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.