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Free download in PDF Class 12 Maths Chapter 12 Linear Programming Multiple Choice Questions and Answers for Board, JEE, NEET, AIIMS, JIPMER, IIT-JEE, AIEE and other competitive exams. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. These short solved questions or quizzes are provided by Gkseries. These will help the students for preparation of their examination./p>
(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)
(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)
(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)
(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)
(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)
(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
(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
(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
(9)
Region represented by x ≥ 0, y ≥ 0 is
[A]
first quadrant
[B]
second quadrant
[C]
third quadrant
[D]
fourth 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
(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)
(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)
(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)
(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)
(18)
In a LPP, the objective function is always
[A]
Linear
[B]
Quadratic
[C]
Cubic
[D]
Biquadratic
(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
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