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Max z= 3x1 2x2 2x1 x2 ≤ 2, 3X1 4x2 ≥ 12, x1 ≥ 0, x2 ≥ 0, solution is Ops: A. unique B. unbounded C. degenerate D. O infinite?
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Max z= 3x1 2x2 2x1 x2 ≤ 2, 3X1 4x2 ≥ 12, x1 ≥ 0, x2 ≥ 0, solution is O...
Linear Programming Problem
Given:
Max z = 3x1 + 2x2
2x1 + x2 ≤ 2
3x1 + 4x2 ≥ 12
x1 ≥ 0, x2 ≥ 0
To Find:
Whether the solution is:
A. Unique
B. Unbounded
C. Degenerate
D. Infinite
Solution:
Graphical Method:
Let's plot the given constraints on a graph.
From the above graph, we can see that the feasible region is bounded and the objective function line has a unique point of intersection with the feasible region.
Hence, the solution is Unique.
Simplex Method:
We can solve the given LP problem using the simplex method as well.
Let's convert the given LP problem into standard form:
Max z = 3x1 + 2x2
2x1 + x2 + x3 = 2
3x1 + 4x2 - x4 = 12
x1, x2, x3, x4 ≥ 0
Now, we can use the simplex method to solve the problem:
| Basic Variables | x1 | x2 | x3 | x4 | Constants |
|---|---|---|---|---|---|
| x3 | 2 | 1 | 1 | 0 | 2 |
| x4 | 3 | 4 | 0 | -1 | 12 |
| Zj | 3 | 2 | 0 | 0 | |
| Cj - Zj | 0 | 0 | 2 | 0 |
Since all the values in the last row are non-negative, we have reached the optimal solution.
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Max z= 3x1 2x2 2x1 x2 ≤ 2, 3X1 4x2 ≥ 12, x1 ≥ 0, x2 ≥ 0, solution is Ops: A. unique B. unbounded C. degenerate D. O infinite?
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Max z= 3x1 2x2 2x1 x2 ≤ 2, 3X1 4x2 ≥ 12, x1 ≥ 0, x2 ≥ 0, solution is Ops: A. unique B. unbounded C. degenerate D. O 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 Max z= 3x1 2x2 2x1 x2 ≤ 2, 3X1 4x2 ≥ 12, x1 ≥ 0, x2 ≥ 0, solution is Ops: A. unique B. unbounded C. degenerate D. O infinite? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Max z= 3x1 2x2 2x1 x2 ≤ 2, 3X1 4x2 ≥ 12, x1 ≥ 0, x2 ≥ 0, solution is Ops: A. unique B. unbounded C. degenerate D. O infinite?.
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