Homework 4
Due:
February 17, 2009
Exercise 3, page 111
Solve Problem 5 (a) of Set 3.4A (page 107) by the twophase method.
Exercise 1, page 118
For the following LP, identify three alternative optimal basic solutions, and then
write a general expression for all the nonbasic alternative optima comprising these
three basis solutions:
maximize
z
=
x
1
+ 2
x
2
+ 3
x
3
subject to
x
1
+ 2
x
2
+ 3
x
3
≤
10
x
1
+
x
2
≤
5
x
1
≤
1
x
1
, x
2
, x
3
≥
0
.
Note: Although the problem has more than three alternative basic solution optima,
you are only required to identify three of them.
Exercise 2, page 120
:
Consider the LP:
maximize
z
= 20
x
1
+ 10
x
2
+
x
3
subject to
3
x
1

3
x
2
+ 5
x
3
≤
50
x
1
+
x
3
≤
10
x
1

x
2
+ 4
x
3
≤
20
x
1
, x
2
, x
3
≥
0
.
(a) By inspecting the constraints, determine the direction (
x
1
, x
2
, or
x
3
) in which
the solution space is unbounded.
(b) Without further computations, what can you conclude regarding the optimum
objective value?
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Exercise 1, Page 134
:
In the TOYCO model, suppose that the changes
D
1
, D
2
, and
D
3
are made
simulta
neously
in the three operations.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '09
 Nedich
 raw material, Tomato sauce, Toyco

Click to edit the document details