Math 486. March 20, 2008 . Midterm
2.
5 problems, 15 points each. Name:________________________
1-3. Solve the linear programs, where all xi
>= 0:
| x1 |
x2 |
-x3 |
-x4 |
x5 |
-1 |
Problem 1
|
| 1011 |
2 |
3 |
5 |
6 |
10-12
|
=- x6 |
| 0 |
-1 |
-2 |
0 |
3 |
1013 |
= -x7 |
| -1 |
0 |
0
|
4 |
-4 |
2300 |
= -x8 |
| 2 |
0 |
3-300 |
0 |
1 |
2 |
= f -> min |
| x1 |
x2 |
x3 |
x4 |
x5 |
-1 |
Problem 2
|
| 1 |
2 |
-3 |
-5 |
6 |
2 |
= -x6 |
| 0 |
-10-100 |
-2 |
0 |
-3 |
-10-300 |
= x7 |
| -1 |
0 |
2 |
4 |
-4 |
-2 |
= x8 |
| 2 |
0 |
3 |
1 |
1 |
0
|
= x9 |
-1
|
-2
|
-10-100 |
0
|
0
|
0
|
= f -> max |
| x1/30000001 |
x1/3000002 |
x3/3000003 |
x4/3000004 |
x5/3000005 |
-1 |
Problem 3
|
| 1/300001 |
-1/3000002 |
1/300003 |
1/300004 |
0 |
-2 |
= -x6 |
1/30001
|
-1/30002 |
-2/3003 |
0 |
0
|
-1 |
= -x7 |
| 1/3001 |
0 |
2/3003 |
3/3004
|
-4/3005 |
2 |
= -x8 |
| 2/301 |
0 |
-1/303 |
0 |
1/305 |
2 |
= f -> 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 |
9 |
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 |
| 0 |
3 |
3 |
0 |
-2 |
0 |
-1 |
| 3+10-100 |
0 |
3 |
0 |
2 |
3 |
0 |
| 0 |
3 |
1 |
4 |
3 |
0 |
4 |