A large decision tree has an outcome branch detailed below. If decisions D1, D2, and D3 are all options in a 1-year time period, find the decision path that maximizes the outcome value. There are specific dollar investments necessary for decision nodes D1, D2, and D3, as indicated on each branch.
 FIGURE 1.png)
Maximize the value at each decision node
 ANSWER.png)
D3: Top: E(value) = $30
Bottom: E(value) = 0.4(100) + 0.6(-50) = $10
Select top at D3 for $30
D1: Top: 0.9(D3 value) + 0.1(final value)
0.9(30) + 0.1(500) = $77
At D1, value = E(value) - investment
Top: 77 - 50 = $27 (larger)
Bottom: 90 - 80 = $10
Select top at D1 for $27
D2: Top: E(value) = 0.3(150 - 30) + 0.4(75) = $66
Middle: E(value) = 0.5(200 - 100) = $50
Bottom: E(value) = $50
At D2, value = E(value) - investment
Top: 66 - 25 = $41 (largest)
Middle: 50 - 30 = $20
Bottom: 50 - 35 = $15
Select top at D2 for $41
Conclusion: Select D2 path and choose top branch ($25 investment)
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