item 10
Open
Topic 5.4
Bounded, Unbounded, and Multiple Optimum Cases
Recognising bounded and unbounded regions, checking existence of optimum values, and interpreting multiple optima
Item 1
Open
Item 2
Open
Item 3
Open
Item 4
Open
Item 5
Open
Item 6
Open
Item 7
Open
Item 8
Open
Item 9
Open
Item 10
Open
Topic 5.5
Applications of Linear Programming
Board-style production, diet, and resource-allocation problems using formulation and corner-point solution
Item 1
Open
Item 2
Open
Item 3
Open
Item 4
Open
Item 5
Open
Item 6
Open
Item 7
Open
Item 8
Open
Item 9
Open
Item 10
Open