Suppose that Mr$.$ William Bell owns a manufacturing facility in Kentucky, which

happens to be in a seismic zone $($i$.$e$.,$ an area where earthquakes tend to happen$).$ It is

known that the probability of an earthquake in the area is $15\%.$ If there is an

earthquake, the estimated total cost of damage to the facility $($and to Mr$.$ Bell's

business$)$ is uniformly distributed between $$30$ million and $$90$ million. There are at

least two options for you to mitigate such a risk. The first option is to retrofit your

facility to make it more resistant to seismic activities. The retrofit will cost $$40$

million. After the retrofit, you estimate that the total cost of damage after an

earthquake would be uniformly distributed between $10$ and $$30$ million. The second

option is to relocate your facility to an earthquake$-$free area, which would completely

eliminate any potential damage due to earthquakes. But the cost will be $$50$ million.

$($Note: You can ignore the time value of the money when answering the following

questions.$)$

a$.(20$ pts$)$ Draw a decision tree for this decision. For the continuous

distributions, please use either the extended Pearson$-$Tukey method or the

bracket median method to discretize them. $($Make sure to write out the

appropriate numbers at appropriate places of the tree.$)$