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\begin{document}
\centerline{\bf Comments on Assignment 2}
\bigskip

Question 1:  When referring to $A_{B}$ (and $A_{B}^{-1}$) you should be
using the data (i.e. the vectors corresponding to the basic variables)
from the original tableau/dictionary. As well, if you learn to use 
Matlab/LPMovie you will ensure that you don't make calculation errors. 

Question 2:  Most people did quite well on this question. A few problems 
occurred when people got hung up on invertibility of a matrix (as opposed to 
column rank). A few people didn't even understand the meaning of linear 
independence - LEARN IT!!!

Question 3:  Many people mistakenly took for an example an initial dictionary
and a single pivot in which, of course, a basic variable becomes non-basic.
However, the question states that the variable we are considering must have
just become basic {\it on an iteration of the simplex method}, not simply 
initialization.  Any invalid pivots used, or pivoting when in reality the 
problem becomes clearly unbounded were not credited. 


Question 4:  If you did not get this question, please look at the 
solutions.  The second part is quite easily demonstrated if you have the 
formula.

Question 5: Be very careful of the sign of the phase one objective function,
i.e., min $w=x_{6}+x_{7}+x_{8}$ becomes max $w=-x_{6}-x_{7}-x_{8}$.  When
performing a pivot, note that if any of the basic variables has a negative
value, the current dictionary is infeasible and so some pivot was bad.  
For part (c), note that we can discard the artificial variables from (b)
once (if) a feasible solution is found as they all must have value zero.
Also, write the given objective function in terms of the feasible basis 
found in (b).




\end{document}




