JEE Exam > JEE Questions > Consider the following linear programming pr...
Start Learning for Free
Consider the following linear programming problem (LPP).
Maximize z = 2x + 3y
Subject to
2x + 3y ≤ 12
2x - 3y ≤ 0
y ≤ 2
x, y ≥ 0
It has
- a)no feasible solution
- b)unique optimal solution
- c)alternative optimal solutions
- d)unbounded solution
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
Consider the following linear programming problem (LPP).Maximize z = ...
Problem:
Maximize z = 2x - 3y
Subject to
2x - 3y ≤ 12
2x - 3y ≤ 0
y ≤ 2x
y ≥ 0
Feasible Region:
To find the feasible region, we need to graph the given inequalities and identify the region that satisfies all the constraints.
The first constraint, 2x - 3y ≤ 12, can be rewritten as y ≥ (2/3)x - 4. We can graph this line by plotting the points (0, -4) and (6, 0) and drawing a line through them.
The second constraint, 2x - 3y ≤ 0, can be rewritten as y ≥ (2/3)x. We can graph this line by plotting the points (0, 0) and (3, 2) and drawing a line through them.
The third constraint, y ≤ 2x, can be graphed by plotting the points (0, 0) and (1, 2) and drawing a line through them.
Finally, the constraint y ≥ 0 represents the non-negative region of the y-axis.
After graphing all the constraints, we can shade the region that satisfies all the constraints. The feasible region is the intersection of all the shaded regions.
Analysis:
In this case, the feasible region is a bounded region consisting of a triangle. Since the objective function is linear, it will have a maximum value at one of the corner points of the feasible region.
Corner Points:
To find the corner points, we need to find the intersections of the lines representing the constraints.
- Intersection of (2/3)x - 4 and (2/3)x: (6, 0)
- Intersection of (2/3)x - 4 and 2x: (3, 2)
- Intersection of (2/3)x and 2x: (0, 0)
Objective Function:
Now, we evaluate the objective function z = 2x - 3y at each of the corner points.
- At (6, 0): z = 2(6) - 3(0) = 12
- At (3, 2): z = 2(3) - 3(2) = 0
- At (0, 0): z = 2(0) - 3(0) = 0
Optimal Solution:
The maximum value of z is 12, which occurs at the corner point (6, 0). Therefore, the LPP has a unique optimal solution.
Conclusion:
The correct answer is option 'B', which states that the LPP has a unique optimal solution.
Maximize z = 2x - 3y
Subject to
2x - 3y ≤ 12
2x - 3y ≤ 0
y ≤ 2x
y ≥ 0
Feasible Region:
To find the feasible region, we need to graph the given inequalities and identify the region that satisfies all the constraints.
The first constraint, 2x - 3y ≤ 12, can be rewritten as y ≥ (2/3)x - 4. We can graph this line by plotting the points (0, -4) and (6, 0) and drawing a line through them.
The second constraint, 2x - 3y ≤ 0, can be rewritten as y ≥ (2/3)x. We can graph this line by plotting the points (0, 0) and (3, 2) and drawing a line through them.
The third constraint, y ≤ 2x, can be graphed by plotting the points (0, 0) and (1, 2) and drawing a line through them.
Finally, the constraint y ≥ 0 represents the non-negative region of the y-axis.
After graphing all the constraints, we can shade the region that satisfies all the constraints. The feasible region is the intersection of all the shaded regions.
Analysis:
In this case, the feasible region is a bounded region consisting of a triangle. Since the objective function is linear, it will have a maximum value at one of the corner points of the feasible region.
Corner Points:
To find the corner points, we need to find the intersections of the lines representing the constraints.
- Intersection of (2/3)x - 4 and (2/3)x: (6, 0)
- Intersection of (2/3)x - 4 and 2x: (3, 2)
- Intersection of (2/3)x and 2x: (0, 0)
Objective Function:
Now, we evaluate the objective function z = 2x - 3y at each of the corner points.
- At (6, 0): z = 2(6) - 3(0) = 12
- At (3, 2): z = 2(3) - 3(2) = 0
- At (0, 0): z = 2(0) - 3(0) = 0
Optimal Solution:
The maximum value of z is 12, which occurs at the corner point (6, 0). Therefore, the LPP has a unique optimal solution.
Conclusion:
The correct answer is option 'B', which states that the LPP has a unique optimal solution.
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
Consider the following linear programming problem (LPP).Maximize z = 2x + 3ySubject to2x + 3y ≤ 122x - 3y ≤ 0y ≤ 2x, y ≥ 0It hasa)no feasible solutionb)unique optimal solutionc)alternative optimal solutionsd)unbounded solutionCorrect answer is option 'B'. Can you explain this answer?
Question Description
Consider the following linear programming problem (LPP).Maximize z = 2x + 3ySubject to2x + 3y ≤ 122x - 3y ≤ 0y ≤ 2x, y ≥ 0It hasa)no feasible solutionb)unique optimal solutionc)alternative optimal solutionsd)unbounded solutionCorrect answer is option 'B'. 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 Consider the following linear programming problem (LPP).Maximize z = 2x + 3ySubject to2x + 3y ≤ 122x - 3y ≤ 0y ≤ 2x, y ≥ 0It hasa)no feasible solutionb)unique optimal solutionc)alternative optimal solutionsd)unbounded solutionCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following linear programming problem (LPP).Maximize z = 2x + 3ySubject to2x + 3y ≤ 122x - 3y ≤ 0y ≤ 2x, y ≥ 0It hasa)no feasible solutionb)unique optimal solutionc)alternative optimal solutionsd)unbounded solutionCorrect answer is option 'B'. Can you explain this answer?.
Consider the following linear programming problem (LPP).Maximize z = 2x + 3ySubject to2x + 3y ≤ 122x - 3y ≤ 0y ≤ 2x, y ≥ 0It hasa)no feasible solutionb)unique optimal solutionc)alternative optimal solutionsd)unbounded solutionCorrect answer is option 'B'. 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 Consider the following linear programming problem (LPP).Maximize z = 2x + 3ySubject to2x + 3y ≤ 122x - 3y ≤ 0y ≤ 2x, y ≥ 0It hasa)no feasible solutionb)unique optimal solutionc)alternative optimal solutionsd)unbounded solutionCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following linear programming problem (LPP).Maximize z = 2x + 3ySubject to2x + 3y ≤ 122x - 3y ≤ 0y ≤ 2x, y ≥ 0It hasa)no feasible solutionb)unique optimal solutionc)alternative optimal solutionsd)unbounded solutionCorrect answer is option 'B'. Can you explain this answer?.
Solutions for Consider the following linear programming problem (LPP).Maximize z = 2x + 3ySubject to2x + 3y ≤ 122x - 3y ≤ 0y ≤ 2x, y ≥ 0It hasa)no feasible solutionb)unique optimal solutionc)alternative optimal solutionsd)unbounded solutionCorrect answer is option 'B'. 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 Consider the following linear programming problem (LPP).Maximize z = 2x + 3ySubject to2x + 3y ≤ 122x - 3y ≤ 0y ≤ 2x, y ≥ 0It hasa)no feasible solutionb)unique optimal solutionc)alternative optimal solutionsd)unbounded solutionCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Consider the following linear programming problem (LPP).Maximize z = 2x + 3ySubject to2x + 3y ≤ 122x - 3y ≤ 0y ≤ 2x, y ≥ 0It hasa)no feasible solutionb)unique optimal solutionc)alternative optimal solutionsd)unbounded solutionCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for Consider the following linear programming problem (LPP).Maximize z = 2x + 3ySubject to2x + 3y ≤ 122x - 3y ≤ 0y ≤ 2x, y ≥ 0It hasa)no feasible solutionb)unique optimal solutionc)alternative optimal solutionsd)unbounded solutionCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of Consider the following linear programming problem (LPP).Maximize z = 2x + 3ySubject to2x + 3y ≤ 122x - 3y ≤ 0y ≤ 2x, y ≥ 0It hasa)no feasible solutionb)unique optimal solutionc)alternative optimal solutionsd)unbounded solutionCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Consider the following linear programming problem (LPP).Maximize z = 2x + 3ySubject to2x + 3y ≤ 122x - 3y ≤ 0y ≤ 2x, y ≥ 0It hasa)no feasible solutionb)unique optimal solutionc)alternative optimal solutionsd)unbounded solutionCorrect answer is option 'B'. 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 on EduRev and stay on top of your study goals
10M+ students crushing their study goals daily