Maximize LaTeX: \displaystyle p = 2 x + 2 y subject to LaTeX: \displaystyle \begin{cases}54 x + 37 y \leq 1998 \\ 17 x + 76 y \leq 1292 \\ 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{104044}{3475}, \ \frac{35802}{3475}\right) . Making a table gives to test the verticies in LaTeX: \displaystyle p=2 x + 2 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( 37, \ 0\right) & LaTeX: \displaystyle 74 \\[3pt] \hline LaTeX: \displaystyle \left( \frac{104044}{3475}, \ \frac{35802}{3475}\right) & LaTeX: \displaystyle \frac{279692}{3475} \\[3pt] \hline LaTeX: \displaystyle \left( 0, \ 17\right) & LaTeX: \displaystyle 34 \\[3pt] \hline \end{tabular}
The gives the maximum value of LaTeX: \displaystyle \frac{279692}{3475} located at LaTeX: \displaystyle \left( \frac{104044}{3475}, \ \frac{35802}{3475}\right) .