## NCERT Solutions for Class 12 Maths Chapter 12 Linear Programming MCQ’s with Answers

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## NCERT **Maths MCQs for Class 12 Question and Answers Chapter 12 Linear Programming PDF**

### Q1. Z = 20×1 + 20×2, subject to x1 ≥ 0, x2 ≥ 0, x1 + 2×2 ≥ 8, 3×1 + 2×2 ≥ 15, 5×1 + 2×2 ≥ 20. The minimum value of Z occurs at

(a) (8, 0)

(b) (5/2, 7/2)

(c) (7/2,9/4)

(d) (0, 10)

Option c – (7/2,9/4)

### Q2. Minimize Z = 20×1 + 9×2, subject to x1 ≥ 0, x2 ≥ 0, 2×1 + 2×2 ≥ 36, 6×1 + x2 ≥ 60.

(a) 360 at (18, 0)

(b) 336 at (6, 4)

(c) 540 at (0, 60)

(d) 0 at (0, 0)

Option b – 336 at (6, 4)

### Q3. 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)( (1 , 5)

(c) (7, 0)

(d) (0, 5)

Option d – (0, 5)

### Q4. Z = 4×1 + 5×2, subject to 2×1 + x2 ≥ 7, 2×1 + 3×2 ≤ 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)

Option a – (3.5, 0)

### Q5. 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

Option d – none of these

### Q6. 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

Option b – a function to be optimised

### Q7. 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

Option c – a which are comer points of the feascible region

### Q8. 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

Option d – None of these

### Q9. 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

Option a – 220

### Q10. 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

Option d – none of these

### Q11. 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)

Option b – 60 at (4, 2)

### Q12. 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)

Option b – (2, 5)

### Q13. 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)

Option d – 36 at (0, 6)

### Q14. 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)

Option b – (1.5, 4)

### Q15. 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

Option b – 2x + y ≥ 10, x ≥ 0, y ≥ 0