write Fortran77.f in Microsoft Visual Studio and Open matlab file during calculation

I read the topics related to Fortran and MATLAB link (Mex or MATLAB Engine API) but I am a bit confused. Can you guide me to this project that is attached?

In fact, I want to write a Fortran file(Fortran77.f) in the Visual Studio software, which will open the MATLAB software during the calculations and take the Fortran inputs and perform a series of calculations and then return the outputs to the Fortran.

To avoid complicating the understanding of these files, two simple examples have been sent to the attachment.

Thank you for your answer and guidance