PLE has developed a prototype for a new snow blower for the consumer market.

This can exploit the company's expertise in small$-$gasoline$-$engine technology and also balance seasonal demand cycles in the North American and European markets to provide additional revenues during the winter months. Initially, PLE faces two possible decisions: introduce the product globally at a cost of $$850,000$ or evaluate it in a North American test market at a cost of $$200,000.$ If it introduces the product globally, PLE might find either a high or low response to the product. The probabilities of these events are estimated to be $0\mathrm{.}6$ and $0\mathrm{.}4,$ respectively. With a high response, gross revenues of $$2,000,000$ are expected; with a low response, the figure is $$450,000.$ If PLE starts with a North American test market, it might find a low response or a high response, with probabilities of $0\mathrm{.}3$ and $0\mathrm{.}7,$ respectively. This may or may not reflect the global market potential. In any case, after conducting the marketing research, PLE next needs to decide whether to keep sales only in North America, market globally, or drop the product. If the North American response is high and PLE stays only in North America, the expected revenue is $$1,200,000.$ If it markets globally $($at an additional cost of $$200,000),$ the probability of a high global response is $0\mathrm{.}9$ with revenues of $($$$450,000$ if the global response is low$).$ If the North American response is low and it remains in North America, the expected revenue is $$200,000.$ If it markets globally $($at an additional cost of $$600,000),$ the probability of a high global response is with revenues of $$2,000,000($$$450,000$ if the global response is low$).$

Construct a decision tree, determine the optimal strategy, and develop a risk profile associated with the optimal strategy. Evaluate the sensitivity of the optimal strategy to changes in the probability estimates. Summarize all your results, including your recommendation and justification for it$,$ in a formal report to the executive committee, who will ultimately make this decision. explain the outcome of the decision tree and why is this the best option for the company. probabilities to explain other possible outcomes if any and then summarize everything