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The problem involves a company deciding whether to sell a tract of land or to conduct seismic testing and potentially drill for oil. Let's break down the key components of the problem and construct the decision tree.

### Problem Breakdown:

1. **Initial Probability of Oil**: There is a 1 in 4 chance of finding oil (25% or 0.25 probability of oil).
2. **Offer to Purchase the Land**: Another company offers to buy the land for $90,000.
3. **Costs & Revenue if Drilling**:
   - Drilling costs: $100,000.
   - Expected revenue from oil: $800,000 (if oil is found).
4. **Seismic Survey**:
   - Cost of survey: $30,000.
   - If there is oil, the probability of an unfavorable seismic sound is 0.4.
   - If there is no oil, the probability of an unfavorable seismic sound is 0.8.

### Steps to Create the Decision Tree:

1. **First Decision Node**: The company decides whether to sell the land for $90,000 or proceed with further analysis (survey).
2. **Survey Branch**: If the company does the survey, it must decide to drill or not based on the survey results.
   - **If favorable seismic sound**:
     - Drill or not drill (expected value calculation based on drilling cost, oil probability, and revenue).
   - **If unfavorable seismic sound**:
     - Drill or not drill (expected value considering low oil likelihood).

3. **Final Payoff Calculation**: For each branch (selling, drilling after seismic testing, not drilling), calculate the expected value based on the probabilities and costs involved.

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I'll calculate the values in the decision tree next to determine the best course of action for the company, using the provided probabilities and costs. Let me do the detailed calculation.

The expected monetary values (EMVs) for each decision are as follows:

1. **Drill without Survey**: $100,000
2. **Sell the Land**: $90,000
3. **Conduct the Survey and then Decide**: $4,000

### Conclusion:
- The best decision is **to drill without conducting a survey**, as it has the highest EMV of $100,000.
- Selling the land gives a lower payoff of $90,000.
- Conducting a seismic survey yields a significantly lower EMV of approximately $4,000, indicating that it is not a favorable option.

Would you like further clarification or more details on this process?

### Follow-up Questions:
1. How would the decision change if the cost of drilling increased?
2. What impact does the probability of oil have on the decision?
3. How would the decision change if the land purchase offer was higher?
4. What if the seismic survey had a lower cost?
5. How do unfavorable seismic sounds affect the overall strategy?

### Tip:
When making business decisions, always compare the **expected value** of each option, as it accounts for both risks and rewards.

A company owns a tract of land that may contain oil. A consulting geologist has reported that there is 1 chance in 4 of oil being present. Another company has offered to buy the land for $90,000. The cost of drilling is $100,000. If oil is found, the expected revenue will be $800,000. A seismic survey, costing $30,000, indicates whether the geological structure is favorable for oil presence. Based on past experience, if there is oil, the probability of unfavorable seismic sound is 0.4; if there is no oil, it is 0.8. Draw a decision tree and find the final decision whether to drill or to sell the land.

Explore how to use decision trees and expected value calculations to make informed decisions in the oil industry. This problem involves determining whether to drill for oil or sell land based on probabilities, costs, and potential revenues.

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