$($a$).$ Consider a typical major road network in Figure $1.$ It represents part of

the road network of downtown Ipoh, Perak. The streets are all one$-$way

with four intersections $($A$,$ B$,$ C and D$),$ and the arrows indicating the

direction of traffic flow. The flow of "traffic in$"$ and "traffic out" of the

network is measured in terms of vehicles per hour $($vph$).$ The figure

given here is based on midweek peak traffic hours, which are from $7$

A$.$M$.$ to $9$ A$.$M$.$ and $4$ P$.$M$.$ to $6$ P$.$M$.$ Assume all traffic entering an

intersection must leave that intersection.

$($i$).$ Identify FOUR $(4)$ mathematical equations that describe the

traffic flow in the road network depicted in Figure $1$;

$($ii$).$ By solving the mathematical equations identified in $($i$)$ using

Gauss$-$Jordan elimination method, determine the minimum

possible amount of traffic flow $($in vph$)$ that can be expected

along branch CD$.$ Assume all traffic flows are non$-$negative.