Maximize LaTeX: \displaystyle p = 5 x + 16 y subject to LaTeX: \displaystyle \begin{cases}93 x + 18 y \leq 1674 \\ 12 x + 50 y \leq 600 \\ 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{12150}{739}, \ \frac{5952}{739}\right) . Making a table gives to test the verticies in LaTeX: \displaystyle p=5 x + 16 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 90 \\[3pt] \hline LaTeX: \displaystyle \left( \frac{12150}{739}, \ \frac{5952}{739}\right) & LaTeX: \displaystyle \frac{155982}{739} \\[3pt] \hline LaTeX: \displaystyle \left( 0, \ 12\right) & LaTeX: \displaystyle 192 \\[3pt] \hline \end{tabular}
The gives the maximum value of LaTeX: \displaystyle \frac{155982}{739} located at LaTeX: \displaystyle \left( \frac{12150}{739}, \ \frac{5952}{739}\right) .