
Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780813349107
Author: Steven H. Strogatz
Publisher: PERSEUS D
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Question
Chapter 4.5, Problem 3E
Interpretation Introduction
Interpretation:
The system
Concept Introduction:
Fixed points are the points where
If the flow is towards the right
Stable points are points at which the local flow is toward them.
Unstable points are points at which the local flow is away from them.
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Students have asked these similar questions
For the Big-M tableau (of a maximization LP and row0 at bottom and M=1000),
Z
Ꮖ 1
x2
x3
81
82
83
e4
a4
RHS
0
7
0
0
1
0 4
3
-3
20
0
-4.5
0
0
0
1
-8 -2.5
2.5
6
0
7
0
1
0
0 8
3
-3
4
0
-1
50
1
0
0
0-2
-1
1
4
0000
0
30 970 200
If the original value of c₁ is increased by 60, what is the updated value of c₁ (meaning keeping the same set for BV. -10?
Having made that change, what is the new optimal value for ž?
Here is the optimal tableau for a standard Max problem.
zx1
x2
x3
24
81
82
83
rhs
1
0
5
3
0
6
0
1
.3
7.5 0
-
.1
.2
0 0
28
360
0
-8
522
0
2700
0
6
12
1
60
0
0
-1/15-3
1
1/15 -1/10 0
2
Using that the dual solution y = CBy B-1 and finding B = (B-¹)-¹
we find the original CBV and rhs b.
The allowable increase for b₂ is
If b₂ is increased by 3 then, using Dual Theorem, the new value for * is
If c₂ is increased by 10, then the new value for optimal > is
i.e. if no change to BV, then just a change to profit on selling product 2.
The original coefficients c₁ =
=☐ a
and c4 = 5
If c4 is changed to 512, then (first adjusting other columns of row0 by adding Delta times row belonging to x4
or using B-matrix method to update row0)
the new optimal value, after doing more simplex algorithm, for > is
Please show in mathematical form.
Chapter 4 Solutions
Nonlinear Dynamics and Chaos
Ch. 4.1 - Prob. 1ECh. 4.1 - Prob. 2ECh. 4.1 - Prob. 3ECh. 4.1 - Prob. 4ECh. 4.1 - Prob. 5ECh. 4.1 - Prob. 6ECh. 4.1 - Prob. 7ECh. 4.1 - Prob. 8ECh. 4.1 - Prob. 9ECh. 4.2 - Prob. 1E
Ch. 4.2 - Prob. 2ECh. 4.2 - Prob. 3ECh. 4.3 - Prob. 1ECh. 4.3 - Prob. 2ECh. 4.3 - Prob. 3ECh. 4.3 - Prob. 4ECh. 4.3 - Prob. 5ECh. 4.3 - Prob. 6ECh. 4.3 - Prob. 7ECh. 4.3 - Prob. 8ECh. 4.3 - Prob. 9ECh. 4.3 - Prob. 10ECh. 4.4 - Prob. 1ECh. 4.4 - Prob. 2ECh. 4.4 - Prob. 3ECh. 4.4 - Prob. 4ECh. 4.5 - Prob. 1ECh. 4.5 - Prob. 2ECh. 4.5 - Prob. 3ECh. 4.6 - Prob. 1ECh. 4.6 - Prob. 2ECh. 4.6 - Prob. 3ECh. 4.6 - Prob. 4ECh. 4.6 - Prob. 5ECh. 4.6 - Prob. 6E
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