Lance Armstrong is thinking about opening a bicycle shop in his hometown. Lance 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. Because there will be a

five$-$year lease on the building that Lance is thinking about using, he wants to make sure that

he makes the correct decision. Lance is also thinking about hiring his old marketing professor

to conduct a marketing research study. If the study is conducted, the results could either be

positive or negative.

Lance has done some analysis about the profitability of the bicycle shop. If he opens the

shop, he will earn $$600,000$ if the market is favorable, but he will lose $$400,000$ if the market is

unfavorable. At the present time, he believes that there is a $50-50$ chance that the market will

be favorable.

It is estimated that there is a $0\mathrm{.}6$ probability that the study will be positive. Furthermore,

there is a $0\mathrm{.}9$ probability that the market will be favorable given a positive result from the

study. However, the marketing professor has warned Lance that there is only a probability of

$0\mathrm{.}12$ of a favorable market if the results of the study are negative.

$($a$)$ Use a decision tree and the EMV criterion to determine the optimal course of action for

Lance.

$($b$)$ What is the expected value of experimentation $($EVE$)$ in this situation?

$($c$)$ Lance$$s old marketing professor will charge him $$50,000$ for the marketing research. Is it

worth it$?$ Explain why or why not.