Maximize LaTeX: \displaystyle p = 10 x + 14 y subject to LaTeX: \displaystyle \begin{cases}68 x + 12 y \leq 816 \\ 60 x + 82 y \leq 4920 \\ 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{984}{607}, \ \frac{35700}{607}\right) . Making a table gives to test the verticies in LaTeX: \displaystyle p=10 x + 14 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( 12, \ 0\right) & LaTeX: \displaystyle 120 \\[3pt] \hline LaTeX: \displaystyle \left( \frac{984}{607}, \ \frac{35700}{607}\right) & LaTeX: \displaystyle \frac{509640}{607} \\[3pt] \hline LaTeX: \displaystyle \left( 0, \ 60\right) & LaTeX: \displaystyle 840 \\[3pt] \hline \end{tabular}
The gives the maximum value of LaTeX: \displaystyle 840 located at LaTeX: \displaystyle \left( 0, \ 60\right) .