Use the simplex method to maximize LaTeX:  \displaystyle p = 20 x + 8 y subject to LaTeX:  \displaystyle \begin{cases}80 x + 48 y \leq 3840 \\ 10 x + 53 y \leq 530 \\x \geq 0, y \geq 0 \end{cases}

Adding the slack variables LaTeX:  \displaystyle s and LaTeX:  \displaystyle t to the inequalities gives:
LaTeX:  \begin{cases}80 x + 48 y +s = 3840 \\ 10 x + 53 y+t = 530 \\ - 20 x - 8 y+p =0 \end{cases} This gives the first tableau:\begin{tabular}{|c|c|c|c|c|c|c|}\hline LaTeX:  \displaystyle  & LaTeX:  \displaystyle x & LaTeX:  \displaystyle y & LaTeX:  \displaystyle s & LaTeX:  \displaystyle t & LaTeX:  \displaystyle p & LaTeX:  \displaystyle  \\ \hline LaTeX:  \displaystyle s & LaTeX:  \displaystyle 80 & LaTeX:  \displaystyle 48 & LaTeX:  \displaystyle 1 & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 3840 \\ \hline LaTeX:  \displaystyle t & LaTeX:  \displaystyle 10 & LaTeX:  \displaystyle 53 & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 1 & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 530 \\ \hline LaTeX:  \displaystyle p & LaTeX:  \displaystyle -20 & LaTeX:  \displaystyle -8 & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 1 & LaTeX:  \displaystyle 0 \\ \hline \end{tabular}
The pivot row is LaTeX:  \displaystyle s and the pivot column is LaTeX:  \displaystyle x . The departing variable is LaTeX:  \displaystyle s and the incoming variable is LaTeX:  \displaystyle x . Pivoting using the row operations:
LaTeX:  \displaystyle 8R_2-1R_1
LaTeX:  \displaystyle 4R_3+1R_1
\begin{tabular}{|c|c|c|c|c|c|c|}\hline LaTeX:  \displaystyle  & LaTeX:  \displaystyle x & LaTeX:  \displaystyle y & LaTeX:  \displaystyle s & LaTeX:  \displaystyle t & LaTeX:  \displaystyle p & LaTeX:  \displaystyle  \\ \hline LaTeX:  \displaystyle x & LaTeX:  \displaystyle 80 & LaTeX:  \displaystyle 48 & LaTeX:  \displaystyle 1 & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 3840 \\ \hline LaTeX:  \displaystyle t & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 376 & LaTeX:  \displaystyle -1 & LaTeX:  \displaystyle 8 & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 400 \\ \hline LaTeX:  \displaystyle p & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 16 & LaTeX:  \displaystyle 1 & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 4 & LaTeX:  \displaystyle 3840 \\ \hline \end{tabular}
There are no negative values in row LaTeX:  \displaystyle p and this is the final tableau.The value of LaTeX:  \displaystyle x is LaTeX:  \displaystyle 48 . The value of LaTeX:  \displaystyle t is LaTeX:  \displaystyle 50 . The max value is LaTeX:  \displaystyle p = 960