NCERT Class 12 Chapter 12 Maths Linear Programming MCQ

NCERT Class 12 Chapter 12 Maths Linear Programming MCQ | Questions & Answers: Give your try for the NCERT Class 12 Chapter 12 Maths Linear Programming MCQ Quiz and check your expertise in the respective area of interest. Good luck!

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1. Z = 20x₁ + 20x₂, 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. (52,154)

C. (72,94)

D. (0, 10)

2. In maximization problem, optimal solution occurring at corner point yields the

A. highest value of z

B. lowest value of z

C. mid values of z

D. mean values of z

3. In solving the LPP: “minimize f = 6x + 10y subject to constraints x ≥ 6, y ≥ 2, 2x + y ≥ 10, x ≥ 0, y ≥ 0” redundant constraints are

A. x ≥ 6, y ≥ 2

B. 2x + y ≥ 10, x ≥ 0, y ≥ 0

C. x ≥ 6

D. none of these

4. Problems which seek to maximise or, minimise profit or, cost form a general class of problems called ………

A. Simple problems

B. Difficult problems

C. Non-linear problems

D. Optimisation problems

5. Z = 7x + y, subject to 5x + y ≥ 5, x + y ≥ 3, x ≥ 0, y ≥ 0. The minimum value of Z occurs at

A. (3, 0)

B. (12,52)

C. (7, 0)

D. (0, 5)

6. In a LPP, the objective function is always

A. Linear

B. Quadratic

C. Cubic

D. Biquadratic

7. 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

8. A ……… of a feasible region is a point in the region, which is the intersection of two boundary lines.

A. Section point

B. Corner point

C. Reasonable point

D. Vertex point

9. Minimize Z = 20x₁ + 9x₂, subject to x₁ ≥ 0, x₂ ≥ 0, 2x₁ + 2x₂ ≥ 36, 6x₁ + x₂ ≥ 60.

A. 360 at (18, 0)

B. 336 at (6, 4)

C. 540 at (0, 60)

D. 0 at (0, 0)

10. A feasible solution to a linear programming problem

A. Must satisfy all of the problem's constraints simultaneously

B. Need not satisfy all of the constraints, only the non-negativity constraints

C. Must be a corner point of the feasible region

D. Must give the maximum possible profit

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11. Region represented by x ≥ 0, y ≥ 0 is

A. first quadrant

B. second quadrant

C. third quadrant

D. fourth quadrant

12. The linear inequalities or equations or restrictions on the variables of a linear programming problem are called ...... The conditions x ≥ 0 , y ≥ 0 are called .......

A. Objective functions, optimal value

B. Constraints, non-negative restrictions

C. Objective functions, non-negative restrictions

D. Constraints, negative restrictions

13. Z = 8x + 10y, subject to 2x + y ≥ 1, 2x + 3y ≥ 15, y ≥ 2, x ≥ 0, y ≥ 0. The minimum value of Z occurs at

A. (4.5, 2)

B. (1.5, 4)

C. (0, 7)

D. (7, 0)

14. The corner points of the bounded feasible region of a LPP are A(0,50), B(20, 40), C(50, 100) and D(0, 200) and the objective function is Z = x + 2y. Then the maximum value is

A. 400

B. 250

C. 450

D. 100

15. 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

16. The common region determined by all the constraints including non-negative constraints x, y ≥ 0 of a linear programming problem is called the ……...

A. Bounded region

B. Simple region

C. Infeasible region

D. Feasible region

17. The feasible region (shaded) for a L.P.P is shown in the figure. The maximum Z = 5x + 7y is

A. 43

B. 47

C. 45

D. 49

18. The region represented by the inequalities
x ≥ 6, y ≥ 2, 2x + y ≤ 0, x ≥ 0, y ≥ 0 is

A. unbounded

B. a polygon

C. exterior of a triangle

D. None of these

19. Let Z = ax + by is a linear objective function. Variables x and y are called ……… variables.

A. Independent

B. Continuous

C. Decision

D. Dependent

20. The maximum value of f = 4x + 3y subject to constraints x ≥ 0, y ≥ 0, 2x + 3y ≤ 18; x + y ≥ 10 is

A. 35

B. 36

C. 34

D. none of these

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21. 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

22. A linear function of several variables x and y is called ……...

A. Non-linear function

B. Optimal function

C. Objective function

D. Simple function

23. Objective function of a L.P.P.is

A. a constant

B. a function to be optimised

C. a relation between the variables

D. none of these

24. The minimum value of Z = 4x + 3y subjected to the constraints 3x + 2y ≥ 160, 5 + 2y ≥ 200, 2y ≥ 80; x, y ≥ 0 is

A. 220

B. 300

C. 230

D. none of these

25. Every point of feasible region is called a ……… to the problem.

A. Simple solution

B. Normal solution

C. Difficult solution

D. Feasible solution