Maximize LaTeX: \displaystyle p = 8 x + 22 y subject to LaTeX: \displaystyle \begin{cases}79 x + 44 y \leq 3476 \\ 69 x + 98 y \leq 6762 \\ x \geq 0, y \geq 0 \end{cases}

Drawing a graph gives
Solving the system of equations gives the intersection at LaTeX: \displaystyle \left( \frac{21560}{2353}, \ \frac{147177}{2353}\right) . Making a table gives to test the verticies in LaTeX: \displaystyle p=8 x + 22 y gives

\begin{tabular}{|c|c|}\hline Point & Function \\[3pt] \hline LaTeX: \displaystyle \left( 0, \ 0\right) & LaTeX: \displaystyle 0 \\[3pt] \hline LaTeX: \displaystyle \left( 44, \ 0\right) & LaTeX: \displaystyle 352 \\[3pt] \hline LaTeX: \displaystyle \left( \frac{21560}{2353}, \ \frac{147177}{2353}\right) & LaTeX: \displaystyle \frac{3410374}{2353} \\[3pt] \hline LaTeX: \displaystyle \left( 0, \ 69\right) & LaTeX: \displaystyle 1518 \\[3pt] \hline \end{tabular}
The gives the maximum value of LaTeX: \displaystyle 1518 located at LaTeX: \displaystyle \left( 0, \ 69\right) .