4. We consider a two-stage unit commitment problem. Each stage lasts for 1 hour. The initial status of both generators at t=0 is off. The forecast demand at t=1 and 2 is 300 and 400 MW, respectively. There are in total two generators. Note that in the hour when the generator is turned on, it can provide any energy output (within the max/min output range). Parameters of the two generators are given in the following table. For part (a), the minimum reserve capacity constraint is ignored. Generator Max/Min Output (MW) Min Up/Down Ramp up/down Time (Hour) rate constraints Marginal energy cost Start-up cost ($) (MW/hour) ($/MW) 1 2 500/200 300/0 2/4 0/0 100/400 50 1000 300/300 100 0 (a) Formulate the unit commitment problem and solve it. (20 points) (b) Now consider the unit commitment problem with operating reserve constraint. For both generators, the cost of providing operating reserve is zero. Generator 1 can provide up to 100 MW reserve, and generator 2 can provide up to 150 MW reserve. The minimum reserve capacity is set to be 200MW at each stage. Formulate the unit commitment problem. You don't need to solve the formulated problem. (15 points)