From: "Christine Bowers" <clb5335@psu.edu>
Date: December 2, 2010 12:46:10 PM EST
To: Leon Vaserstein <vstein@math.psu.edu>
Subject: Midterm 3 Solutions

1. Saddle Point
Value of Game=1
Optimal Solution for Row Player: (1,0,0,0,0,0)T
Optimal Solution for Column player: (1,0,0,0,0,0,0)

2. No Saddle Points
Value of Game=2
An optimal solution (strategy)  for Row player: (0,0, .5, 0, .5)T
An optimal solution (strategy)  for column player: (0, 2/3, 0, 1/3, 0, 0, 0)

3. No Saddle Points
Value of Game  10/13 (added by LV)  ~0.76923
An approximately optimal solution (strategy)  for row player: (0.15385,0.23077,0.61538)T
An approximately optimal solution (strategy)  for column player: (0.53846,0.30769,0,0.15385)


4.
y=(-3/t) +3
x= (-3t+6)/t
when t ≠ 0;  (added by LV)
no solution when t=0

5. 
mean=22/13
central value=0
mode=0
midrange=3