Question: You have been invited to bid on a construction job for a small airport. The value of the contract depends on the length of time it takes to complete the project. If the project was finished on time, there is a profit of $50,000. If the project was finished later than the completion date, then a penalty cost of $10,000 will be incurred. Weather is the sole determinant of whether the project will be late. If the weather is good, the project will be completed on time; if it is bad, the project will not be completed on schedule. Based on your past experience, your subjective probability of good weather is 20 percent. You, however, have the opportunity to buy a long-range forecast from an independent weather-forecasting company. The weather-forecasting company has a fairly good track record for these long-range forecasts. Its records indicated that 70 percent of the time it successfully predicted good weather, and 80 percent of the time it was able to predict bad weather. In other words,

P(I1\S1) = .7

P(I1\S2) = .2

P(I2\S1) = .3

P(I2\S2) = .8

Where

I1 = prediction of good weather I2 = prediction of bad weather S1 = Good weather S2 = bad weather

The cost of the weather-forecasting service is $5,000. Draw the decision tree and label it properly. What decisions must you make and what is the sequence for those decisions