Consider the two settlement system for a three-bus network in the following figure. There are two generators at bus A and C, with a marginal cost of 50$/MWh and 100 $/MWh, respectively. Let's assume that there is no limit on the power output of each generator. The impendence of the three transmission lines are given in the figure. The line capacity constraints are (a) In the day-ahead market, the forecast demand at bus A, B, C is 0, 0, and 100 Mw, respectively. Formulate the DC-OPF problem, solve it and find the nodal prices (at all three buses) in the day-ahead market . (20 points) (b) In the real-time market, the system operator finds the true demand at bus A, B, C is 0, 0, and 110 MW, respectively. Therefore additional 10MW power needs to procure for bus C in the real-time market. Find the nodal prices (at all three buses) in the real time market. Derive the total revenue for generator A and C (collected from the two- settlement system). (20 points) OMW Gc $100 LC 100MW