Math 484.1  Febr. 17, 2006    Name:_________________________________________
Midterm 1,  5 problems, 10 points each.  Return this page.

1. Find all logical implications between the following 5  constraints on  x, y:
(a)   x2 = 1, (b) 0 >   1, (c) 0=  0, (d) x = 1, (e) y > 1.

2. Solve for x, y
 x
  y
2
 -3
 = a
-3
  5
 = b
where a,b are given numbers.


3-5. Solve linear programs where all xi >= 0:

-2 x1
 1
 -x2 Problem 3
 1 -2 3  4 >= 4
 1 0 x1
  1 <= 3
 0 1 2  0 -> min

x1
 x2
 1
 -x5 Problem 4
 1 2 3  4 = x3
 1 2
 0
  -1 = -x4
 0 -2
 -3
  0 -> max

x1
 x2
 1
 -x5 Problem 5
 1 2 3  4 = x3
 1 2
 0
  -1 = -x4
 0 2
 -3
  0 -> max