A$-$to$-$B data link layer communications channel has a bit rate of $4$Kbps$,$ A$-$to$-$B propogation delay $20$ msec, B$-$to$-$A delay the same, frame size $160$ bits and stop$-$and$-$wait $($that is$,1-$bit sliding window, Protocol $4)$ protocol is used. $($i$)$ Assuming simplex data channel, that is no reverse data traffic, immediate individual ack and ignorable ack transmission time, compute the channel utilization. Show your work. U$=$ tf$/($tp $+$ tf $+$ tp$)$ where,U $=$ line utilizationtf $=$ frame transmission timetp$=$ frame propagation delaytp $+$ tf $+$ tp$=$ time to send and ack a frameU $=1/(1+$ a$)$ if full duplex and all acks tp$=20$msec $($ii$)$ Assuming full$-$duplex channel, the same frame size in reverse direction and immediate piggybacked ack, compute the channel utilization for full$-$duplex channel. Show your work.