**MCQs Questions for Class 12 Maths Chapter 12 Linear Programming**

In this 21^{st} century, Multiple Choice Questions (MCQs) play a vital role to prepare for a competitive examination. CBSE board has also brought a major change in its board exam patterns.

In most of the competitive examinations, only MCQ questions are asked. So, for getting ready for the competitive examinations, we have to practice for MCQ questions to solve. It strengthens the critical thinking and problem solving skills.

In future, if you want to prepare for competitive examination and to crack it, then you should more focus on the MCQ questions. Thus, from the board examinations point of view and competitive examinations point of view, you should practice more on multiple choice questions.

Thus, let’s solve these MCQs Questions to make our foundation very strong.

**MCQs Questions for Class 12 Maths Chapter 12 Linear
Programming**

**1.** The objective function
of a linear programming problem is

(a) a
constraint

(b) a function
to be optimized

(c) a
relation between the variables

(d) none of
these

**Answer: b**

**2.** Given, 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) (1/2, 5/2)

(c) (7, 0)

(d) (0, 5)

**Answer: d**

**3. **The maximum value of Z =
4x + 2y subject to the constraints 2x + 3y ≤ 18, x + y ≥ 10, x, y ≤ 0 is

(a) 36

(b) 40

(c) 30

(d) none of
these

**Answer: d**

**4. **Given** **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**

**5. **The maximum value of Z =
3x + 4y, subject to the constraints x + y ≤ 40, x + 2y ≤ 60, x ≥ 0 and y ≥ 0 is

(a) 140

(b) 120

(c) 100

(d) 160

**Answer: a**

**6.** The equations
3x – y ≥ 3 and 4x – 4y > 4

(a) Have solution for positive x and y

(b) Have no solution for positive x and y

(c) Have solution for all x

(d) Have solution for all y

**Answer: a**

**7.** The region represented
by x ≥ 0 and y ≥ 0 is in the

(a) first
quadrant

(b) second
quadrant

(c) third
quadrant

(d) fourth
quadrant

**Answer: a**

**8.** 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**

**9.** The minimum value of Z
= 4x + 3y, subject 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**

**10.** Maximize Z = 11x + 8y,
subject to the constraints 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**

**11.** Maximize Z = 10 x_{1} +
25 x_{2}, subject to 0 ≤ x_{1} ≤ 3, 0 ≤ x_{2} ≤
3, x_{1} + x_{2} ≤ 5

(a) 80 at
(3, 2)

(b) 75 at
(0, 3)

(c) 30 at
(3, 0)

(d) 95 at
(2, 3)

**Answer: d**

**12.** Maximize Z = 3x + 5y,
subject to the constraints 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**

**13.** The maximum value of the
objective function Z = 5x + 10y, subject to the constraints x + 2y ≤ 120, x + y
≥ 60, x – 2y ≥ 0, x ≥ 0, y ≥ 0 is

(a) 300

(b) 600

(c) 400

(d) 800

**Answer: b**

**14.** Maximize Z = 4x + 6y,
subject to the constraints 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**

**15.** A set of values
of decision variables which satisfies the linear constraints and non-negativity
conditions of a linear programming problem is called its

(a) Unbounded solution

(b) Optimum solution

(c) Feasible solution

(d) None of these

**Answer: c**