5. You have finally decided to get control of your finances. First, from now on, you will not spend any more in a given year than your current wealth. Second, since the things that you purchase provide a benefit outside of their purchase value, you wish to maximize this added benefit, i.e., utility. You have determined that spending c > 0 during a year has a utility of ca. Because you are still working and you have made some investments, by the beginning of the next year, the previous year's ending wealth grows by a factor of k. You would like to use dynamic programming to determine how to spend your wealth. (a) You have chosen 0 0. (c) Suppose fr(w) = bywa. What is the optimal consumption in stage t? Interpret the result. 5. You have finally decided to get control of your finances. First, from now on, you will not spend any more in a given year than your current wealth. Second, since the things that you purchase provide a benefit outside of their purchase value, you wish to maximize this added benefit, i.e., utility. You have determined that spending c > 0 during a year has a utility of ca. Because you are still working and you have made some investments, by the beginning of the next year, the previous year's ending wealth grows by a factor of k. You would like to use dynamic programming to determine how to spend your wealth. (a) You have chosen 0 0. (c) Suppose fr(w) = bywa. What is the optimal consumption in stage t? Interpret the result