This seems like a straightforward problem using either the Problem-Based Optimization Workflow or the solver-based approach. As long as you have a function that takes the 
values and returns 
values numerically, you can get an optimum.
values and returns values numerically, you can get an optimum.In summary, for the problem-based approach you define optimization variables, define the objective function in terms of the variables (you might have to use fcn2optimexpr to do so), and then call solve. For the solver-based approach, you write the objective function in terms of the variable x, which represents the variables you can alter to search for an optimum, and then call the appropriate solver, perhaps fmincon.
Good luck,
Alan Weiss
MATLAB mathematical toolbox documentation
