Please analyze and calculate the problem. Take as much time as you need.

You are a manager of a power company which owns and operates $4$ gas power plants.

Each gas power plants operates on a simple Brayton cycle with a pressure ratio of $9.$ Air

enters the compressor at $300$ K and $100$ kPa while it is $1800$ K at the turbine inlet. Each

gas power plant produces a net power output of $80$ MW $.$ To better utilize the waste heat in

the exhaust gases, you are considering the option of adding one steam power plant $($i$.$e$.,$

the operation of a combined cycle$).$ The steam power plant under consideration is a simple

Rankine cycle operating between the pressure limits of $7$ MPa and $5$ kPa $.$ If the

temperature of exhaust gas leaving the heat exchange is not to be greater than $450$ K and

the temperature of steam entering the turbine is not to be lower than $500^($@$)$C$,$ what will be

your best design of the combined cycle?

You can consider the options of pairing one gas power plant with one steam power plant, or

two gas power plants with one steam power plant $($refer to the diagram below$),$ or four gas

power plants to one steam power plant. In your evaluation, you need to consider

$($a$)$ the total net power output from the steam power plant$($s$),$

$($b$)$ the total power output from the combined power plant,

$($c$)$ the size of your heat exchanger.

$($d$)$ Would it be better if a regenerator is used instead? If so$,$ what would be your

arguments in supporting your decision?