For the first part, Once I pivot and make $x_4,x_5$ enter the basis, we can obtain our original problem. Actually, -35 should be -62 so that we get
$$ min z = 6x_1 + 20 x_3 $$
such that
$$ x_2 + 4 x_3 \leq 10 $$ $$ 30x_1 - x_2 + 2 x_3 \leq 11 $$
do we have to assume that $x_i \geq 0$? to the problem the constraints are of the form $\leq $, does it mean that $x_i \leq 0$??