I have the following simplified optimization problem:
\begin{align}\max &\quad ax+by\\\text{s.t.}&\quad0 \le x \le \overline X\\&\quad0 \le y \le\overline Y\\&\quad z = E-x+\beta\cdot y\end{align}
where $E$, $\beta$, $a$, $b$, $\overline X$ and $\overline Y$ are parameters and the rest are variables. What would be the dual objective function for this optimization problem?