Question: A software development company wants to utilize a network of four servers to manage data processing tasks. Each server is interconnected and must handle not only internal data flow but also interact with external sources and destinations. To maintain a stable and efficient network, it is crucial that each server in our setup manages its data flow in a balanced manner. This means that for every server, the total amount of data entering it must equal the total amount of data exiting. This equilibrium ensures no server becomes a bottleneck, thus maintaining a smooth and continuous data flow throughout the entire network. The IT department is considering the following network configuration:

Server A sends $x_1$ units of data to Server B and $x_2$ units to Server C$,$ as well as receives $100$ units of external data.

Server B sends $x_3$ units of data to Servers C and $x_4$ units to Server D$.$

Server C sends $x_5$ units of data to Server D$.$

Server D sends $x_6$ units of data back to A and also sends $50$ units of data externally.