Linear Programming Practice Questions
Class 12 · Mathematics · 2347 free MCQs with instant results and detailed explanations.
2347
Total
881
Easy
1184
Medium
282
Hard
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Topics in Linear Programming
Feasible Region
814
Graphical Method
795
Optimal Solution
738
Sample Questions from Linear Programming
Here are 10 sample questions. Start a quiz to get randomized questions with scoring.
Q1
Easy
Which of the following represents a feasible solution in a linear programming problem?
A.
(3, 2)
B.
(0, 0)
C.
(5, 6)
D.
(2, -1)
Show Answer & Explanation
Correct Answer: A
(3, 2) is a feasible solution as it satisfies the constraints of the problem.
Q2
Easy
In a linear programming graph, the feasible region is bounded by which of the following?
A.
Feasible points only
B.
Inequalities
C.
Intersection of all constraints
D.
Objective function
Show Answer & Explanation
Correct Answer: C
The feasible region is formed by the intersection of all the constraints.
Q3
Easy
What is the graphical method primarily used for in linear programming?
A.
Finding derivatives
B.
Maximizing or minimizing a linear function
C.
Solving differential equations
D.
Calculating integrals
Show Answer & Explanation
Correct Answer: B
The graphical method is used to maximize or minimize a linear objective function subject to constraints.
Q4
Medium
A farmer wants to plant two crops, A and B. The profit from crop A is ₹50 per acre and from crop B is ₹80 per acre. If the total land available is 100 acres and each crop requires at least 10 acres, what is the maximum profit?
A.
₹5000
B.
₹8000
C.
₹4000
D.
₹6000
Show Answer & Explanation
Correct Answer: B
Maximizing profit occurs at the boundary of available resources.
Q5
Medium
In a graphical method of linear programming, which of the following represents the feasible region?
A.
Intersection of constraints
B.
Union of constraints
C.
Any random area
D.
None of the above
Show Answer & Explanation
Correct Answer: A
The feasible region is where all constraints intersect and satisfy the inequalities.
Q6
Medium
If a linear programming problem has an unbounded feasible region, which of the following is true?
A.
Optimal solution exists
B.
No feasible solution
C.
Objective function can be maximized indefinitely
D.
None of the above
Show Answer & Explanation
Correct Answer: C
An unbounded region indicates that the objective function can increase without limit.
Q7
Medium
Which of the following statements about the graphical method for solving linear programming problems is FALSE?
A.
It can only be used for two variables
B.
The feasible region can be non-convex
C.
It requires plotting constraints
D.
All corner points must be evaluated
Show Answer & Explanation
Correct Answer: B
Feasible regions in linear programming are always convex due to linear constraints.
Q8
Hard
A business has a profit of ₹ 50 for each item of Product X sold and ₹ 80 for each item of Product Y sold. If the company wants to maximize profit while producing no more than 300 items in total, and ensuring that at least 100 items of Product Y are produced, which of the following inequalities represents the constraints?
A.
x + y ≤ 300, y ≥ 100
B.
x + y ≥ 300, y ≤ 100
C.
x + y ≤ 100, y ≥ 300
D.
x ≤ 300, y ≤ 100
Show Answer & Explanation
Correct Answer: A
The total production is limited to 300 items (x + y ≤ 300), and there is a minimum requirement of 100 items of Product Y (y ≥ 100). Thus, option A correctly represents the constraints.
Q9
Hard
Which of the following is NOT a characteristic of the feasible region in a linear programming problem?
A.
It is bounded.
B.
It can be unbounded.
C.
It can be empty.
D.
It is always a single point.
Show Answer & Explanation
Correct Answer: D
The feasible region can be a polygon, unbounded, or empty. It's not always a single point.
Q10
Hard
If a linear programming problem has an unbounded feasible region, what can be inferred about the objective function?
A.
It has a maximum.
B.
It has a minimum.
C.
It is maximized at infinity.
D.
It remains constant.
Show Answer & Explanation
Correct Answer: C
An unbounded feasible region implies the objective function can increase indefinitely.
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Linear Programming — Class 12 Mathematics Practice Questions Online
This page contains 2347 practice MCQs for the chapter Linear Programming in Class 12 Mathematics. The questions are organized by difficulty — 881 easy, 1184 medium, 282 hard — so you can choose the right level for your preparation.
Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 3 topics, giving you comprehensive coverage of the entire chapter.