Find the optimum flow on the network below by applying the network simplex algorithm $(c_{ij},u_{ij}).$

Guidelines:

You can collaborate or compare your assignment with a classmate, but everyone must submit his$/$her own assignment. You should also note your classmate's name.

You are expected to construct an initial feasible solution to start the algorithm. However, you should avoid using a near$-$optimal solution to terminate the algorithm in a short time by observing the problem parameters.

To get full credit, you must implement the algorithm for at least two iterations from beginning to end.