Math 484.1  October 23, 2003.   Name:_________________________________________
Midterm 2,  5 problems, 15 points each.
Solve linear programs where all  xi >= 0:

1.
-2 x2 3 -x3
1 2 3 4 = x1
5 6 7 8 = x4
0 1 2 3 -> min

2.
-2 x2 3 -x1
1 2 3 4 = x1
5 6 7 8 = x4
0 1 2 3 -> min

3.
-2 x2 3 -x3
1 2 3 4 = x1
5 6 7 8 = x1
0 1 2 3 -> max

4.
x3 x2 3 -x3
1 2 3 4 = x1
5 6 7 8 = x4
0 1 2 3 -> min

5.
0 x2 1 -x3
1 2 3 4 = x1
5 6 7 8 = x4
0 1 2 3 -> min