The following tableau gives an optimal solution to a standard linear program: Maximize: Z = cx, Subject to Ax=b, x>0 Cj By CB 2 3 X₁ X₂ C Row 2 X1 1 3 X2 0 1 0 1 X3 -1 2 -3 0 X4 -1 -3 0 X5 -1 -1 RHS Ratio 1 2 Z=8 Assume that (xX4, X5) were the initial basic variables. (A) How much can c₂ be varied without affecting the optimal solution? Find the optimum solution when c₂ =1. (B) Find the optimal solution when a new constraint x₁ + x₂ ≥ 2 is added to the original problem.
The following tableau gives an optimal solution to a standard linear program: Maximize: Z = cx, Subject to Ax=b, x>0 Cj By CB 2 3 X₁ X₂ C Row 2 X1 1 3 X2 0 1 0 1 X3 -1 2 -3 0 X4 -1 -3 0 X5 -1 -1 RHS Ratio 1 2 Z=8 Assume that (xX4, X5) were the initial basic variables. (A) How much can c₂ be varied without affecting the optimal solution? Find the optimum solution when c₂ =1. (B) Find the optimal solution when a new constraint x₁ + x₂ ≥ 2 is added to the original problem.
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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Transcribed Image Text:Problem 2
The following tableau gives an optimal solution to a standard linear
program:
Maximize: Z = cx, Subject to Ax = b, x ≥ 0
3
X2
0
1
0
Св
23
C₁
By
X₁
X₂
C Row
2
X1
1
0
0
1
X3
-1
2
-3
0
X4
3
-1
-3
0
X5
-1
1
-1
RHS
1
2
Ratio
Z=8
Assume that (x4, X5) were the initial basic variables.
(A) How much can c₂ be varied without affecting the optimal solution?
Find the optimum solution when c₂ =1.
(B) Find the optimal solution when a new constraint x₁ + x₂ ≥ 2 is added
to the original problem.
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