You own some land in the Finger Lakes region and you have three options: build a winery, mine minerals, or sell the property.

If you build a winery, the initial cost is $3M. If you mine minerals in the initial cost is $1M. Finally, if you sell the land, you will make $0.1 M. One of your friends is a geologist and estimates that the probability of there being minerals to extract is 0.75, but if you have the minerals then your neighbor does as well. If there are no minerals and you choose to build a winery, your winery will make $13M in revenue. If there are no minerals and you choose to mine, your mine would have no revenue. If there are minerals and you choose to mine the land, your mine will make $3M in revenue. If you build the winery when there are minerals in the land, your neighbor will eventually mine their land, degrading the quality of your winery's location. Thus, you must repurpose your land into a petting zoo with $0.2M in revenue. Assume all payouts have been discounted to the present. Note: Revenue - Cost = Profit.

1. A consulting geologist has a patent on a test to determine the likelihood that there are minerals present on your land. The probability of the test returning HIGH given the presence of minerals is 0.76. The probability of the test returning HIGH given the absence of minerals is 0.12. The consultant will charge $0.5M for the test. Structure a decision tree. Based on expected value, should you perform the test? If you were to perform the test, which decisions should you make based on its results? (10 points)

2. What is the expected value of perfect information (EVPI) with respect to the presence of minerals? Compare this to the expected value of your decision without any information. Note: EVPI is different than the value of the test. (5 points)