2. The tableau is not optimal for either maximization or a minimization problem. Thus, when a nonbasic variable enters the solution it can either increase or decrease Z or leave it unchanged, depending on the parameters of the entering nonbasic variable. Basic x1 X2 X3 X4 X5 X6 X7 Xg solution z O -5 4 -1 -10 598 X8 -2 -3 -1 12 X3 1 1 6 x1 1 -1 0 0 6 -4 0 0 (a) Categorize the variables as basic and nonbasic and provide the current
2. The tableau is not optimal for either maximization or a minimization problem. Thus, when a nonbasic variable enters the solution it can either increase or decrease Z or leave it unchanged, depending on the parameters of the entering nonbasic variable. Basic x1 X2 X3 X4 X5 X6 X7 Xg solution z O -5 4 -1 -10 598 X8 -2 -3 -1 12 X3 1 1 6 x1 1 -1 0 0 6 -4 0 0 (a) Categorize the variables as basic and nonbasic and provide the current
Linear Algebra: A Modern Introduction
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ISBN:9781285463247
Author:David Poole
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Chapter2: Systems Of Linear Equations
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Transcribed Image Text:2. The tableau is not optimal for either maximization or a minimization
problem. Thus, when a nonbasic variable enters the solution it can either
increase or decrease Z or leave it unchanged, depending on the parameters of
the entering nonbasic variable.
Basic x1
X2
X3
X4
X5
X6
X7
Xg
solution
z O
-5
4
-1
-10
598
X8
3
-2
-3
-1
5
1
12
X3
1
1
3
1
3
6
X1
1
-1 0 0 6
-4 0 0
(a) Categorize the variables as basic and nonbasic and provide the current
values of all the variables.
(b) Assuming that the problem is of the maximization type, identify the
nonbasic variables that have the potential to improve the value of Z. If each
such variable enters the basic solution, determine the associated leaving
variable, if any, and the associated change in Z.
(c)Repeat part (b) assuming that the problem is of the minimization
type.
(d)Which nonbasic variable(s) will not cause a change in the value of
Z when selected to enter the solution?
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