Check the below NCERT MCQ Questions for Class 12 Maths Chapter 12 Linear Programming with Answers Pdf free download. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. We have provided Linear Programming Class 12 Maths MCQs Questions with Answers to help students understand the concept very well.

## Q.1 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

## Q.2 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

## Q.3 Region represented by x ≥ 0, y ≥ 0 is

(a) first quadrant

(b) second quadrant

(c) third quadrant

(d) fourth quadrant

## Q.4 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

## Q.5 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

## Q.6 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

## Q.7 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

## Q.8 The maximum value of Z = 3x + 2y, subjected to x + 2y ≤ 2, x + 2y ≥ 8; x, y ≥ 0 is

(a) 32

(b) 24

(c) 40

(d) none of these

## Q.9 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

## Q.10 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

## Q.11 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

## Q.12 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)

## Q.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)

## Q.14 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)

## Q.15 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

## Q.16 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)

## Q.17 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

## Q.18 The point which does not lie in the half plane 2x + 3y -12 < 0 is

(a) (1, 2)

(b) (2, 1)

(c) (2, 3)

(d) (-3, 2)

## Q.19 Refer to Question 18 (Maximum value of Z+ Minimum value of Z) is equal to

(a) 13

(b) 1

(c) -13

(d) -17

## Q.20 The optimal value of the objective function is attained at the points

(a) on X-axis

(b) on Y-axis

(c) which are comer points of the feascible region

(d) none of these

## Q.21 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