Solve the following question using MATLAB:

A gas turbine for an automobile is designed with a regenerator. Air enters the compressor of this engine at $100$ kPa and $30\backslash$deg C$.$ The compressor pressure ratio is $10$; the maximum cycle temperature is $800\backslash$deg C; and the cold air stream leaves the regenerator $10\backslash$deg C cooler than the hot air stream at the inlet of the regenerator. Assuming both the compressor and the turbine to be isentropic$,$ determine the rates of heat addition and rejection for this cycle when it produces $115$ kW$.$ Use constant specific heats at room temperature.