Consider the LP 2x1 + x2x3 x1 + 2x2 + x3 -x1 + x₂ - 2x3 X1, X2, X3 Suppose the following optimal tableau is obtained for the above LP: Maximize subject to $1 X2 x3 1 2 1 1 -2 where s₁ and s2 are the slack variables. 3 -1 -3 -3 1 -8 = -x1 -12 ≤8 4 ≥0 = -82 16 = 1 Suppose the right hand side of the first constraint is changed from 8 to 8 + h₁ and the right hand side of the second constraint is changed from 4 to 4+h₂. Then the adjusted final tableau remains optimal if
Consider the LP 2x1 + x2x3 x1 + 2x2 + x3 -x1 + x₂ - 2x3 X1, X2, X3 Suppose the following optimal tableau is obtained for the above LP: Maximize subject to $1 X2 x3 1 2 1 1 -2 where s₁ and s2 are the slack variables. 3 -1 -3 -3 1 -8 = -x1 -12 ≤8 4 ≥0 = -82 16 = 1 Suppose the right hand side of the first constraint is changed from 8 to 8 + h₁ and the right hand side of the second constraint is changed from 4 to 4+h₂. Then the adjusted final tableau remains optimal if
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
Section2.4: Subtracting Real Numbers
Problem 48WE
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Transcribed Image Text:Consider the LP
2x1 + x2
X3
x₁ + 2x2 + x3
-x1 + x₂ - 2x3
X1, X2, X3
Suppose the following optimal tableau is obtained for the above LP:
Maximize
subject to
$1
1
1
-2
where s₁ and s2 are the slack variables.
X2 X3
1
2
1
-8
3 -1 -12
-3 -3 16
≤8
≤4
≥0
= -x1
= -82
=U
Suppose the right hand side of the first constraint is changed from 8 to 8+ h₁ and
the right hand side of the second constraint is changed from 4 to 4+h₂. Then
the adjusted final tableau remains optimal if
Transcribed Image Text:h₁8, h₁h₂ ≥ −12.
Oh₁ ≥ 8, h₁ + h₂ ≥ 12.
O None of the other four.
Oh₁> -8, h₁ + h₂ ≥ −12.
Ohi-8, h1 - h₂ ≥ 12.
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