$.$ High$-$tech Appliance Manufacturing is considering outsourcing a subcomponent of their oven

line to several new suppliers. They have considered many options, but they are all located in

areas prone to flooding, which can trigger extended faculty outages. They are trying to

determine how many suppliers they should use to minimize risk. They believe the probability of

a super event, that might shut down all the suppliers at the same time, is $1\%.$ Shut down would

cost the company approximately $$400,000.$ They estimate the unique event risk for any of the

suppliers to be $6\%.$ Assuming that the marginal cost of managing an additional supplier is

$$15,000$ per year how many should they use?

a$)$ Calculate the probability of a super event. $(3$ points$)$

b$)$ Create the decision tree for $3$ suppliers $(13$ points$)$

Remember Cost$=($C$*$n$)+$L

c$)$ Calculate the EMV for each option $(3$ points$)$

d$)$ Make a recommendation to minimize the cost of failure.