# MCQ Questions for Class 12 Maths Chapter 12 Linear Programming with answers

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Below you will find MCQ Questions of Chapter 12 Linear Programming Class 12 Maths Free PDF Download that will help you in gaining good marks in the examinations and also cracking competitive exams. These Class 12 MCQ Questions with answers will widen your skills and understand concepts in a better manner.

# MCQ Questions for Class 12 Maths Chapter 12 Linear Programming with answers

1. Let Z = ax + by is a linear objective function. Variables x and y are called ____ variables.​

(a) Independent

(b) Continuous

(c) Decision

(d) Dependent

► (c) Decision

2. How many of the following points satisfy the inequality 2x – 3y > -5?

(1, 1), (-1, 1), (1, -1), (-1, -1), (-2, 1), (2, -1), (-1, 2) and (-2, -1)​

(a) 2

(b) 4

(c) 6

(d) 5

► (d) 5

3. A feasible solution of a LPP if it also optimizes the objective function is called​

(a) Optimal feasible solution﻿

(b) Optimal solution﻿

(c) Feasible solution﻿

(d) None of these

► (a) Optimal feasible solution﻿

4. In a LPP, the objective function is always

(a) cubic

(c) Linear

(d) constant

► (c) Linear

5. 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

► (b) Constraints, non-negative restrictions

6. A toy company manufactures two types of toys A and B. Demand for toy B is atmost half of that if type A. Write the corresponding constraint if x toys of type A and y toys of type B are manufactured.​

(a) x/2 ≤ y

(b) 2y – x ≥ 0

(c) x – 2y ≥ 0

(d) x < 2y

► (c) x – 2y ≥ 0

7. Objective function of a LPP is​

(a) function to be optimized

(b) A constraint

(c) Relation between variables

(d) Equation in a line

► (a) function to be optimized

8. Minimise Z = 13x – 15y subject to the constraints : x + y ≤ 7, 2x – 3y + 6 ≥ 0 , x ≥ 0, y ≥ 0.

(a) – 23

(b) – 32

(c) – 30

(d) – 34

► (c) – 30

9. Infeasibility means that the number of solutions to the linear programming models that satisfies all constraints is​

(a) At least 1

(b) An infinite number

(c) Zero

(d) At least 2

► (c) Zero

10. Shape of the feasible region formed by the following constraints is x + y ≤ 2, x + y ≥ 5, x ≥ 0, y ≥ 0​

(a) No feasible region

(b) Triangular region

(c) Unbounded solution

(d) Trapezium

► (a) No feasible region

11. The set of all feasible solutions of a LPP is a ____ set.​

(a) Concave

(b) Convex

(c) Feasible

(d) None of these

► (b) Convex

12. The optimum value of the objective function is attained at the points​

(a) Corner points of feasible region

(b) Any point of the feasible region

(c) On x-axis

(d) On y-axis

► (a) Corner points of feasible region

13. Maximise the function Z = 11x + 7y, subject to the constraints: x ≤ 3, y ≤ 2,x ≥ 0, y ≥ 0.

(a) 49

(b) 50

(c) 47

(d) 48

► (c) 47

14. Let R be the feasible region for a linear programming problem and let Z = ax + by be the objective function. If R is bounded, then the objective function Z has both a maximum and a minimum value on R and

(a) each of these occurs at a corner point (vertex) of R.

(b) each of these occurs at themidpoints of the edges of R

(c) each of these occurs at the centre of R.

(d) each of these occurs at some points except corner points of R.

► (a) each of these occurs at a corner point (vertex) of R.

15. Minimize Z = 3x + 5y such that x + 3y ≥ 3, x + y ≥ 2, x, y ≥ 0.

(a) Minimum Z = 7 at 3/2,1/2

(b) Minimum Z = 8 at 3/2,1/2

(c) Minimum Z = 9 at 3/2,1/2 110 V 60 Hz

(d) Minimum Z = 10 at 3/2,1/2

► (a) Minimum Z = 7 at 3/2,1/2

16. A maximum or a minimum may not exist for a linear programming problem if

(a) The feasible region is bounded

(b) if the constraints are non linear

(c) if the objective function is continuous

(d) The feasible region is unbounded

► (d) The feasible region is unbounded

17. Let R be the feasible region for a linear programming problem, and let Z = ax + by be the objective function. If R is bounded, then

(a) the objective function Z has only a maximum value on R

(b) the objective function Z has only a minimum value on R

(c) the objective function Z has both a maximum and a minimum value on R

(d) the objective function Z has no minimum value on R

► (c) the objective function Z has both a maximum and a minimum value on R

18. In linear programming feasible region (or solution region) for the problem is

(a) The common region determined by all the constraints including the non – negative constraints x ⩾ 0, y⩾ 0

(b) The common region determined by all the x ⩾ 0 and the objective function

(c) The common region determined by all the objective functions including the non – negative constraints x ⩾ 0, y ⩾ 0

(d) The common region determined by all the x ⩾ 0, y ⩾ 0 and the objective function

► (a) The common region determined by all the constraints including the non – negative constraints x ⩾ 0, y⩾ 0

19. In linear programming problems the optimum solution

(a) satisfies a set of piecewise – linear inequalities (called constraints)

(b) satisfies a set of linear inequalities (called linear constraints)

(c) satisfies a set of quadratic inequalities (calledconstraints)

(d) satisfies a set of cubic inequalities (calledconstraints)

► (b) satisfies a set of linear inequalities (called linear constraints)

20. Find the maximum value of z = 3x + 4y subject to constraints x + y ≤ 4 , x ≥ 0 and y ≥ 0​

(a) 12

(b) 16

(c) 7

(d) 14

► (b) 16

Hope the given MCQ Questions will help you in cracking exams with good marks. These Linear programming MCQ Questions will help you in practising more and more questions in less time.