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Free download in PDF Class 12 Maths Chapter 12 Linear Programming Multiple Choice Questions and Answers for Board, JEE, NEET, AIIMS, JIPMER, IIT-JEE, AIEE and other competitive exams. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. These short solved questions or quizzes are provided by Gkseries. These will help the students for preparation of their examination./p>
(1)
Z = 6x + 21 y, subject to x + 2y ≥ 3, x + 4y ≥ 4, 3x + y ≥ 3, x ≥ 0, y ≥ 0. The minimum value of Z occurs at
[A]
(4, 0)
[B]
(28, 8)
[C]
(2, 7/2)
[D]
(0, 3)
(2)
Maximize Z = 10 x1 + 25 x2, subject to 0 ≤ x1 ≤ 3, 0 ≤ x2 ≤ 3, x1 + x2 ≤ 5
[A]
80 at (3, 2)
[B]
75 at (0, 3)
[C]
30 at (3, 0)
[D]
95 at (2, 3)
(3)
Maximize Z = 4x + 6y, subject to 3x + 2y ≤ 12, x + y ≥ 4, x, y ≥ 0
[A]
16 at (4, 0)
[B]
24 at (0, 4)
[C]
24 at (6, 0)
[D]
36 at (0, 6)
(4)
Maximize Z = 11 x + 8y subject to x ≤ 4, y ≤ 6, x + y ≤ 6, x ≥ 0, y ≥ 0.
[A]
44 at (4, 2)
[B]
60 at (4, 2)
[C]
62 at (4, 0)
[D]
48 at (4, 2)
(5)
The maximum value of the object function Z = 5x + 10 y subject to the constraints x + 2y ≤ 120, x + y ≥ 60, x – 2y ≥ 0, x ≥ 0, y ≥ 0 is
[A]
300
[B]
600
[C]
400
[D]
800
(6)
Objective function of a linear programming problem is
[A]
a constraint
[B]
function to be obtimized
[C]
A relation between the variables
[D]
None of these
Answer: function to be obtimized
(7)
Refer to Question 18 maximum of Z occurs at
[A]
(5, 0)
[B]
(6, 5)
[C]
(6, 8)
[D]
(4, 10)
(8)
Maximize Z = 7x + 11y, subject to 3x + 5y ≤ 26, 5x + 3y ≤ 30, x ≥ 0, y ≥ 0
[A]
59 at (9/2, 5/2)
[B]
42 at (6, 0)
[C]
49 at (7, 0)
[D]
57.2 at (0, 5.2)
(9)
The maximum value of Z = 4x + 2y subject to the constraints 2x + 3y ≤ 18, x + y ≥ 10, x, y ≤ 0 is
[A]
36
[B]
40
[C]
30
[D]
None of these
(10)
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
Answer: Feasible solution
(11)
Z = 20x1 + 202, subject to x1 ≥ 0, x2 ≥ 0, x1 + 2x2 ≥ 8, 3x1 + 2x2 ≥ 15, 5x1 + 2x2 ≥ 20. The minimum value of Z occurs at
[A]
(8, 0)
[B]
(5/2, 15/4)
[C]
(7/2, 9/4)
[D]
(0, 10)
(12)
Maximize Z = 3x + 5y, subject to 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)
(13)
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
Answer: Have solution for positive x and y
(14)
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
Answer: Vertex point of the boundary of the feasible region
(15)
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
Answer: All of the given constraints
(16)
Refer to Question 18 (Maximum value of Z+ Minimum value of Z) is equal to
[A]
13
[B]
1
[C]
-13
[D]
-17
(17)
The maximum value of Z = 3x + 4y subjected to contraints x + y ≤ 40, x + 2y ≤ 60, x ≥ 0 and y ≥ 0 is
[A]
120
[B]
140
[C]
100
[D]
160
(18)
Maximize Z = 6x + 4y, subject to x ≤ 2, x + y ≤ 3, -2x + y ≤ 1, x ≥ 0, y ≥ 0
[A]
12 at (2, 0)
[B]
140/3 at (2/3, 13)
[C]
16 at (2, 1)
[D]
4 at (0, 1)
(19)
The corner point of the feasible region determined by the system of linear constraints are (0, 0), (0, 40), (20, 40), (60, 20), (60, 0). The objective function is Z = 4x + 3y.
Compare the quantity in Column A and Column B
| Column A |
Column B |
| Maximum of Z |
325 |
[A]
The quantity in column A is greater
[B]
The quantity in column B is greater
[C]
The two quantities are equal
[D]
The relationship cannot be determined On the basis of the information supplied
Answer: The quantity in column B is greater
(20)
The feasible region for a LPP is shown shaded in the figure. Let Z = 3x – 4y be the objective function. Minimum of Z occurs at
[A]
(0, 0)
[B]
(0, 8)
[C]
(5, 0)
[D]
(4, 10)
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