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Jerry Smith is thinking about opening a bicycle shop in his hometown. Jerry loves to take his own bike on $50-$mile trips with his friends, but he believes that any small business should be started only if there is a good chance of making a profit. Jerry can open a small shop, a large shop, or no shop at all. The profits will depend on the size of the shop and whether the market is favorable or unfavorable for his products. Because there will be a $5-$year lease on the building that Jerry is thinking about using, he wants to make sure that he makes the correct decision. Jerry is also thinking about hiring his old marketing professor to conduct a marketing research study. If the study is conducted, the study could be favorable $($ie$,$ predicting a favorable market$)$ or unfavorable $($ie$.,$ predicting an unfavorable market$).$

Jerry Smith has done some analysis about the profitability of the bicycle shop. If Jerry builds the large bicycle shop, he will earn $$60,000$ if the market is favorable, but he will lose $$40,000$ if the market is unfavorable. The small shop will return a $$30,000$ profit in a favorable market and a $$10,000$ loss in an unfavorable market. At the present time, he believes that there is a $50-50$ chance that the market will be favorable. His old marketing professor will charge him $$5,000$ for the marketing research. It is estimated that there is a $0\mathrm{.}6$ probability that the survey will be favorable. Furthermore, there is a $0\mathrm{.}9$ probability that the market will be favorable given a favorable outcome from the study. However, the marketing professor has warned Jerry that there is only a probability of $0.12$ of a favorable market if the marketing research results are not favorable. Jerry is confused.

$1.$ What is the EMV that solves this tree?

$2.$ Jerry, however, is unsure the $0\mathrm{.}6$ probability $($P$)$ of a favorable marketing research study is correct. How sensitive is Jerry's decision to this probability value? How far can this probability value deviate from $0\mathrm{.}6$ without causing Jerry to change his decision?

Select one:

$1.1.$ $$45,000$ and $2.$ P$0\mathrm{.}6$

$21$ $$25,000$ and $2$: P$0\mathrm{.}3$

$31$ $$25\mathrm{.}000$ and $2$: P$0\mathrm{.}7$

$4.$ None of the options provided

$051$ $$10,000$ and $2$ P$0\mathrm{.}7$

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