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 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.