Attached is the table for reference

$1\mathrm{.}3$ Mathematical Analysls

Through your work for Section $1\mathrm{.}2$ above where header fields were considered, you saw that as the size of

each segment $($let$\text{'}$s denote it as $S)$ decreases, the End$-$to$-$End delay $($let$\text{'}$s denote it as $D)$ went down then

picked up$.$ So$,$ what is the value of $S$ that would minimize $D?$

To simplify our analysis, let's assume:

The network topology above $($i$.$e$.$ two hosts connected by two routers and three links$)$ is used. The transmission rate of each link is $R$ bps$.$ Size of the original message that the "Source" node sends to the "Destination" node is $F$ bits. The "Source" node conducts message segmentation. The size of each segment is $S$ bits. The "Source" node adds $20$ bits of header fields to each packet it sends.

On the same paper that you used for Section $1\mathrm{.}1,$

Derive a mathematical formula for $D$ as a function of $F,S$ and $R.$

Then, to calculate the value of $S$ which leads to the minimum $D,$ find out the derivative of $D$ with respect

to $S$ and set it to $0.$ Ensure to circle your final answer.

Verify your answer by comparing it with pertaining values in the table for Section $1\mathrm{.}2$ above $($i$.$e$.$ that last

six entries where size of headers is $20$ bits$).$