Math484.2  September 30,2010  Name:_________________________________________

Midterm1,  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 ->  max,

 x4 +  y 2 =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)   x4= y2, (b) 0 >   -2, (c) 0>  0, (d) x = y, (e) x=y=0.