1. **State the problem:** Makutano Company must decide whether to develop and launch a new product. 2. **Identify costs and probabilities:** - Research and development cost: 500000 - Probability of success: 0.7 - Probability of failure: 0.3 3. **If successful, profits depend on popularity:** | Popularity | Probability | Annual Profit | Duration (years) | |------------|-------------|---------------|------------------| | High | 0.2 | 550000 | 2 | | Medium | 0.5 | 450000 | 2 | | Low | 0.3 | 350000 | 2 | 4. **Calculate total profits for each popularity level:** $$\text{Total Profit} = \text{Annual Profit} \times 2$$ - High: $$550000 \times 2 = 1100000$$ - Medium: $$450000 \times 2 = 900000$$ - Low: $$350000 \times 2 = 700000$$ 5. **Calculate expected profit if successful:** $$E(\text{Profit} | \text{Success}) = 0.2 \times 1100000 + 0.5 \times 900000 + 0.3 \times 700000$$ $$= 220000 + 450000 + 210000 = 880000$$ 6. **If failure, possible outcomes:** - Sell R&D work for 100000 with probability 0.6 - Worth nothing with probability 0.4 7. **Calculate expected value if failure:** $$E(\text{Value} | \text{Failure}) = 0.6 \times 100000 + 0.4 \times 0 = 60000$$ 8. **Calculate overall expected value of launching product:** $$E(\text{Launch}) = 0.7 \times 880000 + 0.3 \times 60000 - 500000$$ $$= 616000 + 18000 - 500000 = 134000$$ 9. **Interpretation:** The expected net profit from launching the product is 134000. 10. **Decision tree components:** - Decision node: Launch or not - Chance nodes: Success (0.7) or Failure (0.3) - Success branch: Popularity levels with probabilities and profits - Failure branch: Sell R&D or worthless This completes the decision tree construction with probabilities, decision points, and outcomes.