Hi absad,
I can easy solve the problem for you.
I would formulate the problem as a compact MIP for you, solve it using a state of the art MIP solver and AMPL as input format.
Further, I would provide a short documentation, i.e. the "management report" stated in your problem formulation.
The Report would contain an explanation of the variables and constraints used in the model and a specification of the optimal solution obtained from solving it.
I studied mathematics with a focus on operations research, so I am great for the job.
Feel free to ask for further details.
regards,
Andreas