NCERT Solutions for class 12 Maths | Chapter 12 - Linear Programming

Questions
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)

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)

Answer:95 at (2, 3)

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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)

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)

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

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

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)

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)

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

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

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)

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)

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

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

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

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

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

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)

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

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
A (0, 0)
B (0, 8)
C (5, 0)
D (4, 10)

Answer:(0, 8)

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