This is a question about the push-down machine

Suppose $ G$ is a $ CFG$ with m variables and not right side of production longer than $ l$ . Show that if $ A\Rightarrow^*_G\varepsilon$ , then there is a derivation of no more than $ \frac{l^m-1}{l-1}$ steps by which $ A$ derives $ \varepsilon$ . How close to this bound can you actually come?