I have the following model \begin{align}\max&\quad B_{1} + B_{2}\\\text{s.t.}&\quad 0 \leq B_{1} \leq c_{1}\cdot Y_{1} \\&\quad 0 \leq B_{2} \leq c_{2}\cdot Y_{2} \\&\quad \end{align} where $B_{1}, B_{2}$ are reals, $Y_{1}, Y_{2}$ are binary, and $c_{1}, c_{2}$ are positive constants.
Is the following transformation of advantage when thinking about speeding up B&B?
\begin{align}\max&\quad B_{1} + B_{2} - M_{1} - M_{2}\\\text{s.t.}&\quad B_{1} + M_{1} = c_{1}\cdot Y_{1} \\&\quad B_{2} + M_{2} = c_{2}\cdot Y_{2} \\&\quad\end{align} where $B_{1}, B_{2},M_{1}, M_{2}$ are reals, $Y_{1}, Y_{2}$ are binary, and $c_{1}, c_{2}$ are positive constants.