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

(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
[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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