Consider a power grid consisting of electricity producers that are connected to consumption points on the grid. The consumption points are affiliated with regional retail power companies that then distribute the power to their end users. The undirected graph (attached) gives the structure of the network where nodes 1,2,and 3 are location of the power generation plants and nodes 4,5,7 and 9 are power consumption points. The cost of transmitting power over any edge is 13$ per megawatt hour and there is no capacity constraint on an edge. It is possible for power to traverse both orientations. Each power generator has a max generation capacity in megawatt hours and a cost per megawatt hour generated(attached table below).
Only have to formulate the problem of finding the minimum-cost power generation and distribution strategy over the network to satisfy all consumption points as a linear program
2. Relevant info
The Attempt at a Solution
Tried solving it but i have never done undirected graphs before so i have no clue on how to come up with constraints. Basically I don't know how to incorporate the undirected graph arcs as those arcs can go either way and also because there is more supply than demand(dummy demand node perhaps?).I tried to incorporate the cost of megawatt hours in the main function though it might not be right.
P.S. MIGHT be an engineering question