Class 12 Math Ch-12 Linear Programming MCQs Exam 2027

Section-A: Objective Functions & Basic Principles

1. In a Linear Programming Problem (LPP), the Objective Function is: [BSEB]

(A) A constant

(B) A function to be optimized

(C) A constraint

(D) None of these

2. $Z = ax + by$, where $a, b > 0$ are constants, is called: [BSEB]

(A) Objective Function

(B) Constraint

(C) Feasible Region

(D) None of these

3. The value of the objective function $Z = ax + by$ is maximum: [BSEB]

(A) Only at corner points

(B) At the centroid

(C) On the $x$-axis

(D) On the $y$-axis

4. The objective function of an LPP is: [BSEB]

(A) A constraint

(B) A function for optimization

(C) A relation between variables

(D) None of these

5. In a linear programming problem, the objective function is always: [BSEB]

(A) Linear

(B) Quadratic

(C) Cubic

(D) None of these

6. Which of the following is an objective function? [BSEB]

(A) $Z = 5x + 7y$

(B) $x > 0$

(C) $y > 0$

(D) None of these

7. A feasible region is a set of points that satisfies: [BSEB]

(A) The objective function

(B) Total constraints

(C) All constraints simultaneously

(D) None of these

8. In LPP, the values of $Z$ at the corner points of the feasible region are called: [BSEB]

(A) Optimal values

(B) Zero values

(C) Negative values

(D) None of these

9. $Z = 3x + 2y$ is an example of: [BSEB]

(A) Objective function

(B) Constraint

(C) Inequality

(D) None of these

10. Linear Programming is used in which of the following fields? [BSEB]

(A) Diet problems

(B) Transportation problems

(C) Manufacturing problems

(D) All of the above

Section-B: Constraints & Regions

11. The graph of the constraints $x \ge 0, y \ge 0$ lies in: [BSEB]

(A) First quadrant

(B) Second quadrant

(C) Third quadrant

(D) Fourth quadrant

12. The graph of $x \ge 3$ is a line which is: [BSEB]

(A) Parallel to $x$-axis

(B) Parallel to $y$-axis

(C) Passes through the origin

(D) None of these

13. The graph region of $y \le 4$ will be: [BSEB]

(A) Above the $x$-axis

(B) Below the $x$-axis

(C) To the right of $y$-axis

(D) To the left of $y$-axis

14. What happens at a point outside the feasible region? [BSEB]

(A) No solution is obtained

(B) Maximum value is obtained

(C) Minimum value is obtained

(D) None of these

15. The solution region of the constraint $x + y \le 5$ will be: [BSEB]

(A) Towards the origin

(B) Away from the origin

(C) Only in the first quadrant

(D) None of these

16. The feasible region formed by constraints $x \le 2, y \le 2, x, y \ge 0$ is: [BSEB]

(A) A triangle

(B) A square

(C) A pentagon

(D) Unbounded

17. If the feasible region is unbounded, then the maximum value of the objective function: [BSEB]

(A) Always exists

(B) May or may not exist

(C) Never exists

(D) Is zero

18. The graph of $x + y \ge 0$ is located in: [BSEB]

(A) I and II quadrants

(B) I, II, and IV quadrants

(C) Only I quadrant

(D) All quadrants

19. In the solution region of inequality $3x + 4y < 12$, the point (0,0): [BSEB]

(A) Lies in the region

(B) Does not lie in the region

(C) Lies on the line

(D) None of these

20. The region enclosed by constraints $x + y \le 4, x \ge 0, y \ge 0$ is called: [BSEB]

(A) Feasible region

(B) Invalid region

(C) Open region

(D) None of these

Section-C: Maximum Value

21. Maximum value of $Z = x – 3y$ subject to $x + y \le 13, x \ge 0, y \ge 0$ is: [BSEB]

(A) $39$

(B) $26$

(C) $13$

(D) $-26$

22. Maximum value of $Z = 5x + 7y$ subject to $x + y \le 4, x \ge 0, y \ge 0$ is: [BSEB]

(A) $20$

(B) $28$

(C) $30$

(D) $35$

23. Maximum value of $Z = 2x + y$ subject to $x + y \le 35, x \ge 0, y \ge 0$ is: [BSEB]

(A) $35$

(B) $105$

(C) $70$

(D) $140$

24. Maximum value of $Z = 3x + 2y$ where $x + 2y \le 10, 3x + y \le 15, x \ge 0, y \ge 0$ is: [BSEB]

(A) $0$

(B) $15$

(C) $10$

(D) $18$

25. Maximum value of $Z = 3x + 2y$ where $3x + y \le 15, x \ge 0, y \ge 0$ is: [BSEB]

(A) $30$

(B) $15$

(C) $10$

(D) None of these

26. Maximum value of $Z = x + 2y$ subject to $x + y \le 6, x \ge 0, y \ge 0$ is: [BSEB]

(A) $12$

(B) $6$

(C) $18$

(D) $0$

27. Maximum value of $Z = 3x + 2y$ under $x + y \le 10, x \ge 0, y \ge 0$ will be: [BSEB]

(A) $30$

(B) $20$

(C) $10$

(D) $0$

28. Maximum value of $x + y$ subject to $3x + 5y \le 30, x \ge 0, y \ge 0$ is: [BSEB]

(A) $16$

(B) $10$

(C) $6$

(D) None of these

29. Maximum value of $Z = 3x + y$ under $x + y \le 2, x \ge 0, y \ge 0$ is: [BSEB]

(A) $4$

(B) $6$

(C) $2$

(D) $0$

30. Maximum value of $Z = 4x + y$ under $x + y \le 10, x, y \ge 0$ is: [BSEB]

(A) $36$

(B) $40$

(C) $30$

(D) None of these

31. Maximum value of $Z = 3x + 4y$ where $x + y \le 4, x \ge 0, y \ge 0$ is: [BSEB]

(A) $0$

(B) $12$

(C) $16$

(D) None of these

32. Maximum value of $Z = 3x – y$ subject to $x + y \le 8, x \ge 0, y \ge 0$ is: [BSEB]

(A) $-8$

(B) $24$

(C) $16$

(D) $8$

33. Maximum value of $Z = 6x + 3y$ subject to $x + y \le 25, x \ge 0, y \ge 0$ is: [BSEB]

(A) $150$

(B) $225$

(C) $425$

(D) None of these

34. Maximum value of $Z = 4x + y$ subject to $x + y \le 50, x, y \ge 0$ is: [BSEB]

(A) $50$

(B) $250$

(C) $0$

(D) None of these

35. Maximum value of $Z = 10x + 6y$ where $x + y \le 12, 2x + y \le 20, x, y \ge 0$ is: [BSEB]

(A) $120$

(B) $112$

(C) $104$

(D) $80$

36. The corner points of a feasible region are (0,0), (5,0), (3,4), and (0,5). The maximum value of $Z = 4x + 3y$ will be: [BSEB]

(A) $20$

(B) $24$

(C) $15$

(D) $18$

37. Maximum value of $Z = x + y$ subject to $x + y \le 1, x \ge 0, y \ge 0$ is: [BSEB]

(A) $0$

(B) $1$

(C) $2$

(D) None of these

38. Maximum value of $Z = 7x + 11y$ for $x + y \le 7, x, y \ge 0$ is: [BSEB]

(A) $49$

(B) $77$

(C) $0$

(D) $11$

39. Among the points (0,0), (4,0), (2,4), and (0,5), the maximum value of $Z = 2x + 5y$ occurs at: [BSEB]

(A) (4,0)

(B) (2,4)

(C) (0,5)

(D) (0,0)

40. Maximum value of $Z = x + y$ subject to $x \le 20, y \le 30, x, y \ge 0$ is: [BSEB]

(A) $20$

(B) $30$

(C) $50$

(D) $0$

41. Maximum value of $Z = 5x + 3y$ for $3x + 5y \le 15, 5x + 2y \le 10, x, y \ge 0$ is: [BSEB]

(A) $10$

(B) $15$

(C) $12.35$

(D) $9$

42. Maximum value of $Z = 4x + 6y$ for $3x + 2y \le 12, x + y \le 5, x, y \ge 0$ is: [BSEB]

(A) $18$

(B) $24$

(C) $30$

(D) $15$

43. Maximum value of $Z = 3x + 5y$ for $x + y \le 2, x, y \ge 0$ is: [BSEB]

(A) $6$

(B) $10$

(C) $0$

(D) $15$

44. Maximum value of $Z = 250x + 75y$ subject to $x + y \le 40, 2x + y \le 60, x, y \ge 0$ is: [BSEB]

(A) $7500$

(B) $3000$

(C) $6250$

(D) $8000$

45. Maximum value of $Z = 6x + 3y$ for $x + y \le 5, y \le 3, x, y \ge 0$ is: [BSEB]

(A) $30$

(B) $21$

(C) $15$

(D) $18$

Section-D: Minimum Value

46. Minimum value of $11x + 2y$ subject to $x + y \le 7, x \ge 0, y \ge 0$ is: [BSEB]

(A) $77$

(B) $14$

(C) $0$

(D) $-14$

47. Minimum value of $Z = 7x + 8y$ subject to $3x + 4y \le 24, x \ge 0, y \ge 0$ is: [BSEB]

(A) $56$

(B) $48$

(C) $0$

(D) $-12$

48. Minimum value of $Z = 2x – 3y$ subject to $x + y \le 5, x \ge 0, y \ge 0$ is: [BSEB]

(A) $0$

(B) $-15$

(C) $10$

(D) $-10$

49. Minimum value of $Z = 5x + 3y$ subject to $x + y \le 5, x \ge 0, y \ge 0$ is: [BSEB]

(A) $0$

(B) $15$

(C) $25$

(D) $10$

50. Minimum value of $Z = 3x + 5y$ where $x + 3y \ge 3, x + y \ge 2, x, y \ge 0$ is: [BSEB]

(A) $0$

(B) $9$

(C) $7$

(D) $10$

51. Minimum value of $Z = 2x – 3y$ subject to $x + y \le 2, x \ge 0, y \ge 0$ is: [BSEB]

(A) $0$

(B) $-6$

(C) $-4$

(D) $4$

52. Minimum value of $Z = 2x + 3y$ subject to $x + y \ge 6, x, y \ge 0$ is: [BSEB]

(A) $12$

(B) $18$

(C) $0$

(D) $6$

53. Minimum value of $Z = 3x + 5y$ where $x + y \le 2, x \ge 0, y \ge 0$ is: [BSEB]

(A) $16$

(B) $15$

(C) $0$

(D) None of these

54. Minimum value of $Z = 3x + 9y$ subject to $x + 3y \le 60, x + y \ge 10, x \le y, x, y \ge 0$ is: [BSEB]

(A) $60$

(B) $180$

(C) $90$

(D) $120$

55. Minimum value of $Z = x + 2y$ for $2x + y \ge 3, x + 2y \ge 6, x, y \ge 0$ is: [BSEB]

(A) $3$

(B) $6$

(C) $0$

(D) $9$

56. Minimum value of $Z = 200x + 500y$ for $x + 2y \ge 10, 3x + 4y \le 24, x, y \ge 0$ is: [BSEB]

(A) $2300$

(B) $2500$

(C) $2000$

(D) None of these

57. Minimum value of $Z = 5x + 10y$ for $x + 2y \le 120, x + y \ge 60, x – 2y \ge 0, x, y \ge 0$ is: [BSEB]

(A) $300$

(B) $600$

(C) $100$

(D) $0$

58. For $x \ge 0, y \ge 0$, the minimum value of $Z = x + y$ is always: [BSEB]

(A) $1$

(B) $0$

(C) $-1$

(D) Undefined

59. Minimum value of $Z = 6x + 10y$ for $2x + y \ge 1, x + 3y \ge 3, x, y \ge 0$ is: [BSEB]

(A) $10$

(B) $6$

(C) $3$

(D) $9$

60. Minimum value of $Z = 3x + 2y$ for $x + y \ge 8, 3x + 5y \ge 15, x, y \ge 0$ is: [BSEB]

(A) $16$

(B) $24$

(C) $15$

(D) $10$

Section-E: Applications & Miscellaneous

61. Which of the following is NOT a Linear Programming Problem? [BSEB]

(A) Diet problem

(B) Transportation problem

(C) Manufacturing problem

(D) Quadratic problem

62. The feasible region of constraints $x + y \ge 4, x \le 2, y \le 2$ is: [BSEB]

(A) In the first quadrant

(B) Only one point (2,2)

(C) Unbounded

(D) Does not exist

63. The “Corner Point Method” in Linear Programming is used to find: [BSEB]

(A) Feasible region

(B) Optimal solution

(C) Number of constraints

(D) None of these

64. $x \ge 0, y \ge 0$ means the solution is located in: [BSEB]

(A) I quadrant

(B) II quadrant

(C) III quadrant

(D) IV quadrant

65. A manufacturer makes two products A and B. This problem is a: [BSEB]

(A) Diet problem

(B) Manufacturing problem

(C) Transportation problem

(D) None of these

66. Any point in the feasible region is called: [BSEB]

(A) Optimal solution

(B) Feasible solution

(C) Corner point

(D) Invalid solution

67. If the number of constraints increases, the feasible region: [BSEB]

(A) Increases

(B) Decreases or stays same

(C) Always stays same

(D) None of these

68. In the objective function $Z = 4x + y$, if $x=0, y=0$, then the value of $Z$ will be: [BSEB]

(A) $4$

(B) $1$

(C) $0$

(D) Undefined

69. The graph of linear inequality $2x + 3y \le 6$ is: [BSEB]

(A) A straight line

(B) A half-plane

(C) A circle

(D) None of these

70. For $Z = 3x + 4y$, if corner points are (0,4) and (4,0), the maximum value will be: [BSEB]

(A) $12$

(B) $16$

(C) $28$

(D) $4$

71. In a “Transportation Problem”, the cost is always: [BSEB]

(A) Maximized

(B) Minimized

(C) Set to zero

(D) Kept constant

72. The feasible region of $x + y \le 1$ and $x + y \ge 2$ is: [BSEB]

(A) A triangle

(B) A line

(C) Empty

(D) Unbounded

73. In Linear Programming, the values of variables should always be: [BSEB]

(A) Negative

(B) Non-negative (Zero or positive)

(C) Only positive

(D) Any real number

74. Minimum value of $Z = x – y$ for $x + y \le 1, x, y \ge 0$ is: [BSEB]

(A) $0$

(B) $-1$

(C) $1$

(D) $2$

75. Can an objective function have the same maximum value at two different points? [BSEB]

(A) Yes

(B) No

(C) Only at origin

(D) None of these

76. If $Z$ has the same maximum value at two corner points, then at every point on the line joining them, $Z$ is: [BSEB]

(A) Different

(B) The same maximum value

(C) Zero

(D) Minimum

77. Where is the graph of $y \ge 0$ located? [BSEB]

(A) Above the $x$-axis and on the $x$-axis

(B) Below the $x$-axis

(C) To the left of $y$-axis

(D) To the right of $y$-axis

78. Value of objective function $Z = 3x + 2y$ at point (2,3) is: [BSEB]

(A) $12$

(B) $13$

(C) $5$

(D) $6$

79. Maximum value of $Z = x + y$ for constraints $x \le 5, y \le 5$ is: [BSEB]

(A) $5$

(B) $10$

(C) $0$

(D) $25$

80. In an LPP if $Z = 2x + 5y$ and corner points are (0,2), (3,0), (0,0), then maximum $Z$ is: [BSEB]

(A) $6$

(B) $10$

(C) $0$

(D) $15$

Section-F: Important Repetitive Questions

81. Maximum value of $Z = 5x + 10y$ for $x + 2y \le 120, x + y \ge 60$: [BSEB]

(A) $600$

(B) $300$

(C) $400$

(D) $120$

82. $x \ge 0, y \ge 0$ constraints are called: [BSEB]

(A) Non-negative constraints

(B) Main constraints

(C) Objective constraints

(D) None of these

83. Maximum value of $Z = 3x + 4y$ for $x + y \le 1$ is: [BSEB]

(A) $3$

(B) $4$

(C) $7$

(D) $0$

84. The region of constraints $x + y \le 20, x \ge 0, y \ge 0$ is a: [BSEB]

(A) Triangle

(B) Rectangle

(C) Circle

(D) Line

85. What is the value of $Z = 4x + 2y$ at corner point (2,1)? [BSEB]

(A) $6$

(B) $8$

(C) $10$

(D) $12$

86. In an LPP, $x$ and $y$ are called: [BSEB]

(A) Constants

(B) Decision variables

(C) Coefficients

(D) None of these

87. At which point does the line $x + 2y \le 10$ intersect the $x$-axis? [BSEB]

(A) (0,5)

(B) (10,0)

(C) (5,0)

(D) (0,10)

88. Maximum value of $Z = 10x + y$ for $x \le 5, y \le 10, x, y \ge 0$ is: [BSEB]

(A) $50$

(B) $60$

(C) $10$

(D) $55$

89. Points included in the feasible region are called: [BSEB]

(A) Optimal solutions

(B) Possible solutions

(C) Constraints

(D) None of these

90. Minimum value of $Z = x + y$ for $x \ge 1, y \ge 1$ is: [BSEB]

(A) $0$

(B) $1$

(C) $2$

(D) Undefined

91. In a manufacturing problem, $Z$ usually represents: [BSEB]

(A) Loss

(B) Profit

(C) Time

(D) Distance

92. $x = 0$ is the equation of which axis? [BSEB]

(A) $x$-axis

(B) $y$-axis

(C) Origin

(D) None of these

93. $y = 0$ is the equation of which axis? [BSEB]

(A) $x$-axis

(B) $y$-axis

(C) Origin

(D) None of these

94. What is the maximum value of $Z = 2x + 3y$ for $x + y \le 4$ at corner point (0,4)? [BSEB]

(A) $8$

(B) $12$

(C) $10$

(D) $6$

95. The shape of a feasible region is always a: [BSEB]

(A) Convex Polygon

(B) Concave Polygon

(C) Circle

(D) Parabola

96. If $x + y \le 0$ and $x, y \ge 0$, then the solution is: [BSEB]

(A) Unbounded

(B) Only (0,0)

(C) No solution

(D) Full first quadrant

97. Maximum value of $Z = 3x + y$ for $2x + 3y \le 6$ is: [BSEB]

(A) $9$

(B) $2$

(C) $6$

(D) $3$

98. Who developed Linear Programming? [BSEB]

(A) Newton

(B) George Dantzig

(C) Euclid

(D) Pythagoras

99. Value of $Z = 5x + 4y$ at (1,1) is: [BSEB]

(A) $20$

(B) $9$

(C) $1$

(D) $0$

100. Maximum value of $Z = x + y$ under $x + y \le 100, x \ge 0, y \ge 0$ is: [BSEB]

(A) $50$

(B) $100$

(C) $200$

(D) $0$