$(25$ points$)$ Should a utility add a regenerator to their gas turbine?$$ The regenerator will add $$50$ million dollars to the initial cost of the gas turbine.$$ The regenerator will increase the thermal efficiency of the cycle from $35\%$ to $55\%.$ The net power output for the application is $100$ megawatts for $8,000$ hours each year. The fuel is natural gas which is delivered to fuel meter at $100[$kPa$]$ and $300[$K$].$ The cost of fuel is expected to be $0\mathrm{.}15[$$$/$m$^3]$ over the $40$ year life of the turbine.$$ The utilities minimum acceptable rate of return is $15\%.$