$[$Extra Credit Optional Problem$]$ Consider a steam power plant that operates on the ideal regenerative Rankine cycle with a closed feedwater heater as shown in the figure. The plant maintains the turbine inlet at $3000$ kPa and $350C$ and operates the condenser at $20$ kPa $.24\mathrm{.}37\%$ of the steam is extracted to serve the closed feedwater heater, which discharges into the condenser after being throttled to condenser pressure. Calculate the pressure at which the steam is extracted from the turbine, the work produced by the turbine, the work consumed by the pump, and the heat supply in the boiler for this cycle per unit of boiler flow rate.