Math 484.1  September 29, 2005    Name:_________________________________________
Midterm 1,  5 problems, 15 points each.  Return this page.

1. Solve for x
x
x - 1
 = ax
where a is a given number.

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

3. Solve for x, y :   xy -> min,    |x - 2|  <=  1,  |y - 3| <= 2.

4. Solve for x, y :  

-2 x
 1
 -y Problem 4
 1 2 3  4 >= 4
 1 0 x  1 <= 3
 0 1 2  0 -> max

5. 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.