$(10$ points$)$ Consider a packet switched network with k$-$hops. x$-$bits of data are sent in

packets of size $\text{'}$p$\text{'}$ bits. Each packet has a header of $\text{'}$h$\text{'}$ bits. x$>>($p$+$h$).$ The bit rate is $\text{'}$b$\text{'}$

bps$.$ Assume a negligible propagation delay. What value of $\text{'}$p$\text{'}$ minimizes the total delay?

$($Hint: Total delay is made up of $2$ parts: to transmit the data and the time for each hop

to transmit the data. Also, a bit of calculus $($differentiation$)$ will be needed to find value

of $\text{'}$p$\text{'})$