use the AI:

\begin{eqnarray*}u + 2g & = &\frac{L_1+L_2}{2} - \frac{2m-g}{2} + 2g \\ &=&\frac{L_1+L_2}{2} - (m - \frac{3}{2}g) \end{eqnarray*}



\begin{displaymath}minimizing \quad d=u+2g \quad \iff \quad maximizing \quad s=m - \frac{3}{2}g \end{displaymath}