A factory powered by 450 V single-phase AC contains 20 machines, 7 of which consume 180 kW (each) at a p.f. of 0.8 lagging and 13 of which consume 75 kW (each) at a p.f. of 0.85 lagging. Find the component(s) needed to correct the power factor to unity and calculate how long the component(s) would take to pay for themselves, assuming the factory is charged for apparent power at REUpower's current rate $0.1065/kWh (NOTE: this doesn't actually happen) and considering only the procurement cost of the component(s).