4. (a) Here we will consider an flow problem where we seek to transport electricity in a network with minimal losses. Consider the network in Figure 1 with five nodes and six edges, and where one unit of current enters the network at node A (A is a source) and one unit of current exits the system at node E (E is a sink). The loss in an edge is the square of the current in that edge. (i) Formulate the problem of minimizing the sum of all losses in the network (i.e., sum of losses in all edges) as a QP problem with constraints. The flow in an edge is allowed to go in both directions. (5p) (ii) Solve the optimization problem (e.g., using the nullspace method). . (5p) E A D B Figure 1: Flow network