I want to find the value of u that would maximize Ur(t) at a specific time for the set of functions below.
d(t) = 3 x d(t-1) + 4 x u(t-2) + k
Ur(t) = d(t) x u(t) - f x d(t)
Where f and k are constants
I’m a little rusty on my partial differential equations but his seems like a PDE to me. Am I correct about that and is it solvable? If so how, or what type of problem should I research?
For example can I just take the derivative of Pr with respect to p, hold all other variables constant and plug in the specific t value? Any tips are greatly appreciated.