Consider a message that needs to be transmitted over a $3$ hop path. Assume that the propagation delay for each hop is $2$sec$.$ The message is $12000$ bits, and the transmitter can transmit $1000$ bits$/$sec$.$ Ignoring any queueing delays, compute the time it takes for the entire message to be completely received at the receiver note under the following scenarios. For each case, ignore any queueing delays, and assume that all packets follow the same path.

a$)$ Message switching is used

b$)$ Packet switching is used, with each packet consisting of $3000$ bits

c$)$ Packet switching is used, with each packet consisting of $4000$ bits

d$)$ Cut$-$through switching is used, with negligible header processing time