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
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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
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
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