Rankine cycles are a thermodynamic process that turn heat into mechanical work. They're often employed in generating electrical power, with high pressure steam used to rotate a turbine.
The thermodynamic efficiency of a Rankine cycle is 
where 
is the net work done by the system, and Q is the heat added. Operating parameters are chosen to maximize efficiency - these may be the temperatures or pressures at various points in the system.
A typical regenerative Rankine cycle is illustrated below.
In this application, we will
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define a procedure that calculates the cycle efficiency as a function of the pump outlet pressures at points 2 and 4
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and then find the pump outlet pressures that maximize the efficiency of the cycle.
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