Math 484.1 September 29, 2011 Name:_________________________________________
Midterm 1, 5 problems, 15 points each. Return this page with your name on both sides.
1. Solve for x and y where a is a given number:
a2x + y= a2,
ax +ay = 1.
2. 4x + y 2 -> min,
x2 + y 2 = 10; x and y integers.
3, 4. Solve the linear programs given by the following tableaux with all decision variables xi >= 0:
|
x1 |
x2 |
x3 |
-1 |
Problem 3 |
|
-1 |
0 |
-1 |
2 |
= x4 |
|
1 |
0 |
-1 |
-1 |
-> min |
|
x1 |
x2 |
-x3 |
1 |
Problem 4 |
|
1 |
0 |
1 |
-2 |
=- x4 |
|
1 |
0 |
-1 |
-1 |
-> min |
5. Find all logical implications between the following 5 constraints on x, y:
(a) x2 = y2, (b) 0 < -2, (c) 0 < 1, (d) x = -y, (e) x=y=0.