Problem 3. Consider the following LP. max X1,X2,X3,X4 3x1 + x2 s.t. 2x1 + x2 + X3 = 6 -X1 + x2 + x4 = 3 X1, X2, X3, X4 2 0 1) Use the Simplex method to solve this LP. You can start with any basic feasible solution (BFS). Explicitly %3| show the BFS that you apply in the beginning of your solution.
Problem 3. Consider the following LP. max X1,X2,X3,X4 3x1 + x2 s.t. 2x1 + x2 + X3 = 6 -X1 + x2 + x4 = 3 X1, X2, X3, X4 2 0 1) Use the Simplex method to solve this LP. You can start with any basic feasible solution (BFS). Explicitly %3| show the BFS that you apply in the beginning of your solution.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Problem 3. Consider the following LP.
max
X1,X2,X3,X4
3x1 + x2
s.t.
2x1 + x2 + x3 = 6
-X1 + x2 + X4 = 3
X1, X2, X3, X4 2 0
1) Use the Simplex method to solve this LP. You can start with any basic feasible solution (BFS). Explicitly
show the BFS that you apply in the beginning of your solution.
2) Suppose the coefficient of x, in the first constraint will be changed (currently, it is 2). What is the
range of the coefficient such that the current optimal basis can be kept?
[Hint for part 2): run the simplex method including the change of the coefficient, and apply the
optimality condition(s).]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0e6ffa6d-d4e0-4034-adbc-4fc6b8056438%2Fb7c51f59-f763-42f3-8465-5e415f7ed1bf%2Fkcica9a_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 3. Consider the following LP.
max
X1,X2,X3,X4
3x1 + x2
s.t.
2x1 + x2 + x3 = 6
-X1 + x2 + X4 = 3
X1, X2, X3, X4 2 0
1) Use the Simplex method to solve this LP. You can start with any basic feasible solution (BFS). Explicitly
show the BFS that you apply in the beginning of your solution.
2) Suppose the coefficient of x, in the first constraint will be changed (currently, it is 2). What is the
range of the coefficient such that the current optimal basis can be kept?
[Hint for part 2): run the simplex method including the change of the coefficient, and apply the
optimality condition(s).]
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