3. [25%] An entrepreneur is deciding how to subdivide a large old home to convert it to a Bed-and-Breakfast (B&B). There are four alternatives: Option A renovates all rooms, but leaves all walls intact, so the result would be two double rooms and three single rooms on the top floor, and on the main floor two further single rooms with a shared bathroom. Option B would renovate only the second floor but combine the single rooms in the main floor to create a single room with a bathroom. Option C combines the main floor rooms to create a single room with a bathroom, and combines the three single rooms on the top floor to create two double rooms. Finally option D would create five double rooms, each with its own bathroom. There are three event possibilities, a high demand, an average demand, and a low demand. The entrepreneur believes the probability of each event de pends on the layout and availability of the rooms. Below are the details of the predicted income and the probability of occurrence that accompany each option and demand situation: Annual income under different demand patterns Alternatives High p Average P Low Option A $273,900 0.2 $173,000 0.3 $72,000 0.5 Option B $284,300 0.3 $179,600 0.4 $74,800 0.3 Option C $242,700 0.4 $153,300 0.4 $63,900 0.2 Option D $260,000 0.5 $164,300 0.4 $68.400 0.1 (a) Draw the decision tree for the entrepreneur. (b) Compute the expected income for each option. Which option has the highest expected income? (C) Suppose option A costs $70,000, option B costs $84.000, option C costs $94,000 and option D costs $115,000. Calculate the expected profit (in- come minus cost) of each option. Which option has the highest expected profit? (d) Considering that the costs of renovation would have to be borrowed and re-payed at the end of the first year, which option do you consider is the best option? Why? P