Seminar 7: Network optimization, Problem 1: Solve the maximal flow problem in the network with a source in the node 1 and sink in the node 6. Check the solution using MS Excel. Problem 2: Find a shortest path from the node 1 to the node 7 in the displayed network. Check the solution using MS Excel. Use binary decision variables (xij = 1 if the edge is included and xij = 0 if not) and formulate the problem as minimizing the cost of the unitary flow from the node 1 to the node 7). Problem 3: Find a minimal spanning tree of the displayed network.