Construct a linear programming problem for which both the primal and the dual problem has no feasible solution Construct (that is, find its coefficients) a linear programming problem with at most two variables and two restrictions, for which both the primal and the dual problem has no feasible solution.

For a linear programming problem to have no feasible solution it needs to be either unbounded or just not have a feasible region at all I think. Therefore, I know how I should construct a problem if it would only have to hold for the primal problem. However, could anyone tell me how I should find one for which both the primal and dual problem have no feasible solution? Thank you in advance.

Consider an LP:
$$
\begin{aligned}
\min \; & x_{1}+2 x_{2} \\
\text { s.t. } & x_{1}+x_{2}=1 \\
& 2 x_{1}+2 x_{2}=3
\end{aligned}
$$
and its dual:
$$
\begin{aligned}
\max\; & y_{1}+3 y_{2} \\
\text { s.t. } & y_{1}+2 y_{2}=1 \\
& y_{1}+2 y_{2}=2
\end{aligned}
$$
They are both infeasible.
