Consider the following LP: Basic Z X1, X₂ ≥ 0 The starting solution consists of artificial x4 and x5 for the first and second constraints and slack x6 for the third constraint. Using M = 100 for the artificial variables, the optimal tableau is given as: x2 X3 X1 0 1 0 0 X2 0 Minimize z = 4x₁ + x₂ 0 1 0 3x₁ + x₂ 4x₁ + 3x₂ = 60 X₁ + 2x₂ ≤ 40 X3 0 0 0 1 X4 -98.6 = 30 .4 .2 1 X5 -100 0 0 -1 X6 -.2 -.2 .6 1 Write the associated dual problem, and determine its optimal solution. Solution 34 4 18 10
Consider the following LP: Basic Z X1, X₂ ≥ 0 The starting solution consists of artificial x4 and x5 for the first and second constraints and slack x6 for the third constraint. Using M = 100 for the artificial variables, the optimal tableau is given as: x2 X3 X1 0 1 0 0 X2 0 Minimize z = 4x₁ + x₂ 0 1 0 3x₁ + x₂ 4x₁ + 3x₂ = 60 X₁ + 2x₂ ≤ 40 X3 0 0 0 1 X4 -98.6 = 30 .4 .2 1 X5 -100 0 0 -1 X6 -.2 -.2 .6 1 Write the associated dual problem, and determine its optimal solution. Solution 34 4 18 10
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Consider the following LP:
Basic
Z
X1, X₂ ≥ 0
The starting solution consists of artificial x4 and x5 for the first and second constraints and
slack x6 for the third constraint. Using M = 100 for the artificial variables, the optimal
tableau is given as:
x2
X3
X1
0
1
0
0
X2
0
Minimize z = 4x₁ + x₂
0
1
0
3x₁ + x₂
4x₁ + 3x₂ = 60
X₁ + 2x₂ ≤ 40
X3
0
0
0
1
X4
-98.6
= 30
.4
.2
1
X5
-100
0
0
-1
X6
-.2
-.2
.6
1
Write the associated dual problem, and determine its optimal solution.
Solution
34
4
18
10](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5f19d897-995a-4412-b454-5c7a324725d7%2F27172be0-8c66-4623-95b6-1c398f6930ad%2F5yr2uwc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the following LP:
Basic
Z
X1, X₂ ≥ 0
The starting solution consists of artificial x4 and x5 for the first and second constraints and
slack x6 for the third constraint. Using M = 100 for the artificial variables, the optimal
tableau is given as:
x2
X3
X1
0
1
0
0
X2
0
Minimize z = 4x₁ + x₂
0
1
0
3x₁ + x₂
4x₁ + 3x₂ = 60
X₁ + 2x₂ ≤ 40
X3
0
0
0
1
X4
-98.6
= 30
.4
.2
1
X5
-100
0
0
-1
X6
-.2
-.2
.6
1
Write the associated dual problem, and determine its optimal solution.
Solution
34
4
18
10
Expert Solution
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Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step 1: Introduce slack, surplus, artificial variables in given LPP
VIEWStep 2: Perform first iteration
VIEWSolution
VIEWStep 3: Perform second iteration
VIEWStep 4: Perform third iteration
VIEWStep 5: Perform fourth iteration
VIEWStep 6: Write dual of LPP
VIEWStep 7: Perform first iteration
VIEWStep 8: Perform second iteration
VIEWStep 9: Perform third iteration
VIEWStep 10: Perform fourth iteration and write the optimal solution of the dual of LPP
VIEWStep by step
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