Math
484.1 October 4,
2006 Name:_________________________________________
Midterm
1, 5
problems, 15 points each. Return
this page.
|
x |
y |
z |
1. Solve for x, y . |
|
0 |
2 |
0 |
=u |
|
1 |
0 |
1 |
=v |
2. x + y 2 -> max,
x2 + y 2 = 1.
3.
|
x |
y |
1 |
3. Solve for x, y. |
|
2 -1 |
3 2 |
-x y |
>= 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 |
0 |
=d |
|
1 |
0 |
1 |
-1 |
->min |
|
a |
b |
c |
1 |
Problem 4b |
|
-1 |
0 |
-1 |
-1 |
=d |
|
1 |
0 |
1 |
-1 |
->min |
|
a |
b |
c |
1 |
Problem 4c |
|
1 |
0 |
-1 |
0 |
=d |
|
-1 |
0 |
1 |
-1 |
->min |
5.
Find all logical implications between the following 5
constraints on x, y:
(a) x2 = y2, (b) 0 > 1, (c) 0 >= 0, (d) x = y, (e) y > 1.