$(15\%)$ Three input channels need to be multiplexed using TDM$.$ Their bit rates are $120kbps,80$

kbps$,$ and $40kbps,$ respectively.

$($a$)$ What is the required output bit rate for the TDM$?$

$($b$)$ How to set the relative size of each time slot in one frame?

$($c$)$ What is the minimum frame size and the corresponding frame rate?