Chapter 6.2, Problem 38E

In Problems 37-40, there is a tie for the choice of the first pivot column. Use the simplex method to solve each problem two different ways: first by choosing column $1$ as the first pivot column, and then by choosing column $2$ as the first pivot column. Discuss the relationship between these two solutions.

$\begin{array}{l}\text{Maximize }P=x_1+x_2\\ \text{subject to }{x}_1+2x_2\le 10\\ x_1\le 6\\ x_2\le 4\\ x_1,x_2\ge 0\end{array}$