Maximize LaTeX: \displaystyle p = 20 x + 17 y subject to LaTeX: \displaystyle \begin{cases}94 x + 16 y \leq 1504 \\ 78 x + 86 y \leq 6708 \\ 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{5504}{1709}, \ \frac{128310}{1709}\right) . Making a table gives to test the verticies in LaTeX: \displaystyle p=20 x + 17 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( 16, \ 0\right) & LaTeX: \displaystyle 320 \\[3pt] \hline LaTeX: \displaystyle \left( \frac{5504}{1709}, \ \frac{128310}{1709}\right) & LaTeX: \displaystyle \frac{2291350}{1709} \\[3pt] \hline LaTeX: \displaystyle \left( 0, \ 78\right) & LaTeX: \displaystyle 1326 \\[3pt] \hline \end{tabular}
The gives the maximum value of LaTeX: \displaystyle \frac{2291350}{1709} located at LaTeX: \displaystyle \left( \frac{5504}{1709}, \ \frac{128310}{1709}\right) .