The optimal solution is to invest $10,000 in Option A at time 0, yielding a maximum return of $14,400 at time 1.

[\dotx(t) = v(t)] [\dotv(t) = u(t) - g]

[J(u) = x(T)]

Using optimal control theory, we can model the system dynamics as:

Solving this equation using dynamic programming, we obtain: