From: "Phil Eberhardt" <pae5000@psu.edu>
Date: December 4, 2008 11:39:43 AM EST
To: vstein@math.psu.edu
Subject: Midterm 3 answers

Or at least to the best of my knowledge

    1.    Saddle Point so Value of game = 3
His Optimal = [0,1,0,0,0,0,0]
Her Optimal = [0,1,0,0,0,0,0]
    2.    Got so far to say Value of game = 2
Her optimal = [0,0,0,0,1,0,0]
Domination: c5>c3,c2>c6
    3.    Value of Game = 6/5
Matrix Shifts to [[-2,6],[2,0]] after dominations r3>r1,c2>c1, and (3c2+c4)/4>c3
His optimal=[0,1,4]/5
Her optimal=[0,3,0,2]/5
    4.    x=3(t-4)/(t-8) and y=-6/(t-8),  if t = 8 this is undefined but can simply solve matrix [When t=8, the system has no solutions. –LV].
    5.    Mean=11/4, mid range=2/3, center value=1
[This is wrong. See the other paper for correct answers:

Mean = 33/12 = 2.75 Midrange = 4 Center Value = 3/2 = 1.5. –LV]

]
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From:   pae5000@psu.edu
Subject: Midterm 3 one more thing
Date: December 4, 2008 12:24:51 PM EST

Forgot wanted to send what I got from entering the matrix into the website I used to solve the hw problem.

For 2.

The value is 2.
An optimal strategy for him:  (0.6,0,0.2,0.2,0)
An optimal strategy for for her: (0,0,0,0,1,0,0)