$$v_{out}=v_s A_1 A_2\frac{r_{i1}}{r_{i1}+R_s}\frac{r_{21}}{r_{i2}+r_{o1}}\frac{R_L}{r_{o2}+R_L}$$

To maximize $v_{out}$, we want lower $R_s$, $r_{o1}$, $r_{o2}$, and increase $r_{i1}$, $r_{i2}$, $R_L$, as well as $A_1$ and $A_2$

The power delivered by the source is

$$P_{in}=(i_{in})^2 r_{i1}=[\frac{v_s}{R_s+r_{i1}}]^2 r_{i1}$$

The power dissipated by the load $R_L$ is

$$P_{out}=\frac{v_{out}^2}{R_L}= v^2_s A^2_1 A^2_2[\frac{r_{i1... ...c{r_{21}}{r_{i2}+r_{o1}}\frac{R_L}{r_{o2}+R_L}]^2 \frac{1}{R_L}$$

The power gain is:

$$G_p=\frac{P_{out}}{P_{in}}=A^2_1A^2_2 r_{i1}R_L [\frac{r_{21}}{r_{i2}+r_{o1}}\frac{1}{r_{o2}+R_L}]^2$$