Math 171A:
Mathematical Programming
Instructor: Philip E. Gill
Winter Quarter 2009
Homework Assignment #9
Due Friday March 13, 2009
The final will be held Wednesday, March 18 at 3pm.
Starred exercises require the use of
Matlab
.
Exercise 9.1.
*
For the following linear program, construct an equivalent standardform
problem in which the objective function is
minimized
and the constraints have the form
Ax
=
b
,
x
≥
0. Starting at the vertex where all slack variables are basic, solve the problem using
the standardform simplex method (Algorithm 5.1 in the Class Text). At every iteration,
record (i) the values of the basic variables; (ii) the indices of the basic and nonbasic variables;
(iii) the multiplier
π
and the reduced cost vector
z
N
; (iv) the search direction
p
B
; and (v)
the step to the nearest constraint.
maximize

10
x
1
+ 32
x
2
+ 48
x
3
+ 54
x
4
subject to
2
x
1
+
3
x
2
+
5
x
3
+
x
4
≤
24
5
x
1
+
2
x
2
+
x
3
+
3
x
4
≤
32
8
x
1
+
5
x
2
+
6
x
3
+ 10
x
4
≤
64
3
x
1
+
6
x
2
+
9
x
3
+ 12
x
4
≤
81
x
1
,
x
2
,
x
3
,
x
4
≥
0
.
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 Winter '08
 staff
 Math, matlab, Linear Programming, Optimization, Dual problem, linear program, Philip E. Gill, cTx Ax

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