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

Questions
1 Maximize Z = 10×1 + 25×2, 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)
2 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, 1/3)
C 16 at (2, 1)
D 4 at (0, 1)

Answer:16 at (2, 1)

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3 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)
4 The feasible region for an LPP is shown shaded in the following figure. Minimum of Z = 4x + 3y occurs at the point Class 12 Maths Chapter 12 Linear Programming
A (0, 8)
B (2, 5)
C (4, 3)
D (9, 0)

Answer:(2, 5)
5 Maximize Z = 11x + 8y, subject to x ≤ 4, 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)
6 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

Answer:none of these
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

Answer:220
8 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

Answer:None of these
9 Region represented by x ≥ 0, y ≥ 0 is
A first quadrant
B second quadrant
C third quadrant
D fourth quadrant

Answer:first quadrant
10 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

Answer:2x + y ≥ 10, x ≥ 0, y ≥ 0
11 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

Answer:which are comer points of the feascible region
12 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

Answer:a function to be optimised
13 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

Answer:none of these
14 Z = 4x1 + 5x2, subject to 2x1 + x2 ≥ 7, 2x1 + 3x2 ≤ 15, x2 ≤ 3, x1, x2 ≥ 0. The minimum value of Z occurs at
A (3.5, 0)
B (3, 3)
C (7.5, 0)
D (2, 3)

Answer:(3.5, 0)
15 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)

Answer:(1.5, 4)
16 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)

Answer:336 at (6, 4)
17 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 (1/2,5/2)
C (7, 0)
D (0, 5)

Answer:(0, 5)
18 In a LPP, the objective function is always
A Linear
B Quadratic
C Cubic
D Biquadratic

Answer:Linear
19 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

Answer:highest value of z
20 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

Answer:400

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