3. The simplex method is a typically efficient algorithm for solving linear programs. However,

there is no version of it that has been shown theoretically to solve any linear program in

polynomial time. In fact, it is much worse. In 1972, Klee and Minty came up with an example

in n dimensions that requires 2 - 1 iterations if Dantzig's rule¹ is used to choose entering

variables. These problems are of the form

Fig: 1