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.