Math 486.  November 5, 2009.  Midterm 2.   5 problems, 15 points each. Name:

1-3. Solve the linear programs, where  all x i >=  0:

x1 -2x2 -x1 1

Problem 1

2 2 1 4 = x1
5 6 7 8 = -x3
1 0 1 2 -> max
x1 x2 x3 x4 x5 -1 Problem 2
1 2 -3 -5 6 -2 = -x6
0 10-100 -2 0 -3 1 = x7
-1 0 2 4 -4 2 = x8
2 0 3 1 1 2 = f -> max

x1 x2 -1 Problem 3
1 0 1 = -x3
0 1 1 = -x4
2 2 3 = -x5
3 4 0 -> max


4-5. Solve matrix games:
4.
1 3 5-10-100 7 1 3 2
8 8+10-100 9 8+ 10-100 9 8 9
1 -5 4 3 4 7 10-100
3 5 6 -3 -10-100 1 3
8+10-100 9
9
8 9
8 9-10-100

5.
0 0 0 -2 -2 -1 -2
0 2 0 -1 -2 -1 -1
2 3 3 0 2 4 0
2 0 3 0 2 3 0
0 3 1 4 3 0 4