Why does COIN-OR CBC Solver have both Continuous Solution Unbounded and Dual Infeasible exit statuses?

Question

I am working with COIN-OR CBC solver. I understand that Primal unbounded is dual infeasible. After seeing the exit statuses for CBC Solver, I came to know that both these conditions have their own respective exit statuses in the solver. Why is it so and under what circumstance will I get a dual infeasible status?

This is the source where it is defined

Answer 1

If the primal is unbounded, the dual is infeasible. The converse is not necessarily true. Take the following linear optimization problem:

$\begin{align} \max \{ x_1 : x_2 \leq 1, -x_2 \leq -2, x \geq 0 \} \end{align}$

This problem is clearly infeasible. The dual is:

$\begin{align} \min \{ y_1 - 2 y_2 : 0 y_1 + 0 y_2 \geq 1, y_1-y_2 \geq 0, y \geq 0 \} \end{align}$

which is also infeasible. So, the dual can be infeasible while the primal is not unbounded.