Question: A cable television company is considering extending its services to a rural community. The company's managing director believes that there is a 0.50 chance that profits from the service will be high and amount to $760,000 in the first year, and a 0.50 chance that profits will be low and amount to $400,000 for the year. An alternative operation promises a sure profit of $500,000 for the period in question. The company may test the potential of the rural market for a cost of $25,000. The test has a 90% reliability of correctly detecting the state of nature. Construct the decision tree and determine the optimal decision.