From: "Phil Eberhardt" <pae5000@psu.edu>
Date: October 2, 2008 11:16:15 AM EDT
To: vstein@math.psu.edu
Subject: Midterm 1 solutions

I had time to solve everything in class but I figured I'd send
solutions for bonus.

1)  x=v-u/2-z, y=u/2

2)  x=1, y=0 with min=4 from new objective function 4x-x^2+1
[ correction by Yuknis    max = 4]

3) When simplified tableux found first row had same entries as the
objective function in the last row so min = 3. then solved for the
intersect of the 2 linear contraints above to find x=4/3, y=5/6

4) First had optimal tableux so the basic solution is optimal -
a,b,c=0   d=2  min=-1
    Second had a bad row at d so LP is infeasible, min=-infinity
[correction: min = infinity].
    Last had a bad column at a so LP is unbounded, min=infinity
[correction: a-column is bad, min = -infinity].
5) a->d, b->nothing, c->a,b,d,e, d->a, and everything implies b