A utility has three generators with the following cost functions and generation limits Generator 1: C1(g) = 0.03g2 + 20g + 500 ($/h), minimum generation 200 MW, maximum generation 500 MW. . Generator 2: C2(9) = 0.01g2 + 30g + 100 ($/h), minimum generation 50 MW, maximum generation 200 MW. . Generator 3: C3(g) = 0.02g + 25g + 200 ($/h), minimum generation 100 MW, maximum generation 300 MW. 1. List out the economic dispatch problem if the demand to be supplied is 700 MW. Indicate the optimization variables, use numerical values for all parameters. (10 pts) 2. Ignore the minimum and maximum generation limit for now, solve the dispatch problem with 700 MW demand. List our the generator output results. (10 pts) 3. Is your solution from 2) feasible after considering generation limits? (5 pts) 4. At a given time, the Lagrangian multiplier to the demand balance constraint, a.k.a, the marginal price, is $ 35/MWh, what should be the corresponding demand? (10 pts) 5. Solve the economic dispatch problem again for 1000 MW demand, again ignore the generation limits. (10 pts) 6. Is your solution from 5) feasible after considering generation limits? (5 pts)