Problem $5-$ Brayton cycle $($Optional with Extra Credit $15$ pts$)$

Consider a simple closed Brayton cycle, which uses air as the working fluid at a mass flow rate of $5k\frac{g}{s}.$ The maximum and minimum temperatures within the cycle are $950$ K and $350$ K $,$ respectively. The pressure ratio is $6$:$1.$ The adiabatic turbine has an isentropic efficiency of $80\%,$ while the well$-$insulated compressor is $90\%$ efficient compared to an isentropic one. Assume the cycle operates between a heat source at temperature $1000$ K $,$ and the ambient as the heat sink at temperature $300$ K $.$ There is no pressure drop in the heater and the cooler. The air can be treated as an ideal gas with constant properties $(c_p=1\mathrm{.}004k\frac{J}{k}g-K,$ and $k=1\mathrm{.}4).$ What are the net power output and thermal efficiency?