Math 484.1 September
30, 2010 Name:_________________________________________
Midterm 1, 5
problems, 15 points each. Return this page with your name on both sides.
1.
Solve for x where a is a given number:
a(a+1)(a+2)x
= a2 - 1.
2. 4x + y
2 -> min,
x2 + y 4 = 1.
3, 4. Solve
the linear programs given by the following tableaux with all decision variables
xi ³ 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) x5
= y5, (b) 0 < -2, (c) 0 < 0, (d) x = y, (e)
x=y=0.