Math 484.1.  December 2,  2010.   Midterm 3.  
5 problems, 15 pts each. Name____________________________

  1--3. Solve matrix games: If you cannot find optimal strategies, give the best you can find.
1.
1
 2
 3
 4
 1
 2
 6
0
 1
 4
 5
 4
 6
 5
1
 2
 6
 5
 5
 7
 0
0
 0
 1
 1
 4
 2
 0
1
 1
 4
 3
 2
 4
 0
1
 1
 2
 1
 3
 6
 3


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

3.
2
 0
 2
 -2
2
 -2
 -1
 2
0
 2
 3
 1

4.  Solve for x, y

x+2y = 3
tx+ty=3

where t is a given number.



5. Find the mean, the midrange, the modes, and the  central value for the following numbers:
0,-1, 3,4,5,-1,7,8,0,0, 0, -1,-2.