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Class 12 Maths MCQ Questions of Linear Programming with Answers?

Answer 1

Today, we will help students learn Class 12 Maths MCQ Questions of Linear Programming with Answers. Linear programming is an essential topic in mathematics. MCQ Questions for Class 12 with Answers were prepared based on the latest exam pattern and syllabus. We have provided Linear Programming Class 12 Maths MCQ Questions with Answers to help students understand the concept very well.

The main aim to solve MCQ Questions for Class 12 Maths, is to understand the idea of questions asked in final exams. The main aim to solve MCQ Questions for Class 12 Maths, is to understand the idea of questions asked in final exams. You will start practice the MCQ Questions for Class 12 Maths by Sarthaks eConnect with the important Questions. We will cover the all the topics like characteristics, equations, and application of this topic.

Practice MCQ Question for Class 12 Maths chapter-wise 

1. Feasible region in the set of points which satisfy

(a) The objective functions
(b) Some the given constraints
(c) All of the given constraints
(d) None of these

2. Of all the points of the feasible region for maximum or minimum of objective function the points

(a) Inside the feasible region
(b) At the boundary line of the feasible region
(c) Vertex point of the boundary of the feasible region
(d) None of these

3. Objective function of a linear programming problem is

(a) a constraint
(b) function to be optimized
(c) A relation between the variables
(d) None of these

4. A set of values of decision variables which satisfies the linear constraints and nn-negativity conditions of a L.P.P. is called its

(a) Unbounded solution
(b) Optimum solution
(c) Feasible solution
(d) None of these

5. In Graphical solution the feasible solution is any solution to a LPP which satisfies 

(a) only objective function.
(b) non-negativity restriction.
(c) only constraint.
(d) all the three

6. Region represented by x ≥ 0, y ≥ 0 is:

(a) first quadrant
(b) second quadrant
(c) third quadrant
(d) fourth quadrant

7. 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

8. 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

9. The point which does not lie in the half plane 2x + 3y -12 < 0 is

(a) (1, 2)
(b) (2, 1)
(c) (2, 3)
(d) (-3, 2).

10. Which of the following statement is correct?

(a) Every LPP admits an optimal solution.
(b) Every LPP admits unique optimal solution.
(c) If a LPP gives two optimal solutions it has infinite number of solutions.
(d) None of these

11. The solution set of the inequation 3x + 2y > 3 is

(a) half plane not containing the origin
(b) half plane containing the origin
(c) the point being on the line 3x + 2y = 3
(d) None of these

12. The optimal value of the objective function is attained at the point is

(a) given by the intersection of inequations with axes only
(b) given by the intersection of inequations with X-axis only
(c) given by corner points of the feasible region
(d) None of the above

13. If the constraints in a linear programming problem are changed

(a) solution is not defined
(b) the objective function has to be modified
(c) the problems is to be re-evaluated
(d) none of these

14. The maximum value of Z = 4x + 3y subjected to the constraints 2x + 3y ≤ 18, x + y ≥ 10; x, y ≥ 0 is

(a) 36
(b) 40
(c) 20
(d) none of these

15. 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

16. 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)

17. 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

18. 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

19. In equation 3x – y ≥ 3 and 4x – 4y > 4

(a) Have solution for positive x and y
(b) Have no solution for positive x and y
(c) Have solution for all x
(d) Have solution for all y

20. 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 2

1. Answer: (c) All of the given constraints

2. Answer: (c) Vertex point of the boundary of the feasible region

3. Answer: (b) function to be optimized

Explanation: The objective of Linear Programming Problems (LPP) is to minimize or maximize the function.

4. Answer: (c) Feasible solution

5. Answer: (b) non-negativity restriction.

Explanation: The feasible region is the set of all the points that satisfy all the given constraints . The variables of the linear programs must always take the non-negative values (i.e., x≥0 and y≥0). These are used because x and y are usually the number of items produced and we cannot produce the negative number of items. The least possible number of items could be zero.
Therefore, the feasible solution should satisfy the non-negativity restriction.

6. Answer: (a) first quadrant

Explanation: All the positive values of x and y will lie in the first quadrant.

7. Answer: (a) a constraint

8. Answer: (c) Feasible solution

9. Answer: (c) (2, 3)

Explanation: Putting (2, 3) in 2x + 3y – 12.
Which becomes:
2(2)+ 3(3) – 12 = 4 + 9 – 12 = 1 > 0 and not ≤ 0.

10. Answer: (b) Every LPP admits unique optimal solution.

11. Answer: (a) half plane not containing the origin

12. Answer: (c) given by corner points of the feasible region

Explanation: The optimal value of the objective function is attained at the point is given by corner points of the feasible region.

13. Answer: (c) the problems is to be re-evaluated

14. Answer: (d) none of these

Explanation: Z = 4x + 2y

Subject to constraints

2x + 3y ≤ 18,

x + y ≥ 10 and

x , y ≥ 0

There is no common area in the first quadrant. Hence, the objective function Z cannot be maximized.

15. 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)

16. 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.

17. 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.

18. Answer: (d) All of the above

19. Answer: (a) Have a solution for positive x and y

Explanation: The following figure will be obtained on drawing the graphs of given inequations.

From 3x−y≥3,x/1 + y/−3 = 1

From 4x−y>4,x/1 + y/−4 = 1

Clearly the common region of both is true for positive value of (x, y). It is also true for positive value of x and negative value of y.

20. 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).

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