Use the simplex method to maximize LaTeX:  \displaystyle p = 14 x + 5 y subject to LaTeX:  \displaystyle \begin{cases}59 x + 25 y \leq 1475 \\ 20 x + 73 y \leq 1460 \\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}59 x + 25 y +s = 1475 \\ 20 x + 73 y+t = 1460 \\ - 14 x - 5 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 59 & LaTeX:  \displaystyle 25 & LaTeX:  \displaystyle 1 & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 1475 \\ \hline LaTeX:  \displaystyle t & LaTeX:  \displaystyle 20 & LaTeX:  \displaystyle 73 & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 1 & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 1460 \\ \hline LaTeX:  \displaystyle p & LaTeX:  \displaystyle -14 & LaTeX:  \displaystyle -5 & 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 59R_2-20R_1
LaTeX:  \displaystyle 59R_3+14R_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 59 & LaTeX:  \displaystyle 25 & LaTeX:  \displaystyle 1 & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 1475 \\ \hline LaTeX:  \displaystyle t & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 3807 & LaTeX:  \displaystyle -20 & LaTeX:  \displaystyle 59 & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 56640 \\ \hline LaTeX:  \displaystyle p & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 55 & LaTeX:  \displaystyle 14 & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 59 & LaTeX:  \displaystyle 20650 \\ \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 25 . The value of LaTeX:  \displaystyle t is LaTeX:  \displaystyle 960 . The max value is LaTeX:  \displaystyle p = 350