I have to find maximum of $x_1 - x_2 - x_3 + x_4 - 2x_5$ with constraints:
$-x_1 +x_2 + x_3 = 2$
$x_1 + 2x_2 + x_4 = 10$
$x_1 - x_2 + x_5 = 4$
of course $x_i \ge 0$.
From constrains I have:
$x_3 = 2 + x_1 - x_2$
$x_4 = 10-x_1-2x_2$
$x_5 = 4 + x_2 - x_1$
If i put it into
$x_1 - x_2 - x_3 + x_4 - 2x_5$
i will have
$f(x_1,x_2) = x_1 - 4x_2$
What now I can do with it?