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6.Practice Questions
Class 12 • Mathematics • NCERT
Practice Questions – Linear Programming
[ Embed Revision / Practice Video Here ]
This practice set is designed strictly according to NCERT Class 12 Linear Programming syllabus, covering formulation, graphical method, feasible region, and optimization problems.
Instructions
- All questions are based on NCERT syllabus.
- Graphs must be neat and clearly labeled.
- Show all necessary steps in board exams.
Section A – Very Short Answer Questions
- Define Linear Programming.
- What is meant by optimization?
- What are decision variables?
- What is an objective function?
- State any one non-negativity condition.
- How many variables are allowed in graphical method?
- What is a feasible solution?
- What is a feasible region?
Section B – Short Answer Questions
- Differentiate between feasible and infeasible solutions.
- Explain why non-negativity conditions are required in LPP.
- What is meant by bounded feasible region?
- Why does the optimal solution lie at a corner point?
- State the steps involved in solving an LPP graphically.
- Can a feasible region be empty? Explain.
Section C – Long Answer / Numerical Questions
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Formulate the LPP for the following:
A factory produces two products A and B. Each unit of A requires 2 hours and each unit of B requires 1 hour of machine time. The total machine time available is 10 hours. Profit per unit of A is ₹40 and B is ₹30. -
Solve the following LPP graphically:
Maximize Z = 3x + 2y
subject to:
x + y ≤ 4
x ≤ 2
y ≤ 3
x ≥ 0, y ≥ 0 -
Find the minimum value of Z = 5x + 4y subject to:
x + y ≥ 6
x + 3y ≥ 9
x ≥ 0, y ≥ 0 -
Draw the feasible region for the constraints:
2x + y ≤ 8
x + 2y ≤ 8
x ≥ 0, y ≥ 0
Section D – Assertion / Reason (Board Pattern)
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Assertion (A): The optimal value of an LPP occurs at a corner point.
Reason (R): The feasible region of an LPP is always bounded. -
Assertion (A): Graphical method cannot be used for more than two variables.
Reason (R): Graphical method is based on coordinate geometry.
✅ Show Answer Key (Brief)
- Section A: Definitions based on NCERT
- Section B: Conceptual explanations
- Section C: Graphical solutions & formulation
- Section D: (1) A true, R false (2) A true, R true
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