Math 486. November 5, 2009. Midterm
2.
5 problems, 15 points each. Name:
1-3. Solve the linear programs, where all x i >= 0:
| x1 |
-2x2 |
-x1 |
1 |
Problem 1 |
| 2 |
2 |
1 |
4 |
= x1 |
| 5 |
6 |
7 |
8 |
= -x3 |
| 1 |
0 |
1 |
2 |
-> max |
| x1 |
x2 |
x3 |
x4 |
x5 |
-1 |
Problem 2
|
| 1 |
2 |
-3 |
-5 |
6 |
-2 |
= -x6 |
| 0 |
10-100 |
-2 |
0 |
-3 |
1 |
= x7 |
| -1 |
0 |
2 |
4 |
-4 |
2 |
= x8 |
| 2 |
0 |
3 |
1 |
1 |
2 |
= f -> max |
| x1 |
x2 |
-1 |
Problem 3 |
| 1 |
0 |
1 |
= -x3 |
| 0 |
1 |
1 |
= -x4 |
| 2 |
2 |
3 |
= -x5 |
| 3 |
4 |
0 |
-> max |
4-5. Solve matrix games:
4.
| 1 |
3 |
5-10-100 |
7 |
1 |
3 |
2 |
| 8 |
8+10-100 |
9 |
8+ 10-100 |
9 |
8 |
9 |
| 1 |
-5 |
4 |
3 |
4 |
7 |
10-100 |
| 3 |
5 |
6 |
-3 |
-10-100 |
1 |
3 |
| 8+10-100 |
9
|
9
|
8 |
9
|
8 |
9-10-100 |
5.
| 0 |
0 |
0 |
-2 |
-2 |
-1 |
-2 |
| 0 |
2 |
0 |
-1 |
-2 |
-1 |
-1 |
| 2 |
3 |
3 |
0 |
2 |
4 |
0 |
| 2 |
0 |
3 |
0 |
2 |
3 |
0 |
| 0 |
3 |
1 |
4 |
3 |
0 |
4 |