MCQ On Class 12 Maths Chapter 12 Linear Programming

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)

View Answer

Answer:(2, 7/2)

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)

View Answer

Answer: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)

View Answer

Answer: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)

View Answer

Answer:60 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

View Answer

Answer:600

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

View Answer

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)

View Answer

Answer:(5, 0)

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)

View Answer

Answer:59 at (9/2, 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

View Answer

Answer: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

View Answer

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)

View Answer

Answer:(7/2, 9/4)

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)

View Answer

Answer:37 at (4, 5)

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

View Answer

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

View Answer

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

View Answer

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

View Answer

Answer:-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

View Answer

Answer:140

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)

View Answer

Answer:16 at (2, 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

View Answer

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 Class 12 Maths Chapter 12 Linear Programming