Similarly to a flow network with demands, we can define a flow network with supplies where each node v V now has an integer supply sv so that if sv > 0, v is a source and if sv < 0, it is a sink, and the supply constraint for every v V is f out(v) f in(v) = sv. In a min-cost flow problem, the input is a flow network with supplies where each edge (i, j) E also has a cost aij (per unit of flow). Given a flow network with supplies and costs, the goal is to find a feasible flow f : E R+ that is, a flow satisfying edge capacity constraints and node supplies that minimizes the total cost of the flow. (a) Show that max flow can be formulated as a min-cost flow problem. (b) Formulate a linear program for the min-cost flow problem