Math 484.2 October 25, 2005. Name:_________________________________________
Midterm 2, 5 problems, 15 points each.
Return this page.
Solve linear programs where all xi >= 0:
| -3 | x1 | 2 | x3 | Problem 1
|
| 1 | 2 | 3 | 4 | = x1 |
| x2 | 0 | -x1 | 1 | =- x4 |
| 0 | 1 | 2 | 3 | -> min |
Answer: LP is infeasible.
| 2 | x2 | 3 | -x1 | Problem 2
|
| 1 | 2 | 3 | 4 | =- x1 |
| x3 | 6 | 7 | 0 | = x4 |
| 0 | 1 | 2 | 3 | -> min |
Answer: LP is unbounded
| -2 | x2 | 3 | -x3 | Problem 3
|
| 1 | -2 | -3 | 4 | = x1 |
| -5 | 0 | 1 | 1 | = x1 |
| 0 | 1 | -2 | 3 | -> max |
Answer: LP is infeasible.
| x3 | x2 | 3 | -x3 | Problem 4
|
| 1 | 2 | 3 | 4 | = x1 |
| 5 | 1 | 0 | -1 | = x4 |
| 0 | 1 | -2 | 3 | -> min |
Answer: LP is unbounded
| 0 | x2 | 1 | -x3 | Problem 5
|
| 0 | -1
| 3 | 0 | = x1 |
| 5 | 6 | -1 | -1 | = x2 |
| 0 | 1 | 2 | 0 | -> min |
min = 2 at x1 = 3, x2 = 0, x3 = 1.