$(20$ points$)$ Alice and Bob are connected by a communication link with bandwidth of

$60$ Mbps $($i$.$e$.6^{**}{10}^7$ bits per second$).$ The link has a $($one$-$way$)$ propagation delay of

$50$ msec $($milliseconds$).$ Alice would like to send a file to Bob using the Go$-$back$-$N

protocol. However, Alice's ISP is monitoring the link usage and is going to charge

her if her link utilization exceeds $85\%.$ Note that she would not be charged as long as

her link utilization is no more than $85\%,$ where the utilization at a sender side is

defined as the fraction of time that the sender is busy with sending.

$($a$)$ Suppose that the segment size is $2$ Mb $,$ what is the largest sender window that

Alice can use without being charged?

$($b$)$ Assuming a send window of size $N=4$ to ensure that Alice can send messages

reliably to Bob, what is the minimum segment size that ensures a link utilization

of at least $65\%?$ Justify your answer.