Daily Practice Problems undefined Linear Programming

Question1:

L.P.P is a process of finding [Level: Easy]

(a) Maximum value of objective function

(b) Minimum value of objective function

(d) none of these.

Question2:

Maximum value of Z = x + 2y subject to the constraints

x + 2y 100, 2x – y 0, 2x + y 200 & x, y 0 is __________. [Level: Difficult]

Question3:

A Linear Programming Problem is as follows:

Minimise z = 2x + y

Subject to the constraints x 3, x 9, y 0

x - y 0, x + y 14

The feasible region has [Level: Difficult]

(a) 5 corner point including (0, 0) and (9, 5)

(b) 5 corner point including (7, 7) and (3, 3)

(d) 5 corner point including (3, 6) and (9, 5)

Question4:

The corner points of the feasible region for a Linear Programming Problem are P(0, 5), Q(1,5), R(4,2) and S(12,0). The minimum value of the objective function Z = 2x + 5y is at the point [Level: Difficult]

(a) P

(b) Q

(d) S

Question5:

For an L.P.P. the objective function is Z = 4x + 3y, and the feasible region determined by a set of constraints (linear inequations) is shown in the graph.

Which one of the following statements is true? [Level: Moderate]

(a) Maximum value of Z is at R.

(b) Maximum value of Z is at Q.

(d) Value of Z at Q is less than the value at R.

Question6:

The corner points of the feasible region determined by a set of constraints (linear inequalities) are P(0, 5), Q(3, 5), R(5, 0) and S(4, 1) and the objective function is Z = ax + 2by where a, b > 0. The condition on a and b such that the maximum Z occurs at Q and S is [Level: Difficult]

(a)

(b)

(c)

(d) .

Question7:

A Linear Programming Problem is as follows

Maximise / Minimise objective function Z = 2x – y + 5

Subject to the constraints

3x + 4y 60

x + 3y 30

x 0, y 0

If the corner points of the feasible region are A(0, 10), B(12, 6), C(20, 0) and O(0, 0), then which of the following is true ? [Level: Difficult]

(a) Maximum value of Z is 40

(b) Minimum value of Z is - 5

(d) At two corner points, value of Z is equal.

Question8:

If the number of available constraints is 3 and the number of parameters to be optimized is 4, then [Level: Moderate]

(a) the objective function can be optimized

(b) the constraints are short in number

(d) none of these

Question9:

Which of the following statements is correct? [Level: Moderate]

(a) Every L.P.P. admits an optimal solution.

(b) A L.P.P. admits a unique optimal solution.

(d) The set of all feasible solutions of a L.P.P. is not a convex set.

Question10:

If , then [Level: Moderate]

(a)

(b)

(c)

(d)

Question11:

If the constraints in a linear programming problem are changed [Level: Easy]

(a) the problem is to be re-evaluated

(b) solution is not defined

(d) the change in constraints is ignored.

Question12.

L.P.P. has constraints of [Level: Moderate]

(a) one variable

(b) two variables

(d) two or more variables.

Question13.

Which of these terms is not used in a linear programming problem? [Level: Easy]

(a) Convex region

(b) Objective function

(d) Feasible solution

Question14.

The optimal value of the objective function is attained at the points [Level: Moderate]

(a) given by intersection of inequations with axes only

(b) given by intersection of inequations with - axis only

(d) none of these

Question15.

If x and b are real numbers and then implies the interval as __________. [Level: Moderate]

Question16.

Corner points of feasible region of inequalities gives __________. [Level: Moderate]

Question17.

The corner points of the feasible region determined by the system of linear inequalities are (0, 0), (4, 0), (2, 4) and (0, 5). If the maximum value of z = ax + by, where a, b > 0 occurs at both (2, 4) and (4, 0), then [Level: Moderate]

(a) a = 2b

(b) 2a = b

(d) 3a = b

Question18.

A furniture trader deals in only two items - chairs and tables. He has ₹ 50,000 to invest and a space to store at most 35 items. A chair costs him ₹ 1,000 and a table costs him ₹ 2,000. The trader earns a profit of ₹ 150 and ₹ 250 on a chair and table, respectively. The maximum profit after solving the LPP is __________. [Level: Difficult]

Question19.

The feasible region is always [Level: Moderate]

(a) present in any LPP

(b) a concave region

(d) none of these.

Question20.

If the feasible region ‘R’ is bounded, then the objective function has [Level: Moderate]

(a) only maximum value at the corner point of ‘R’

(b) only minimum value at the corner point of ‘R’

(d) none of these.

**********

Problem-solving on Class 12 Maths Linear Programming NCERT Chapter 12 after learning a theoretical concept is crucial for several reasons:

Application of Knowledge: Problem-solving allows you to apply the theoretical concepts of the topic Class 12 Maths Linear Programming you have learned to real-life situations. It helps you bridge the gap between abstract knowledge and practical scenarios, making the learning more relevant and meaningful.
Understanding Deeper Concepts: When you encounter problems related to a theoretical concept that you learned in Class 12 Maths Linear Programming NCERT Chapter 12, you are forced to delve deeper into its intricacies. This deeper understanding enhances your comprehension of the subject and strengthens your grasp of the underlying principles.
Critical Thinking: Problem-solving encourages critical thinking and analytical skills. It requires you to analyze the problem, identify relevant information, and devise a logical solution. This process sharpens your mind and improves your ability to approach complex challenges effectively.
Retention and Recall: Actively engaging in problem-solving reinforces your memory and improves long-term retention. Applying the concepts learned in Linear Programming Class 12 Maths in practical scenarios helps you remember them better than passive reading or memorization.
Identifying Knowledge Gaps: When you attempt to solve problems, you may encounter areas where your understanding is lacking. These knowledge gaps become evident during problem-solving, and you can then focus on filling those gaps through further study and practice. You can refer Linear Programming Class 12 Maths Notes on LearnoHub.com
Boosting Confidence: Successfully solving problems after learning a theoretical concept boosts your confidence in your abilities to handle Linear Programming. This confidence motivates you to tackle more challenging tasks and improves your overall performance in the subject.
Preparation for Exams and Challenges: Many exams, especially in science, mathematics, and engineering, involve problem-solving tasks. Regular practice in problem-solving prepares you to face these exams with confidence and perform well. It is also advised to take tests on Linear Programming Class 12 Maths Online Tests at LearnoHub.com.
Enhancing Creativity: Problem-solving often requires thinking outside the box and exploring various approaches. This fosters creativity and innovation, enabling you to come up with novel solutions to different problems.
Life Skills Development: Problem-solving is a valuable life skill that extends beyond academics. It equips you with the ability to tackle various challenges you may encounter in personal and professional life.
Improving Decision Making: Problem-solving involves making decisions based on available information and logical reasoning. Practicing problem-solving enhances your decision-making skills, making you more effective in making informed choices.

In summary, problem-solving after learning a theoretical concept on CBSE Linear Programming Class 12 Maths is an essential part of the learning process. It enhances your understanding, critical thinking abilities, and retention of knowledge. Moreover, it equips you with valuable skills that are applicable in academic, personal, and professional contexts.

You must have heard of the phrase “Practice makes a man perfect”. Well, not just a man, practice indeed enhances perfection of every individual.

Practicing questions plays a pivotal role in achieving excellence in exams. Just as the adage goes, "Practice makes perfect," dedicating time to solve a diverse range of exam-related questions yields manifold benefits. Firstly, practicing questions allows students to familiarize themselves with the exam format and types of problems they might encounter. This familiarity instills confidence, reducing anxiety and improving performance on the actual exam day. Secondly, continuous practice sharpens problem-solving skills and enhances critical thinking, enabling students to approach complex problems with clarity and efficiency. Thirdly, it aids in identifying weak areas, allowing students to focus their efforts on improving specific topics. Moreover, practice aids in memory retention, as active engagement with the material reinforces learning. Regular practice also hones time management skills, ensuring that students can allocate appropriate time to each question during the exam. Overall, practicing questions not only boosts exam performance but also instills a deeper understanding of the subject matter, fostering a holistic and effective learning experience.

All About Daily Practice Problems on Class 12 Maths Linear Programming NCERT Chapter 12

Our Daily Practice Problems (DPPs) offer a diverse range of question types, including Multiple Choice Questions (MCQs) as well as short and long answer types. These questions are categorized into Easy, Moderate, and Difficult levels, allowing students to gradually progress and challenge themselves accordingly. Additionally, comprehensive solutions are provided for each question, available for download in PDF format - Download pdf solutions as well as Download pdf Questions. This approach fosters a holistic learning experience, catering to different learning styles, promoting self-assessment, and improving problem-solving skills. With our well-structured DPPs, students can excel in exams while gaining a deeper understanding of the subject matter. Hope you found the content on Class 12 Maths Linear Programming NCERT Chapter 12 useful.

Last but not least, to get the best hold on Class 12 Maths Linear Programming NCERT Chapter 12, do not forget to check out:

Linear Programming Class 12 Maths Best videos
Linear Programming Class 12 Maths NCERT Solutions
Class 12 Maths Linear Programming Revision notes
Linear Programming Class 12 Maths DPPs, Download PDF of solutions
Class 12 Maths Linear Programming Online Tests
Class 12 Maths Sample papers