I have experience of the Matlab programming, using C - coded functions in the MatLab code and conversion m-code to C. There is an experience of the working with MatLAB Engine from C++ and C# code. Total experience is 5+ years.
But task description is too common so bid is only approximate.
I don't expect any problem to write m-code by known C code for a computation program. But if C-code is using Win32/64 API, some GUI tools, graphic libraries so on - it may be not such simple task.