1. Determine if $x_1 = 0$, $x_2 = 4/3$, $x_3 = 2/3$, $x_4 = 5/3$, $x_5 = 0$ is optimal for the problem:
$\text{Max } \{7x_1 + 6x_2 + 5x_3 - 2x_4 + 3x_5\}
\text{s.t. } \begin{cases} x_1 + 3x_2 + 5x_3 - 2x_4 + 2x_5 \le 4\\4x_1 + 2x_2 - 2x_3 + x_4 + x_5 \le 3\\2x_1 + 4x_2 + 4x_3 - 2x_4 + 5x_5 \le 5\\3x_1 + x_2 + 2x_3 - x_4 - 2x_5 \le 1\\x_1, x_2, x_3, x_4, x_5 \ge 0\end{cases}$