Write an EES code for this problem: Consider the cogeneration plant shown below. Steam enters the turbine at $7$ MPa and $500^($@$)$C$.$ Some steam is extracted from the turbine at $500$ kPa for process heating. The remaining steam continues to expand to $5$ kPa $.$Steam is then condensed at constant pressure and pumped to the boiler pressure of $7$ MPa $.$ At times of high demand for process heat, some steam leaving the boiler is throttled to $500$ kPa and is routed to the process heater.The extraction fractions are adjusted so that steam leaves the process heater as a saturated liquid at $500$ kPa $.$ It is then pumped to $7$ MPa $.$ The mass flow rate of steam through the boiler is $15$kg$//$s$.$ Neglecting pressure drops and heat losses in the piping and assuming the turbine and

the pump to be isentropic$,$ determine $($a$)$ the maximum rate at which process heat can be supplied, $($b$)$ the power produced

and the utilization factor when no process heat is supplied, and $($c$)$ the rate of process heat supply when $10$ percent of the steam

is extracted before it enters the turbine and $70$ percent of the steam is extracted from the turbine at $500$ kPa for process heating.