In an industrial factory, the daily energy consumption of the factory is 800 kWh and 600 kVArh from 7 am to 5 pm, 200 kWh from 5 pm to 7 pm, and 960 kWh and 720 kVArh from 7 pm to 7 am. The distribution utility charges a penalty for industrial customers having power factors below 0.96. The penalty is applied as 10$/kVArh. The factory owner didn't want to make a payment to the distribution company. Because of this, the power factor correction was applied to the factory by the factory owner. Find the following unknowns. a. The rating of the capacitor system. (15 pts.) b. Explain how the capacitor system was operated. (15 pts.) c. The factory will add a new machine between 7 am and 5 pm. The machine consumes 50 kW with 0.8. Under this condition, what happens in terms of the penalty and find the amount of penalty (15 pts)