JEE Exam > JEE Questions > The optimum value of the objective function i...
Start Learning for Free
The optimum value of the objective function is attained at the points
- a)Corner points of feasible region
- b)Any point of the feasible region
- c)On x-axis
- d)On y-axis
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The optimum value of the objective function is attained at the points&...
Given that,
• There is an objective function
• There are optimal values
From the definition of optimal value of a Linear Programming Problem(LPP):
An optimal/ feasible solution is any point in the feasible region that gives a maximum or minimum value if substituted in the objective function.
Here feasible region of an LPP is defined as:
A feasible region is that common region determined by all the constraints including the non-negative constraints of the LPP.
So the Feasible region of a LPP is a convex polygon where, its vertices (or corner points) determine the optimal values (either maximum/minimum) of the objective function.
For Example,
5x + y ≤ 100 ; x + y ≤ 60 ; x ≥ 0 ; y ≥ 0
The feasible solution of the LPP is given by the convex polygon OADC.
Here, points O, A ,D and C will be optimal solutions of the taken LPP
View all questions of this test
• There is an objective function
• There are optimal values
From the definition of optimal value of a Linear Programming Problem(LPP):
An optimal/ feasible solution is any point in the feasible region that gives a maximum or minimum value if substituted in the objective function.
Here feasible region of an LPP is defined as:
A feasible region is that common region determined by all the constraints including the non-negative constraints of the LPP.
So the Feasible region of a LPP is a convex polygon where, its vertices (or corner points) determine the optimal values (either maximum/minimum) of the objective function.
For Example,
5x + y ≤ 100 ; x + y ≤ 60 ; x ≥ 0 ; y ≥ 0
The feasible solution of the LPP is given by the convex polygon OADC.
Here, points O, A ,D and C will be optimal solutions of the taken LPP
Most Upvoted Answer
The optimum value of the objective function is attained at the points&...
Explanation:
The optimal value of the objective function is the highest or lowest value that the function can take in a feasible region. The feasible region is the area that satisfies all the constraints of the problem.
The optimal value can be attained at various points in the feasible region, but the best point to attain the optimal value is at the corner points of the feasible region.
This is because the corner points are the intersection of two or more constraints, and any movement from the corner point will violate one or more constraints. Therefore, the optimal value can only be attained at the corner points.
For example, consider the following linear programming problem:
Maximize: z = 3x + 4y
Subject to:
x + y ≤ 5
2x + y ≤ 8
x ≥ 0, y ≥ 0
The feasible region for this problem is the shaded area in the following graph:
The corner points of the feasible region are (0,0), (0,5), and (4,1). The optimal value of the objective function can only be attained at these corner points.
At point (0,0), z = 3(0) + 4(0) = 0
At point (0,5), z = 3(0) + 4(5) = 20
At point (4,1), z = 3(4) + 4(1) = 16
Therefore, the optimal value of the objective function is attained at point (0,5), and the maximum value of the objective function is 20.
Conclusion:
In conclusion, the optimal value of the objective function is attained at the corner points of the feasible region. This is because any movement from the corner point will violate one or more constraints, and the optimal value can only be attained by satisfying all the constraints.
The optimal value of the objective function is the highest or lowest value that the function can take in a feasible region. The feasible region is the area that satisfies all the constraints of the problem.
The optimal value can be attained at various points in the feasible region, but the best point to attain the optimal value is at the corner points of the feasible region.
This is because the corner points are the intersection of two or more constraints, and any movement from the corner point will violate one or more constraints. Therefore, the optimal value can only be attained at the corner points.
For example, consider the following linear programming problem:
Maximize: z = 3x + 4y
Subject to:
x + y ≤ 5
2x + y ≤ 8
x ≥ 0, y ≥ 0
The feasible region for this problem is the shaded area in the following graph:
The corner points of the feasible region are (0,0), (0,5), and (4,1). The optimal value of the objective function can only be attained at these corner points.
At point (0,0), z = 3(0) + 4(0) = 0
At point (0,5), z = 3(0) + 4(5) = 20
At point (4,1), z = 3(4) + 4(1) = 16
Therefore, the optimal value of the objective function is attained at point (0,5), and the maximum value of the objective function is 20.
Conclusion:
In conclusion, the optimal value of the objective function is attained at the corner points of the feasible region. This is because any movement from the corner point will violate one or more constraints, and the optimal value can only be attained by satisfying all the constraints.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
The optimum value of the objective function is attained at the pointsa)Corner points of feasible regionb)Any point of the feasible regionc)On x-axisd)On y-axisCorrect answer is option 'A'. Can you explain this answer?
Question Description
The optimum value of the objective function is attained at the pointsa)Corner points of feasible regionb)Any point of the feasible regionc)On x-axisd)On y-axisCorrect answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The optimum value of the objective function is attained at the pointsa)Corner points of feasible regionb)Any point of the feasible regionc)On x-axisd)On y-axisCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The optimum value of the objective function is attained at the pointsa)Corner points of feasible regionb)Any point of the feasible regionc)On x-axisd)On y-axisCorrect answer is option 'A'. Can you explain this answer?.
The optimum value of the objective function is attained at the pointsa)Corner points of feasible regionb)Any point of the feasible regionc)On x-axisd)On y-axisCorrect answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The optimum value of the objective function is attained at the pointsa)Corner points of feasible regionb)Any point of the feasible regionc)On x-axisd)On y-axisCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The optimum value of the objective function is attained at the pointsa)Corner points of feasible regionb)Any point of the feasible regionc)On x-axisd)On y-axisCorrect answer is option 'A'. Can you explain this answer?.
Solutions for The optimum value of the objective function is attained at the pointsa)Corner points of feasible regionb)Any point of the feasible regionc)On x-axisd)On y-axisCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of The optimum value of the objective function is attained at the pointsa)Corner points of feasible regionb)Any point of the feasible regionc)On x-axisd)On y-axisCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The optimum value of the objective function is attained at the pointsa)Corner points of feasible regionb)Any point of the feasible regionc)On x-axisd)On y-axisCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for The optimum value of the objective function is attained at the pointsa)Corner points of feasible regionb)Any point of the feasible regionc)On x-axisd)On y-axisCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of The optimum value of the objective function is attained at the pointsa)Corner points of feasible regionb)Any point of the feasible regionc)On x-axisd)On y-axisCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The optimum value of the objective function is attained at the pointsa)Corner points of feasible regionb)Any point of the feasible regionc)On x-axisd)On y-axisCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup