Find the optimal unit commitment schedule for the units to

Question

You are given three generating units and asked to find the optimal unit commitment schedule for the units to supply load over a 4-h time period.

Hour	MW load
1	400
2	1000
3	1600
4	400

Gen 1:F₁(P₁) = 2200 + 25P₁ + 0.025*P₁² where 220<=P₁<=600 MW

Gen 2:F₂(P₂) = 1500 + 11P₂ + 0.02*P₂² where 350<=P₂<=800 MW

Gen 3:F₃(P₃) = 1000 + 20P₃ + 0.015*P₃² where 150<=P₃<=600

Each generator has a start-up cost that must be factored in when the unit starts. You should assume that this start-up cost is incurred even if the unit was on then off for only one or two hours and then gets turned back on.

Generating Unit	Start-Up cost
1	2400
2	3000
3	3400

Find the optimal unit commitment schedule.