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 = 20x_{1} + 20x_{2}, subject to x_{1} ≥ 0, x_{2} ≥ 0, x_{1} + 2x_{2} ≥ 8, 3x_{1} + 2x_{2} ≥ 15, 5x_{1} + 2x_{2} ≥ 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 = 20x_{1} + 9x_{2}, subject to x_{1} ≥ 0, x_{2} ≥ 0, 2x_{1} + 2x_{2} ≥ 36, 6x_{1} + x_{2} ≥ 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 = 4x_{1} + 5x_{2}, subject to 2x_{1} + x_{2} ≥ 7, 2x_{1} + 3x_{2} ≤ 15, x_{2} ≤ 3, x_{1}, x_{2} ≥ 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)