Math 486.  March 17, 2011 .  Midterm 2.   5 problems, 15 points each. Name (here and on every page):
1-3. Solve the linear programs, where  all xi >=  0:

x1 x2 -x3 -x4 x5 -1 Problem 1
1011 2 0 0 6 -1
=- x6
0 -1 -2 0 3 -2 = -x7
-1 0 0
4 -4 3 = -x8
2 0 3-300 0 1 2 = f -> min

2.
x1, x2 >= 0,     2x1+ 3x2<= 6,  3x1 + 2 x -> max.
 
x1/3000 x1/3000002 x3/3000003 x4/3000004 x5/3000005 -1 Problem 3
1/300001 -1/3000002 1/300003 1/300004 0 -2 = -x6
-1/3000002
-1/3000002 -2/3003 0 0
1 = -x7
1/3001 0 2/3003 -1/3000002
-4/3005 2 = -x8
2/301 0 1/3000002 0 1/305 2 = f -> min
4-5. Solve matrix games:
4.
2 0 0 0 3-10-100 5 10
0 2 0 0 2 1 4
0 0 2 0 2 0 3-10-100
0 0 0 2 2 3-10-100 0
0 0 0 -10-100 0 0 3-10-100

  5.
-10100 3-10-100 3-10-100 3-10-100 3-10-100 3-10-100 3-10-100
0 2 0 -1 -2 -1 -1
0 3 3 0 -2 0 -1
-1 0 3 0 2 3 0
0 3 1 4 3 0 4