Maximize LaTeX: \displaystyle p = 15 x + 6 y subject to LaTeX: \displaystyle \begin{cases}56 x + 13 y \leq 728 \\ 55 x + 89 y \leq 4895 \\ 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{1157}{4269}, \ \frac{234080}{4269}\right) . Making a table gives to test the verticies in LaTeX: \displaystyle p=15 x + 6 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( 13, \ 0\right) & LaTeX: \displaystyle 195 \\[3pt] \hline LaTeX: \displaystyle \left( \frac{1157}{4269}, \ \frac{234080}{4269}\right) & LaTeX: \displaystyle \frac{473945}{1423} \\[3pt] \hline LaTeX: \displaystyle \left( 0, \ 55\right) & LaTeX: \displaystyle 330 \\[3pt] \hline \end{tabular}
The gives the maximum value of LaTeX: \displaystyle \frac{473945}{1423} located at LaTeX: \displaystyle \left( \frac{1157}{4269}, \ \frac{234080}{4269}\right) .