1. (4.1A 4) Write the dual for each of the following primal problems:
a. Minimize $z = 6x_1 + 3x_2$
s.t. $6x_1 - 3x_2 + x_3 \ge 2$
$3x_1 + 4x_2 + x_3 \ge 5$
$x_1, x_2, x_3 \ge 0$
b. Minimize $z = 4x_1 + x_2$
s.t. $3x_1 + x_2 = 30$
$4x_1 + 3x_2 \ge 60$
$x_1 + 2x_2 \le 40$
$x_1 \ge 0, x_2 \le 0$
c. Maximize $z = x_1 + x_2$
s.t. $2x_1 + x_2 = 5$
$3x_1 - x_2 = 6$
$x_1, x_2$ unrestricted