2. Consider the following LP problem:
minimize $f(x_1, x_2) = x_1 + x_2$
subject to: $x_1 + 2x_2 \geq 3$
$2x_1 + x_2 \geq 3$
$x_1, x_2 \geq 0$
(a) Give the dual of the problem.
(b) Convert the dual problem to standard form, and solve the dual.
(c) The solution to the original problem is $x^* = \begin{bmatrix} 1\\1 \end{bmatrix}$. Verify that the (strong) duality theorem holds.
