Math 484.2.  December 1  2011.   Midterm 3.  
5 problems, 15 pts each. Name____________________________

On the scantron, choose one of 5 answers.  Use #2 pencil. 
For me, write  down details.
6-8.   Matrix game is given by its payoff matrix.
6.
0
2
3
4
2
3
3
0
1
4
2
4
6
3
1
2
2
5
2
7
0
0
0
1
1
4
2
0
1
1
4
3
2
4
0
3
3
3
3
3
6
3
The value of game is (A) 0 , (B) 1, (C) 2, (D) 3, (E) 4.

7.
1
2
3
1
2
4
3
3
1
4
4
2
4
0
3
3
2
0
4
3
1
4
1
4
0
2
3
2
3
1
2
4
2
1
3
An optimal strategy q   for  the column player is
(A) [0,0,1/2,0,1/3,0,0], (B) [0, 2/3, 0,  1/3,0,0,0],   (C) [0,0, 0,1/2,1/2, 0,0],  (D) [1/2, 0, 0, 0, 0, 0, 1/2], (E) [1/2, 1/2, 0,0,0,0,0].

8.
2
2
1.5
1.5
2
1
1
2
4
2
2
1
The value of game is (A) 0 , (B) 1, (C) 2, (D) 3, (E) 1.5.

9.   Consider the system of two equations for two unknowns x, y, where t is a given number:
x+y = 3,  x+t2y=6. Then 
(A) the system is not linear because the second equation is not linear,
(B) there is t such that the system  has no solutions,
(C) there is  t such that the system has infinitely many solutions.
(D) the system cannot be solved, (E) 0 = 1.

10.  An optimal solution x for
2x2 + (x-1)2 + (x-3)2 -> min
is (A) 0 , (B) 1, (C) 2, (D) 3, (E) 2.5.