  Kitahara and Mizuno (2010) get two upper bounds for the number of different
basic feasible solutions generated by Dantzig's simplex method. The size of the
bounds highly depends on the ratio between the maximum and minimum values of
all the positive elements of basic feasible solutions. In this paper, we show
some relations between the ratio and the number of iterations by using an
example of LP, which is a simple variant of Klee-Minty's LP. We see that the
ratio for the variant is equal to the number of iterations by Dantzig's simplex
method for solving it. This implies that it is impossible to get a better upper
bound than the ratio. We also give improved results of the upper bounds.

Optimization and Control