Although the student designing the B$^6$ is sad that the greedy algorithm will not always work for dispensing change in this universe, you (an EECS 376 student) have learned that you can find the optimal number of coins for any set of coin denominations using dynamic programming. Write base case(s) and the recurrence relation for computing $\textsc{OPT-COIN-CHANGE}(C)$, where $C$ is the amount of change you want to make. You can only use 1$\cent$, $k\cent$ and 17$\cent$ coins ($k$ is the value you found in (b)). Briefly justify why this will be optimal regardless of denominations.

Your company is starting a new r& d initiative: a development of a new drug that dramatically reduces the addiction to smoking. the expert team estimates the probability of developing the drug succesfully at 60% and a chance of losing the investment of 40%. if the project is successful, your company would earn profits (after deducting the investment) of 9,000 (thousand usd). if the development is unsuccessful, the whole investment will be lost -1,000 (thousand usd). your company's risk preference is given by the expected utility function: u(x) v1000 +x, where x is the monetary outcome of a project. calculate the expected profit of the project . calculate the expected utility of the project . find the certainty equivalent of this r& d initiative . find the risk premium of this r& d initiative e is the company risk-averse, risk-loving or risk-neutral? why do you think so?