Identify the Different Sets of Basic Variables That Might Be $\mathrm { MAX } : \quad \mathbf { 8 \mathbf { X } _ { 1 } } + 4 \mathbf { X } _ { \mathbf { 2 } }$

Essay

Identify the different sets of basic variables that might be used to obtain a solution to this problem.
$\mathrm { MAX } : \quad \mathbf { 8 \mathbf { X } _ { 1 } } + 4 \mathbf { X } _ { \mathbf { 2 } }$
Subject to:
$\begin{array} { l } 5 \mathbf { X } _ { 1 } + 5 \mathbf { X } _ { 2 } \leq 20 \\6 \mathbf { X } _ { 1 } + 2 \mathbf { X } _ { 2 } \leq 18 \\\mathbf { X } _ { 1 } , \mathbf { X } _ { \mathbf { 2 } } \geq 0\end{array}$