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.