Math
484.2 October 2,
2008 Name:_________________________________________
Midterm
1, 5
problems, 15 points each. Return
this page.
|
x |
y |
z |
1. Solve for x, y . |
|
1 |
2 |
0 |
=u |
|
1 |
0 |
2 |
=v |
2. 4x + y 2 -> min,
x2 + y 2 = 1
3.
|
x |
y |
1 |
3. Solve for x, y. |
|
1 -1 |
1 1 |
-x 2 |
>= 3 <= 2 |
|
1 |
2 |
0 |
- > 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 |
-2 |
->min |
|
a |
b |
c |
1 |
Problem 4b |
|
-2 |
-1 |
-1 |
-3 |
=d |
|
1 |
0 |
1 |
-1 |
->min |
|
a |
b |
c |
1 |
Problem 4c |
|
-1 |
0 |
1 |
0 |
=d |
|
-2 |
1 |
-1 |
-1 |
->min |
5.
Find all logical implications between the following 5
constraints on x, y:
(a) x3 = y3, (b) 0 > -1, (c) 2y>x , (d) 1/3 > 1/2, (e) y >= x.