Maximize LaTeX: \displaystyle p = x + 25 y subject to LaTeX: \displaystyle \begin{cases}57 x + 4 y \leq 228 \\ 40 x + 50 y \leq 2000 \\ 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{340}{269}, \ \frac{10488}{269}\right) . Making a table gives to test the verticies in LaTeX: \displaystyle p=x + 25 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( 4, \ 0\right) & LaTeX: \displaystyle 4 \\[3pt] \hline LaTeX: \displaystyle \left( \frac{340}{269}, \ \frac{10488}{269}\right) & LaTeX: \displaystyle \frac{262540}{269} \\[3pt] \hline LaTeX: \displaystyle \left( 0, \ 40\right) & LaTeX: \displaystyle 1000 \\[3pt] \hline \end{tabular}
The gives the maximum value of LaTeX: \displaystyle 1000 located at LaTeX: \displaystyle \left( 0, \ 40\right) .