For the given system, write a Unit Commitment Optimization Problem which maximized the profit of the project owner.

Note that the ending storages MUST be equal to the Initial Storages.

LMP 1 Units Capacity Limits (MW) Pmin Pmax Superior 0 20 High 0 75 Middle 0 45 Low 0 30 Start up Cost ($) Duty Factors (cfs/MWh) 1000 2500 10 2000 15 1500 25 Superior High Middle Low $ $ $ $ 2 3 4 5 50 $ 45 $ 40 $ 35 $ 40 $ 52 $ 50 $ 50 $ 30 $ 20$ 35 $ 30 $ 25 $ 25 $ 30 $ 100 $ 125 $175 $ 189 $ 50 $ 6 7 50 $ 70 S 80 $ 90S (10) $ (10) $ 25 $ 90 $ 8 9 10 11 12 13 90 S 50 S 30 $ 10 $ (10) $ (20) $ 100 S 50 $ 30 $ 10 $ 5$ 71 $ (80) S (70) S (30) $190) S (100) $ (20) S 130$ 49 $ 30 $ 25$ 20$ 25$ 14 (20) $ 10 $ (35) $ 75$ 15 16 (5) $ 35 $ 50 $ 55 $ (60) $ (25) $ 85$ 100 S 17 18 19 20 21 40 $ 80 $ 100 S 150 $ 125$ 70 $ 100 $ 200 $ 250$ 25$ 10 $ 25$ 50 $ 70 $ 72 $ 140 $ 180 $ 250 300$ 325$ 22 100 $ 200 $ 75 $ 200 $ 23 80$ 100 $ 60$ 150 $ 24 65 75 30 100 Reservoir Elevation Limits Min Max Roseville 8000 10000 Sacramento 2500 3500 Folsom 250 350 El Dorado 2000 3000 Rancho 600 Initial 9000 3000 300 2500 500 End 9000 3000 300 2500 500 Auburn Dam Fish Flow 6.7 cfs 4 cfs San Fransisco Creek 4.7 cfs Auburn Reservoir Natural flows | 30 Natural Flows Low Land Middle Land High Land Superior Land Sacramento River 10 cfs Rancho Cordova Reservoir Yuba River El Dorado Canal 25 El Dorado Reservoir Folsom Fish Sacramento Reservoir cfs Folsom Reservoir Roseville Fish Sacrmaneto Fish Flow 8.3 cfs Roseville Reservoir 400 cfs 9 cfs 0 cfs Residential Customers 10 cfs Davis cfs Creek 5 cfs Residential Customers Irrigators 8 Natural Flows cfs 20 cfs Natural Flows 10 cfs Davis Reservoir LMP 1 Units Capacity Limits (MW) Pmin Pmax Superior 0 20 High 0 75 Middle 0 45 Low 0 30 Start up Cost ($) Duty Factors (cfs/MWh) 1000 2500 10 2000 15 1500 25 Superior High Middle Low $ $ $ $ 2 3 4 5 50 $ 45 $ 40 $ 35 $ 40 $ 52 $ 50 $ 50 $ 30 $ 20$ 35 $ 30 $ 25 $ 25 $ 30 $ 100 $ 125 $175 $ 189 $ 50 $ 6 7 50 $ 70 S 80 $ 90S (10) $ (10) $ 25 $ 90 $ 8 9 10 11 12 13 90 S 50 S 30 $ 10 $ (10) $ (20) $ 100 S 50 $ 30 $ 10 $ 5$ 71 $ (80) S (70) S (30) $190) S (100) $ (20) S 130$ 49 $ 30 $ 25$ 20$ 25$ 14 (20) $ 10 $ (35) $ 75$ 15 16 (5) $ 35 $ 50 $ 55 $ (60) $ (25) $ 85$ 100 S 17 18 19 20 21 40 $ 80 $ 100 S 150 $ 125$ 70 $ 100 $ 200 $ 250$ 25$ 10 $ 25$ 50 $ 70 $ 72 $ 140 $ 180 $ 250 300$ 325$ 22 100 $ 200 $ 75 $ 200 $ 23 80$ 100 $ 60$ 150 $ 24 65 75 30 100 Reservoir Elevation Limits Min Max Roseville 8000 10000 Sacramento 2500 3500 Folsom 250 350 El Dorado 2000 3000 Rancho 600 Initial 9000 3000 300 2500 500 End 9000 3000 300 2500 500 Auburn Dam Fish Flow 6.7 cfs 4 cfs San Fransisco Creek 4.7 cfs Auburn Reservoir Natural flows | 30 Natural Flows Low Land Middle Land High Land Superior Land Sacramento River 10 cfs Rancho Cordova Reservoir Yuba River El Dorado Canal 25 El Dorado Reservoir Folsom Fish Sacramento Reservoir cfs Folsom Reservoir Roseville Fish Sacrmaneto Fish Flow 8.3 cfs Roseville Reservoir 400 cfs 9 cfs 0 cfs Residential Customers 10 cfs Davis cfs Creek 5 cfs Residential Customers Irrigators 8 Natural Flows cfs 20 cfs Natural Flows 10 cfs Davis Reservoir