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
 (a) a constant
Answer: (b) a function to be optimised
Question 2. The optimal value of the objective function is attained at the points

 (a) on Xaxis
(b) on Yaxis
(c) which are comer points of the feascible region
(d) none of these
 (a) on Xaxis
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
 (a) x ≥ 6, y ≥ 2
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
 (a) first 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
 (a) unbounded
Answer: (d) None of these
Question 6. 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)
 (a) 20 at (1, 0)
Answer: (c) 37 at (4, 5)
Question 7. 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)
 (a) 16 at (4, 0)
Answer: (d) 36 at (0, 6)
Question 8. Maximize Z = 6x + 4y, subject to x ≤ 2, x + y ≤ 3, 2x + y ≤ 1, x ≥ 0, y ≥ 0.

 (a) 12 at (2, 0)
(b) 1403 at (23, 13)
(c) 16 at (2, 1)
(d) 4 at (0, 1)
 (a) 12 at (2, 0)
Answer: (c) 16 at (2, 1)
Question 9. 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)
 (a) 80 at (3, 2)
Answer: (d) 95 at (2, 3)
Bihar Board 12th math chapter 12 most mcq notes and solution
Question 10. 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) (52,154)
(c) (72,94)
(d) (0, 10)
 (a) (8, 0)
Answer: (c) (72,94)
Question 11. 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) (12,52)
(c) (7, 0)
(d) (0, 5)
 (a) (3, 0)
Answer: (d) (0, 5)
Question 12. 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)
 (a) 360 at (18, 0)
Answer: (b) 336 at (6, 4)
Question 13. 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)
 (a) (4.5, 2)
Answer: (b) (1.5, 4)
Question 14. 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)
 (a) (3.5, 0)
Answer: (a) (3.5, 0)
Question 15. 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
 (a) 35
Answer: (d) none of these
Question 16. 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
 (a) 220
Answer: (a) 220
Question 17. 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
 (a) 32
Answer: (d) none of these
Question 18. 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)
 (a) 44 at (4, 2)
Answer: (b) 60 at (4, 2)
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