Let $S = \{ z \in \mathbb { C } : | z - 3 | \leq 1$ and $z ( 4 + 3 i ) + \bar { z } ( 4 - 3 i ) \leq 24 \}$. If $\alpha + i \beta$ is the point in $S$ which is closest to $4 i$, then $25 ( \alpha + \beta )$ is equal to $\_\_\_\_$.
Let $S = \{ z \in \mathbb { C } : | z - 3 | \leq 1$ and $z ( 4 + 3 i ) + \bar { z } ( 4 - 3 i ) \leq 24 \}$. If $\alpha + i \beta$ is the point in $S$ which is closest to $4 i$, then $25 ( \alpha + \beta )$ is equal to $\_\_\_\_$.