A factory has a maximum demand of 1.5MVA at a lagging power factor of 0.7. The factory works on full load for 10 hours a day and 25 days in every month of a year. For the remaining times, it works on half load at a lagging power factor of 0.8. The cost of the loss-free capacitor is $500 per kVAr, and the depreciation and interest of the capital investment may be taken as 1.25% per month. The two-part tariff offered to the factory is as follow: Maximum demand charge: Energy charge : (Assume 30 days in a month) $60 per kVA per month. $0.6 per kWh consumed. Determine: (a) the most economical value of power factor of the factory; (b) the saving per annum if the power factor is corrected to the value in part (a), and; (c) the electricity charge paid per annum at this value