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Introduction to Linear Optimization and Extensions with MATLAB®
book

Introduction to Linear Optimization and Extensions with MATLAB®

by Roy H. Kwon
September 2013
Intermediate to advanced content levelIntermediate to advanced
362 pages
8h 44m
English
CRC Press
Content preview from Introduction to Linear Optimization and Extensions with MATLAB®
100 Introduction to Linear Optimization and Extensions with MATLAB
R
non-basic variables are x
N
=
x
4
x
3
=
0
0
.
The updated basis matrix B =
1 1
1 2
, the updated non-basis matrix is
N =
0 1
1 0
, c
B
=
c
2
c
1
=
1
1
, and c
N
=
c
4
c
3
=
0
0
.
Go to Step 1.
Third Iteration
Step 1: Check the optimality of x
(2)
. The reduced costs r
4
= c
4
c
T
B
B
1
N
4
= 0 0 and r
3
= c
3
c
T
B
B
1
N
3
= 1 0
so x
(2)
=
x
B
x
N
=
x
2
x
1
x
4
x
3
=
2
2
0
0
is an optimal solution with objective
function value (2 2) = 4 and the simplex method stops.
It turns out that x
(2)
is not the only optimal solution. For instance, if x
4
is increased while x
3
remains at 0, we get
x
B
= B
1
b B
1
N
4
x
4
=
x
2
x
1
=
2
2
1
1
x
4
=
2 + x
4
2 x
4
.
Thus, for any x
4
2, any point of the form
x
2
x
1
x
4
x
3
=
2 + x
4
2 x
4
x
4
0
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Publisher Resources

ISBN: 9781439862636