Problem $1.(50$ pts$)$ Part I. Conduct a simplified design of a cogeneration power plant modified with regeneration as shown. Steam is available into the turbine at $6$ MPa and $450C.$ It is required to generate $17$ MW of power from the turbine and $20$ MW for process heating. Assume that $60\%$ of the steam is extracted from the turbine into the process heater and the remainder expands to the condenser pressure of $10$ kPa $.$ Assume the following:

$($i$)$ the process heater, feedwater heater and mixing chamber operate at the same extraction pressure $($to be selected to meet the design requirements$),$

$($ii$)$ saturated liquid leaves the process heater and the open feedwater heater.

Show the process on a T$-$s diagram then determine:

$($a$)$ The minimum mass flow rate required in the boiler and process heater, and

$($b$)$ The utilization factor of this cycle

Part II$.$ Using Excel, Matlab, EES or other software, investigate the effect of the extraction pressure on the required mass flow rate of the steam in the boiler and on the rate of heat supply from the process heater. Plot the mass flow rate through the boiler as a function of the extraction pressure, and plot the rate of heat supply from the process heater as a function of the extraction pressure $($You can show both plots on the same graph with different y$-$axis for mass flow rate and process heat flow rate$).$ Discuss the results.