Bihar Board 12th Maths Objective Answers Chapter 12 Linear Programming

Bihar Board 12th Maths Objective Questions and Answers

Bihar Board 12th Maths Objective Answers Chapter 12 Linear Programming

Question 1.
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:
(b) a function to be optimised

Question 2.
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:
(c) which are comer points of the feascible region

Question 3.
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:
(b) 2x + y ≥ 10, x ≥ 0, y ≥ 0

Question 4.
Region represented by x ≥ 0, y ≥ 0 is
(a) first quadrant
(b) second quadrant
(c) third quadrant
(d) fourth quadrant
Answer:
(a) first quadrant

Question 5.
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:
(d) None of these

Question 6.
Feasible region for an LPP is shown shaded in the following 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:
(b) (2, 5)

Question 7.
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:
(c) 37 at (4, 5)

Question 8.
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:
(d) 36 at (0, 6)

Question 9.
Maximize Z = 6x + 4y, subject to x ≤ 2, x + y ≤ 3, -2x + y ≤ 1, x ≥ 0, y ≥ 0.
(a) 12 at (2, 0)
(b) \(\frac{140}{3}\) at (\(\frac{2}{3}\), \(\frac{1}{3}\))
(c) 16 at (2, 1)
(d) 4 at (0, 1)
Answer:
(c) 16 at (2, 1)

Question 10.
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:
(d) 95 at (2, 3)

Question 11.
Z = 20x₁ + 20x₂, 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) \(\left(\frac{5}{2}, \frac{15}{4}\right)\)
(c) \(\left(\frac{7}{2}, \frac{9}{4}\right)\)
(d) (0, 10)
Answer:
(c) \(\left(\frac{7}{2}, \frac{9}{4}\right)\)

Question 12.
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) \(\left(\frac{1}{2}, \frac{5}{2}\right)\)
(c) (7, 0)
(d) (0, 5)
Answer:
(d) (0, 5)

Question 13.
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:
(b) 336 at (6, 4)

Question 14.
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:
(b) (1.5, 4)

Question 15.
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:
(a) (3.5, 0)

Question 16.
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:
(d) none of these

Question 17.
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:
(a) 220

Question 18.
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:
(d) none of these

Question 19.
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:
(b) 60 at (4, 2)

Question 20.
The feasible, region for an LPP is shown shaded in the figure. Let Z = 3x – 4y be the objective function. Minimum of Z occurs at

(a) (0, 0)
(b) (0, 8)
(c) (5, 0)
(d) (4, 10)
Answer:
(b) (0, 8)