Please answer it using Mathematica if possible. Handwritten anser is fine too. Thanks!

3. In this problem, we study the consumption and investment decisions made by the residents of a small open economy. The approach adopted is that of the representative agent; that is, the consumption and investment decisions made by all the economic agents - consumers and firms - can be thought of as the outcomes of the utility maximization of a representative agent who lives forever. In the problem, time is discrete and denoted by t, t = 0, 1, Suppose that the small open economy - often called the home economy - begins at date t=0 with B, as the amount of foreign assets and K, as the capital stock it owns. The home economy faces a constant world interest rate r at each datet, t = 0, 1, ... Let B, be the stock of foreign assets that the home economy owns at the beginning of period t. The interest income earned at the end of period t is thus equal to r Bt. Another source of income for the home economy comes from its production activities. The output, at the end of period t, of the home economy is assumed to be given by Y = A+ F[K], where A is the total factor productivity in period t and he is the capital stock available at the beginning of that period. We shall assume that F[0] = 0, F'[K]>0, F"[K]0, "[C]0, F"[K]0, "[C]