Maximize LaTeX: \displaystyle p = 9 x + 15 y subject to LaTeX: \displaystyle \begin{cases}68 x + 18 y \leq 1224 \\ 49 x + 56 y \leq 2744 \\ 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{72}{11}, \ \frac{476}{11}\right) . Making a table gives to test the verticies in LaTeX: \displaystyle p=9 x + 15 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( 18, \ 0\right) & LaTeX: \displaystyle 162 \\[3pt] \hline LaTeX: \displaystyle \left( \frac{72}{11}, \ \frac{476}{11}\right) & LaTeX: \displaystyle 708 \\[3pt] \hline LaTeX: \displaystyle \left( 0, \ 49\right) & LaTeX: \displaystyle 735 \\[3pt] \hline \end{tabular}
The gives the maximum value of LaTeX: \displaystyle 735 located at LaTeX: \displaystyle \left( 0, \ 49\right) .