Math 484.1.  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
 5
 3
 3
0
 1
 4
 5
 4
 6
 3
1
 2
 6
 5
 5
 7
 0
0
 0
 1
 1
 4
 2
 0
1
 1
 4
 3
 2
 4
 0
3
 2
 2
 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 p   for  the row player is the transpose  of
(A) [0,0,0.5,0,0.5], (B) [1/2, 1/2, 0, 0, 0],   (C) [0,0, 0,0.5,0.5],  (D) [1/2, 0, 0, 0, 1/2], (E) [1/2, 1/2, 0].

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

9.   Consider the system of two equations for two unknowns x, y, where t is a given number:
x+ty = 3, 2x+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-5)2 + (x-3)2 -> min
is (A) 0 , (B) 1, (C) 2, (D) 3, (E) 2.5.