FF Web Services is a company, located in Phoenix, Arizona, US$,$ that offers cloud computing services to its clients. In the most recent

year the company$$s growth rate has dipped significantly. The Chief Executive Officer $($CEO$)$ ordered an investigation which found that

all new potential clients require stronger security software than the company currently offers for their cloud computing. The

company$$s business analysis team approached a number of vendors that offer security software for cloud services. They have

decided that among these, the best option was Megabowl Defense, which uses machine learning algorithms to identify abnormal

behaviour and threats on the cloud server. They also think that FF Web Services has the capacity to develop its own in$-$house

advanced security system. However, they are uncertain whether this will be cheaper.

The CEO has asked the business analysis team to provide a recommendation between three options: buy software from Megabowl

Defense at $$8$ million one$-$time cost; develop its own software at $$5$ million one$-$time cost; or stay put $($i$.$e$.,$ do nothing$)$ and accept the

decline in growth.

The business analysis team is preparing a business case that is considering the next five years. If the company stays put and

accepts the decline in growth, its projected revenue will be $$505$ million over the next five years. If the company purchases Megabowl

Defence, its projected revenue will be $$530$ million over the next five years. If the company develops its own software, its projected

revenue will be $$525$ million if the security that the in$-$house software offers is as strong as Megabowl Defence. However, if the inhouse software is weaker than Megabowl Defense, the projected revenue will be $$505$ million, and if it is stronger then the projected

revenue will be $$535$ million. There is a $50\%$ chance the in$-$house software will be as strong as Megabowl Defense and a $45\%$

chance it will be weaker. Lastly, the remaining probability, is that it will be stronger.

i$.$ Construct a decision tree to represent the decision problem, including noting probabilities and outcomes.

ii$.$ By conducting the appropriate analysis using your decision tree, what should the business analysis team recommend to the

CEO?