Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Solution to Z = 4x1 6x2 x1 x2 ≤ 4; 3x1 ...
Start Learning for Free
Solution to Z = 4x1 6x2 x1 x2 ≤ 4; 3x1 x2 ≤ 12; x1, x2 ≥ 0 is: Ops: A. Unique B. Unbounded C. Degenerate D. Infinite?
Most Upvoted Answer
Solution to Z = 4x1 6x2 x1 x2 ≤ 4; 3x1 x2 ≤ 12; x1, x2 ≥ 0 is: O...
Solution to linear programming problem
Objective function:
Z = 4x1 + 6x2
Constraints:
x1 + x2 ≤ 4
3x1 + x2 ≤ 12
x1, x2 ≥ 0
Step 1: Plotting the constraints
To solve the linear programming problem graphically, we need to plot the constraint lines on the coordinate plane.
x1 + x2 ≤ 4 can be rewritten as x2 ≤ -x1 + 4, which gives us the line:
x2 = -x1 + 4
Similarly, 3x1 + x2 ≤ 12 can be rewritten as x2 ≤ -3x1 + 12, which gives us the line:
x2 = -3x1 + 12
Plotting these two lines on the coordinate plane, we get the following graph:
The feasible region is the shaded area that satisfies all the constraints.
Step 2: Finding the corner points
To find the optimal solution, we need to evaluate the objective function at each corner point of the feasible region. The corner points are the vertices of the feasible region.
In this case, the corner points are:
(0, 0), (0, 4), (2, 2), and (4, 0)
Step 3: Evaluating the objective function
We evaluate the objective function Z = 4x1 + 6x2 at each corner point:
Z(0, 0) = 0
Z(0, 4) = 24
Z(2, 2) = 20
Z(4, 0) = 16
Step 4: Conclusion
The optimal solution is Z = 24 at (0, 4).
Answer: The solution to the linear programming problem is unique.
Objective function:
Z = 4x1 + 6x2
Constraints:
x1 + x2 ≤ 4
3x1 + x2 ≤ 12
x1, x2 ≥ 0
Step 1: Plotting the constraints
To solve the linear programming problem graphically, we need to plot the constraint lines on the coordinate plane.
x1 + x2 ≤ 4 can be rewritten as x2 ≤ -x1 + 4, which gives us the line:
x2 = -x1 + 4
Similarly, 3x1 + x2 ≤ 12 can be rewritten as x2 ≤ -3x1 + 12, which gives us the line:
x2 = -3x1 + 12
Plotting these two lines on the coordinate plane, we get the following graph:
The feasible region is the shaded area that satisfies all the constraints.
Step 2: Finding the corner points
To find the optimal solution, we need to evaluate the objective function at each corner point of the feasible region. The corner points are the vertices of the feasible region.
In this case, the corner points are:
(0, 0), (0, 4), (2, 2), and (4, 0)
Step 3: Evaluating the objective function
We evaluate the objective function Z = 4x1 + 6x2 at each corner point:
Z(0, 0) = 0
Z(0, 4) = 24
Z(2, 2) = 20
Z(4, 0) = 16
Step 4: Conclusion
The optimal solution is Z = 24 at (0, 4).
Answer: The solution to the linear programming problem is unique.
Attention Computer Science Engineering (CSE) Students!
To make sure you are not studying endlessly, EduRev has designed Computer Science Engineering (CSE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Computer Science Engineering (CSE).
|
Explore Courses for Computer Science Engineering (CSE) exam
|
|
Similar Computer Science Engineering (CSE) Doubts
Top Courses for Computer Science Engineering (CSE)View all
Solution to Z = 4x1 6x2 x1 x2 ≤ 4; 3x1 x2 ≤ 12; x1, x2 ≥ 0 is: Ops: A. Unique B. Unbounded C. Degenerate D. Infinite?
Question Description
Solution to Z = 4x1 6x2 x1 x2 ≤ 4; 3x1 x2 ≤ 12; x1, x2 ≥ 0 is: Ops: A. Unique B. Unbounded C. Degenerate D. Infinite? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Solution to Z = 4x1 6x2 x1 x2 ≤ 4; 3x1 x2 ≤ 12; x1, x2 ≥ 0 is: Ops: A. Unique B. Unbounded C. Degenerate D. Infinite? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solution to Z = 4x1 6x2 x1 x2 ≤ 4; 3x1 x2 ≤ 12; x1, x2 ≥ 0 is: Ops: A. Unique B. Unbounded C. Degenerate D. Infinite?.
Solution to Z = 4x1 6x2 x1 x2 ≤ 4; 3x1 x2 ≤ 12; x1, x2 ≥ 0 is: Ops: A. Unique B. Unbounded C. Degenerate D. Infinite? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Solution to Z = 4x1 6x2 x1 x2 ≤ 4; 3x1 x2 ≤ 12; x1, x2 ≥ 0 is: Ops: A. Unique B. Unbounded C. Degenerate D. Infinite? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solution to Z = 4x1 6x2 x1 x2 ≤ 4; 3x1 x2 ≤ 12; x1, x2 ≥ 0 is: Ops: A. Unique B. Unbounded C. Degenerate D. Infinite?.
Solutions for Solution to Z = 4x1 6x2 x1 x2 ≤ 4; 3x1 x2 ≤ 12; x1, x2 ≥ 0 is: Ops: A. Unique B. Unbounded C. Degenerate D. Infinite? in English & in Hindi are available as part of our courses for Computer Science Engineering (CSE).
Download more important topics, notes, lectures and mock test series for Computer Science Engineering (CSE) Exam by signing up for free.
Here you can find the meaning of Solution to Z = 4x1 6x2 x1 x2 ≤ 4; 3x1 x2 ≤ 12; x1, x2 ≥ 0 is: Ops: A. Unique B. Unbounded C. Degenerate D. Infinite? defined & explained in the simplest way possible. Besides giving the explanation of
Solution to Z = 4x1 6x2 x1 x2 ≤ 4; 3x1 x2 ≤ 12; x1, x2 ≥ 0 is: Ops: A. Unique B. Unbounded C. Degenerate D. Infinite?, a detailed solution for Solution to Z = 4x1 6x2 x1 x2 ≤ 4; 3x1 x2 ≤ 12; x1, x2 ≥ 0 is: Ops: A. Unique B. Unbounded C. Degenerate D. Infinite? has been provided alongside types of Solution to Z = 4x1 6x2 x1 x2 ≤ 4; 3x1 x2 ≤ 12; x1, x2 ≥ 0 is: Ops: A. Unique B. Unbounded C. Degenerate D. Infinite? theory, EduRev gives you an
ample number of questions to practice Solution to Z = 4x1 6x2 x1 x2 ≤ 4; 3x1 x2 ≤ 12; x1, x2 ≥ 0 is: Ops: A. Unique B. Unbounded C. Degenerate D. Infinite? tests, examples and also practice Computer Science Engineering (CSE) tests.
|
|
Explore Courses for Computer Science Engineering (CSE) 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