Part B$2$: Assignment for Network$/$Traffic Flow

The following figure represents the traffic entering and leaving a "roundabout" road junction. Construct a mathematical model that describes the flow of traffic along the various branches using the values of Flow $1,$ Flow $2,$ Flow $3,$ Flow $4$ as input variables.

Part B$2\mathrm{.}1$: Write a program in PYTHON that accepts the four different flow numbers as input values. $($Flow $1,$ Flow $2,$ Flow $3,$ Flow $4).$ Create an augmented matrix from the constraints on the traffic described by the system of linear equations.

Part B$2\mathrm{.}2$: Solve this system using the Gauss$-$Jordan elimination method $($use a library$)$ and output the resulting matrix.