Solve the following problem using EES$-$Software

Consider a steam power plant that operates on an ideal reheat$-$regenerative Rankine cycle with one open feedwater heater, and one reheater. Steam enters the turbine at $15$ MPa and $600C$ and is condensed in the condenser at a pressure of $10$ kPa $.$ Some steam is extracted from the turbine at $4$ MPa for the closed feedwater heater, and the remaining steam is heated at the same pressure to $600C.$ The extracted steam is completely condensed in the heater and is pumped to $15$ MPa before it mixes with the feedwater at the same pressure. Steam for the open feedwater heater is extracted from the low pressure turbine at a pressure of $0\mathrm{.}5$ MPa. Determine:

$($a$)$ the fractions of steam extract from the turbines,

$($b$)$ the heat input and output of the cycle, in $(k\frac{J}{k}g),$

$($c$)$ the work interactions for each turbine and compressor, in $(k\frac{J}{k}g),$

$($d$)$ the thermal efficiency of the cycle.

Parametric study: Study $($graph$)$ the effect of changing the intermediate $($extracted steam$)$ pressure on the cycle efficiency. Take this pressure values to be between $1$ MPa to $5$ MPa with an increment of $500$ kPa $.$