Class 12 Maths Chapter 12 Linear Programming MCQs are available for students with answers. The multiple-choice questions are prepared according to the latest exam pattern. The chapter-wise Class 12 Maths MCQs are formulated by our experts as per the CBSE syllabus (2022-2023) and NCERT curriculum. The Linear programming MCQs provided here will help students to score good marks in the Maths board exam.
Linear Programming Class 12 MCQs with Solutions
Find mcqs for class 12 chapter 12 linear programming with solutions here.
Download PDF – Chapter 12 Linear programming MCQs
Q.1: Region represented by x ≥ 0, y ≥ 0 is:
A. first quadrant
B. second quadrant
C. third quadrant
D. fourth quadrant
Answer: A. first quadrant
Explanation: All the positive values of x and y will lie in the first quadrant.
Q.2: The objective function of a linear programming problem is:
A. a constraint
B. function to be optimised
C. A relation between the variables
D. None of these
Answer: B. function to be optimised
Q.3: The linear inequalities or equations or restrictions on the variables of a linear programming problem are called:
A. a constraint
B. Decision variables
C. Objective function
D. None of the above
Answer: A. a constraint
Q.4: A set of values of decision variables that satisfies the linear constraints and non-negativity conditions of an L.P.P. is called its:
A. Unbounded solution
B. Optimum solution
C. Feasible solution
D. None of these
Answer: C. Feasible solution
Q.5: The maximum value of Z = 3x + 4y subjected to constraints x + y ≤ 4, x ≥ 0 and y ≥ 0 is:
A. 12
B. 14
C. 16
D. None of the above
Answer: C. 16
Explanation: The feasible region determined by the constraints, x + y ≤ 4, x ≥ 0, y ≥ 0, is given below
O (0, 0), A (4, 0), and B (0, 4) are the corner points of the feasible region. The values of Z at these points are given below:
| Corner point | Z = 3x + 4y |
| O (0, 0) | 0 |
| A (4, 0) | 12 |
| B (0, 4) | 16 |
Hence, the maximum value of Z is 16 at point B (0, 4)
Q.6: The minimum value of Z = 3x + 5y subjected to constraints x + 3y ≥ 3, x + y ≥ 2, x, y ≥ 0 is:
A. 5
B. 7
C. 10
D. 11
Answer: B. 7
Explanation: The feasible region determined by the system of constraints, x + 3y ≥ 3, x + y ≥ 2, and x, y ≥ 0 is given below
It can be seen that the feasible region is unbounded.
The corner points of the feasible region are A (3, 0), B (3 / 2, 1 / 2) and C (0, 2)
The values of Z at these corner points are given below
| Corner point | Z = 3x + 5y | |
| A (3, 0) | 9 | |
| B (3 / 2, 1 / 2) | 7 | Smallest |
| C (0, 2) | 10 |
7 may or may not be the minimum value of Z because the feasible region is unbounded
For this purpose, we draw the graph of the inequality, 3x + 5y < 7 and check the resulting half-plane have common points with the feasible region or not. Hence, it can be seen that the feasible region has no common point with 3x + 5y < 7.
Thus, the minimum value of Z is 7 at point B (3/2, 1/2).
Q.7: Maximize Z = 3x + 5y, subject to constraints: x + 4y ≤ 24, 3x + y ≤ 21, x + y ≤ 9, x ≥ 0, y ≥ 0
A. 20 at (1, 0)
B. 30 at (0, 6)
C. 37 at (4, 5)
D. 33 at (6, 3)
Answer: C. 37 at (4, 5)
Explanation: Find the maximum value of Z = 3x + 5y referring to the explanation of Q.5.
Q.8: The point which does not lie in the half-plane 2x + 3y -12 < 0 is:
A. (2,1)
B. (1,2)
C. (-2,3)
D. (2,3)
Answer: D. (2,3)
Explanation: By putting the value of point (2,3) in 2x + 3y – 12, we get;
2(2) + 3(3) – 12
= 4 + 9 – 12
= 13 – 12
= 1 which is greater than 0.
Q.9: The optimal value of the objective function is attained at the points:
A. on X-axis
B. on Y-axis
C. corner points of the feasible region
D. none of these
Answer: C. corner points of the feasible region
Explanation: Any point in the feasible region that gives the optimal value (maximum or minimum) of the objective function is called an optimal solution.
Q.10: Which of the following is a type of Linear programming problem?
A. Manufacturing problem
B. Diet problem
C. Transportation problems
D. All of the above
Answer: D. All of the above
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