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Maths (commerce) MCQ

Linear Programming (p-2) · Maharashtra Board STD 12 Commerce / Arts (MSBSHSE - English Medium). 15 questions.

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MCQ

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15 questions · auto-graded multiple-choice test.

MCQ 11 Mark
Solution of LPP to minimize z = 2x + 3y subjected to x ≥ 0, y ≥ 0, 1 ≤ x + 2y ≤ 10 is
  • ✓
    $x=0, y=\frac{1}{2}$
  • B
    $x=\frac{1}{2}, y=0$
  • C
    $x=1, y=-2$
  • D
    $x=y=\frac{1}{2}$
Answer
Correct option: A.
$x=0, y=\frac{1}{2}$
$x=0, y=\frac{1}{2}$
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MCQ 21 Mark
Feasible region; the set of points which satisfy
  • A
    The objective function
  • ✓
    All of the given function
  • C
    Some of the given constraints
  • D
    Only non-negative constraints
Answer
Correct option: B.
All of the given function
All of the given function
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MCQ 31 Mark
Of all the points of the feasible region the optimal value of z is obtained at a point
  • A
    Inside the feasible region
  • B
    at the boundary of the feasible region
  • ✓
    at vertex of feasible region
  • D
    on x -axis
Answer
Correct option: C.
at vertex of feasible region
at vertex of feasible region
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MCQ 41 Mark
The point at which the maximum value of z = x + y subject to the constraint x + 2y ≤ 70, 2x + y ≤ 15, x ≥ 0, y ≥ 0 is
  • A
    $(36,25)$
  • B
    $(20,35)$
  • C
    $(35,20)$
  • ✓
    $(40,15)$
Answer
Correct option: D.
$(40,15)$
$(40,15)$
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MCQ 51 Mark
The maximum value of z = 10x + 6y. subject to the constraints 3x + y ≤ 12, 2x + 5y ≤ 34, x ≥ 0, y ≥ 0 is.
  • ✓
    56
  • B
    65
  • C
    55
  • D
    66
Answer
Correct option: A.
56
56
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MCQ 61 Mark
The maximum value of z = 5x + 3y. subject to the constraints 3x + 5y = 15; 5x + 2y ≤ 10, x, y ≥ 0 is
  • A
    235
  • B
    $\frac{235}{9}$
  • ✓
    $\frac{235}{19}$
  • D
    $\frac{235}{3}$
Answer
Correct option: C.
$\frac{235}{19}$
$\frac{235}{19}$
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MCQ 71 Mark
Objective function of LPP is
  • A
    a constraint
  • ✓
    a function to be maximized or minimized
  • C
    a relation between the decision variables
  • D
    a feasible region
Answer
Correct option: B.
a function to be maximized or minimized
a function to be maximized or minimized
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MCQ 81 Mark
Which of the following is correct?
  • A
    Every LPP has on optional solution
  • B
    Every LPP has unique optional solution
  • ✓
    If LPP has two optional solutions then it has infinitely many solutions
  • D
    The set of all feasible solutions LPP may not be a convex set
Answer
Correct option: C.
If LPP has two optional solutions then it has infinitely many solutions
If LPP has two optional solutions then it has infinitely many solutions
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MCQ 91 Mark
The half plane represented by 4x + 3y ≥ 14 contains the point
  • A
    (0, 0)
  • B
    (2, 2)
  • ✓
    (3, 4)
  • D
    (1, 1)
Answer
Correct option: C.
(3, 4)
(3, 4)
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MCQ 101 Mark
The half plane represented by 3x + 2y ≤ 0 contains the point.
  • A
    $\left(1, \frac{5}{2}\right)$
  • B
    (2, 1)
  • ✓
    (0, 0)
  • D
    (5, 1)
Answer
Correct option: C.
(0, 0)
(0, 0)
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MCQ 111 Mark
If the comer points of the feasible region are (0, 10), (2, 2), and (4, 0) then the point of minimum z = 3x + 2y is.
  • ✓
    (2, 2)
  • B
    (0, 10)
  • C
    (4, 0)
  • D
    (2, 4)
Answer
Correct option: A.
(2, 2)
(2, 2)
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MCQ 121 Mark
If the corner points of the feasible region are $(0,0),(3,0),(2,1)$ and $\left(0, \frac{7}{3}\right)$ the maximum value of $z=4 x+5 y$ is
  • A
    12
  • ✓
    13
  • C
    $\frac{35}{2}$
  • D
    $0$
Answer
Correct option: B.
13
13
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MCQ 131 Mark
The corner point of the feasible region are $(0,0),(2,0),\left(\frac{12}{7}, \frac{3}{7}\right)$ and $(0,1)$ then the point of maximum $z=6.5 x+y=13$
  • A
    $(0,0)$
  • ✓
    $(2,0)$
  • C
    $\left(\frac{11}{7}, \frac{3}{7}\right)$
  • D
    $(0,1)$
Answer
Correct option: B.
$(2,0)$
$(2,0)$
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MCQ 141 Mark
The corner points of the feasible region given by the inequation x + y ≤ 4, 2x + y ≤ 7, x ≥ 0, y ≥ 0, are
  • A
    $(0,0),(4,0),(3,1),(0,4)$
  • ✓
    $(0,0),\left(\frac{7}{2}, 0\right),(3,1),(0,4)$
  • C
    $(0,0),\left(\frac{7}{2}, 0\right),(3,1),(5,7)$
  • D
    $(6,0),(4,0),(3,1),(0,7)$
Answer
Correct option: B.
$(0,0),\left(\frac{7}{2}, 0\right),(3,1),(0,4)$
$(0,0),\left(\frac{7}{2}, 0\right),(3,1),(0,4)$
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MCQ 151 Mark
The value of objective function is maximized under linear constraints.
  • ✓
    at the centre of feasible region
  • B
    at (0, 0)
  • C
    at any vertex of feasible region.
  • D
    The vertex which is at maximum distance from (0, 0)
Answer
Correct option: A.
at the centre of feasible region
at the centre of feasible region
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