Math 484.1.  April 19, 2013.   Midterm 3.  
5 problems,10 pts each.   Write your name here ____________________________  and return the page even if you wrote nothing else on it.

36.  The value of the matrix game  with payoff matrix

is  (A) 2.5, (B) 8/3,  (C)   2.6,  (D) 3.5.

37.  Consider the matrix game with payoff matrix

0  -2   1

2 0  -1

-1 1   0

An optimal strategy for the column player is

(A) [1, 1, 1]/3, (B)    [1,2, 1]/4 ,    (C)  [2, 1, 1]    (D) [1,1, 2]/4 .

38.   The least-squares solution (x, y)  for the system

x+y = 7,  x + 2y = 7,  x+3y =  8   is

(A) (3,1), (B) (6.5, 0.5),  (C)  (19/3, 1/2), (D) (1, 0).

39.     |2x| +  |x-1| +  |3x - 3| +  |x- 5| ->  min.

The optimal solution is  (A) 0, (B)  0 ≤ x ≤ 1,  (C)   1, (D) 2.

40.   max( |2x|,   |x-1| ,   |x - 3| ,   |x- 5| ) ->  min.

The optimal solution is (A) 1, (B) 1.5,  (C)   1.8, (D) 5/3.