C: ANSWERS TO SELECTED PROBLEMS
Chapter 8.1, Maximum Problems and Slack Variables
1. 
.
3a. 
. 3b. 
.
3c.
|
x |
y |
u |
v |
f |
1 |
|
1 |
1 |
1 |
0 |
0 |
6 |
|
0 |
1 |
0 |
1 |
0 |
5 |
|
Ð1 |
Ð2 |
0 |
0 |
1 |
0 |
3d. 2 3e. 2
5a. 
. 5b. 
.
5c.
|
x |
y |
u |
v |
w |
f |
1 |
|
3 |
2 |
1 |
0 |
0 |
0 |
12 |
|
1 |
1 |
0 |
1 |
0 |
0 |
5 |
|
4 |
6 |
0 |
0 |
1 |
0 |
13 |
|
Ð5 |
Ð4 |
0 |
0 |
0 |
1 |
0 |
5d. 2 5e. 3
7a. 
. 7b. 
.
7c.
|
x |
y |
z |
u |
v |
w |
f |
1 |
|
3 |
Ð2 |
1 |
1 |
0 |
0 |
0 |
8 |
|
Ð4 |
3 |
2 |
0 |
1 |
0 |
0 |
4 |
|
3 |
1 |
Ð6 |
0 |
0 |
1 |
0 |
6 |
|
0 |
2 |
Ð5 |
0 |
0 |
0 |
1 |
0 |
7d. 3 7e. 3
Chapter 8.2, The Simplex Method
1. 
. 3. 
.
5. 
. 7. 
.
9. 
. 11. Max profit $90, 0
A, 0 B, and 3 C.
13. Max income
$20,220, 16 inexpensive, 30 expensive, and 14 medium.
15. Max income $82
million, $0 home, $600 million car, and $200 million securities.
Chapter 8.3, Duality and Minimum Problems
1. 
3. No solution.
5. Primal solution: 
.
7. Primal solution: 
.
9. Minimal cost 
11. 4 days A and 2
days B.
Chapter 8.4, Mixed-Constraint Linear Programs
No
problems in this section.
Chapter 8.5, Chapter Review
1. 
.
3. 
.
5. 
.
7. 
.
9. 
.
11. Max $82,500, 125
X, 50 Y, and 0 Z