Math
484.1 October 4,
2007 Name:_________________________________________
Midterm
1, 5
problems, 15 points each. Return
this page.
|
x |
y |
z |
1. Solve for y,
z |
|
0 |
2 |
1 |
=u |
|
1 |
0 |
1 |
=v |
2. x - y 3 -> min,
x2 + 2y 3 = 1.
3.
|
x |
y |
1 |
3. Solve for x, y |
|
1 -1 |
2 1 |
-x 2x |
>= 3 <= 2 |
|
-2 |
1 |
x |
- > min |
4. Solve the linear programs given by the following standard tableaux:
|
a |
b |
c |
1 |
Problem 4a |
|
1 |
0 |
-1 |
1 |
=d |
|
-1 |
0 |
1 |
-1 |
->min |
|
a |
b |
c |
1 |
Problem 4b |
|
-1 |
-2 |
-1 |
-1 |
=d |
|
1 |
0 |
1 |
0 |
->min |
|
a |
b |
c |
1 |
Problem 4c |
|
1 |
0 |
-1 |
3 |
=d |
|
2 |
0 |
1 |
-1 |
->min |
5.
Find all logical implications between the following 5
constraints on x, y:
(a) x2 = y2, (b) x = y= 1, (c) x >= y , (d) x + y = 2, (e) y > 0.