Question $1$

In a network of $n$ computers and $m$ printers, each computer and each printer is connected to a

hub using full duplex wires.

a$)$ Derive a general formula for the number of full duplex wires needed for the network. $[2]$

b$)$ Derive a general formula for the number of ports needed for the network. $[2]$

c$)$ If the network consists of $60$ computers and $20$ printers, calculate the number of the full

duplex wires required. $[2]$

d$)$ If instead of full duplex wires, half duplex wires are used and data needs to be

transmitted simultaneously in both directions, derive a general formula for the number

of half duplex wires required. Then, calculate the number of half duplex wires required

for the network of $30$ computers and $40$ printers. $[4]$