Math
484.1. November 3, 2011. Midterm 2.
5 problems, 15 pts each. \Write your name here
____________________________ and on the other side.
Write down how you got your answer.
1 Solve the
linear program where all xi ≥ 0:
|
x1 |
x2 |
-2 |
-x4 |
|
|
1 |
-2 |
3 |
4 |
= x3 |
|
1 |
2 |
1 |
-3 |
= -x2 |
|
2 |
2 |
-3 |
0 |
--> max |
2. Check
whether x1 = 0, x2 =0, x3 =4/ 3, x4 = 5/2, x5 = 0, x6 =0, x7 =6,
x8 = 0 is an optimal solution for the LP written in a standard tableau:
|
x1 |
x2 |
x3 |
x4 |
x5 |
1 |
|
|
1 |
-2 |
3 |
-4 |
5 |
6 |
= x6 |
|
-1 |
2 |
-3 |
4 |
-5 |
0 |
= x7 |
|
2 |
1 |
0 |
2 |
1 |
-5 |
= x8 |
|
2 |
0 |
1 |
-1 |
3 |
1 |
-> min |
3-4. Solve
transportation problems:
|
2 |
1 |
3 |
2 |
1 |
2 |
1 |
2 |
1 |
9 |
|
1 |
2 |
3 |
1 |
1 |
1 |
1 |
3 |
1 |
8 |
|
2 |
2 |
1 |
3 |
1 |
1 |
3 |
1 |
2 |
9 |
|
1
|
1 |
1 |
1 |
2 |
1 |
2 |
3 |
4 |
8 |
|
6 |
1 |
6 |
1 |
6 |
1 |
6 |
1 |
6 |
dem \ sup |
|
3 |
1 |
3 |
2 |
1 |
2 |
1 |
2 |
1 |
9 |
|
1 |
1 |
3 |
1 |
1 |
1 |
1 |
3 |
1 |
8 |
|
2 |
2 |
1 |
3 |
1 |
1 |
3 |
1 |
2 |
9 |
|
2 |
3 |
1 |
1 |
2 |
1 |
2 |
1 |
2 |
8 |
|
6 |
1 |
6 |
1 |
6 |
1 |
6 |
1 |
6 |
dem \ sup |
5. Solve job
assignment problem
|
1 |
2 |
3 |
4 |
2 |
|
2 |
3 |
0 |
1 |
2 |
|
3 |
2 |
1 |
3 |
1 |
|
1 |
3 |
0 |
5 |
1 |
|
1 |
5 |
2 |
1 |
0 |