Please show all your work because (i) partial credit will sometimes be awarded and (ii) full creditwill NOT be awarded for answers that appear without accompanying work. Please write youranswers according to the order of the questions.

 3. (Total 30 points) Bryan Beaver is about to build his dam and lodge. There are two rivers that hecan choose from: Rainbow River and Rose River. At Rainbow River, there is a 50% chance offlash flood, but the view along the river is rather plain. Whereas, at Rose River, there is amagnificent view of the rose valley, but the probability of flash flood is 75%. His value ofhaving his dam and lodge located at both rivers are given in the following table:

【題組】

(a) (5 points) Suppose that Bryan's utility function is

. In this case, where should hebuild his dam and lodge? Please explain.Now the River God is offering insurance to Bryan. Despite the location, the insurance that paysback $1 costs $0.8.