# Maths MCQs for Class 12 with Answers Chapter 12 Linear Programming

Free PDF Download of CBSE Maths Multiple Choice Questions for Class 12 with Answers Chapter 12 Linear Programming. Maths MCQs for Class 12 Chapter Wise with Answers PDF Download was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 12 Maths Linear Programming MCQs Pdf with Answers to know their preparation level.

## Linear Programming Class 12 Maths MCQs Pdf

Question 1.
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)
(c) $$\left(\frac{7}{2}, \frac{9}{4}\right)$$

Question 2.
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)
(d) (0, 5)

Question 3.
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)
(b) 336 at (6, 4)

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

Question 5.
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)
(a) (3.5, 0)

Question 6.
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
(d) none of these

Question 7.
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
(b) a function to be optimised

Question 8.
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
(c) which are comer points of the feascible region

Question 9.
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
(b) 2x + y ≥ 10, x ≥ 0, y ≥ 0

Question 10.
Region represented by x ≥ 0, y ≥ 0 is

Question 11.
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
(d) None of these

Question 12.
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

Question 13.
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
(d) none of these

Question 14.
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)
(b) 60 at (4, 2)

Question 15.
The feasible, region for an LPP is shown shaded in the figure. Let Z = 3x – 4y be the objective function. A minimum of Z occurs at

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

Question 16.
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)
(b) (2, 5)

Question 17.
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)
(c) 37 at (4, 5)

Question 18.
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)
(d) 36 at (0, 6)

Question 19.
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)