Chapter 6.2, Problem 36E

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.

$\begin{array}{l}\text{Maximize }P=2x_1+2x_2+x_3\\ \text{subject to }{x}_1+x_2+3x_3\le 10\\ \text{ 2}{x}_1+4x_2+5x_3\le 24\\ x_1,x_2,x_3\ge 0\end{array}$