Use the simplex method to maximize LaTeX:  \displaystyle p = 24 x + 3 y subject to LaTeX:  \displaystyle \begin{cases}76 x + 47 y \leq 3572 \\ 62 x + 59 y \leq 3658 \\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}76 x + 47 y +s = 3572 \\ 62 x + 59 y+t = 3658 \\ - 24 x - 3 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 76 & LaTeX:  \displaystyle 47 & LaTeX:  \displaystyle 1 & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 3572 \\ \hline LaTeX:  \displaystyle t & LaTeX:  \displaystyle 62 & LaTeX:  \displaystyle 59 & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 1 & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 3658 \\ \hline LaTeX:  \displaystyle p & LaTeX:  \displaystyle -24 & LaTeX:  \displaystyle -3 & 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 38R_2-31R_1
LaTeX:  \displaystyle 19R_3+6R_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 76 & LaTeX:  \displaystyle 47 & LaTeX:  \displaystyle 1 & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 3572 \\ \hline LaTeX:  \displaystyle t & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 785 & LaTeX:  \displaystyle -31 & LaTeX:  \displaystyle 38 & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 28272 \\ \hline LaTeX:  \displaystyle p & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 225 & LaTeX:  \displaystyle 6 & LaTeX:  \displaystyle 0 & LaTeX:  \displaystyle 19 & LaTeX:  \displaystyle 21432 \\ \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 47 . The value of LaTeX:  \displaystyle t is LaTeX:  \displaystyle 744 . The max value is LaTeX:  \displaystyle p = 1128