P8.1. Flows 1 and 2 use the network as shown in figure 8.14. Flow 1 uses link AB and BC with capacities an and b, respectively. Flow 2 uses only link AB. Let x=(x1,x2) where x1 and x2 denote the rates of the flows 1 and 2 respectively. A) find x that maximizes x1+x2 subject to the capacity constraints. B) find x that maximizes min(x1,x2) and satisfies the capacity contraints. C) find x that maximizes log(x1) + log (X2) subject to the capacity constraints. D) write the gradient algorithm that solves the primal dual problem of part c