Visual representation of decision tree analysis for plant investment decisions.

Problem Description:

The image presents a Decision Tree Analysis for choosing between two options: building a new plant or upgrading an existing plant. Each option has associated costs and potential outcomes based on demand (strong or weak). The goal is to determine the optimal decision by calculating the expected net value for each option.

Key Elements in the Decision Tree:

1. Decision Node: The initial choice between "Build New Plant" and "Upgrade Plant."
2. Chance Nodes: Probabilities of strong or weak demand for each decision.
3. Net Value: The monetary value associated with each outcome, adjusted for the cost of the decision.

Steps to Solve the Problem:

#### Step 1: Define the Costs
- Build New Plant: Initial cost = $120
- Upgrade Plant: Initial cost = $70

#### Step 2: Calculate Expected Net Value for "Build New Plant"
The expected net value is calculated as:
\[
\text{Expected Net Value} = (\text{Probability of Strong Demand} \times \text{Value under Strong Demand}) + (\text{Probability of Weak Demand} \times \text{Value under Weak Demand}) - \text{Initial Cost}
\]

- Strong Demand:
- Probability = 65% = 0.65
- Value = $80
- Contribution = \(0.65 \times 80 = 52\)

- Weak Demand:
- Probability = 35% = 0.35
- Value = $35
- Contribution = \(0.35 \times 35 = 12.25\)

- Total Expected Value before Cost:
\[
52 + 12.25 = 64.25
\]

- Subtract Initial Cost:
\[
64.25 - 120 = -55.75
\]

So, the Expected Net Value for Building a New Plant is:
\[
-55.75
\]

#### Step 3: Calculate Expected Net Value for "Upgrade Plant"
Similarly, we calculate the expected net value for upgrading the plant.

- Strong Demand:
- Probability = 60% = 0.60
- Value = $70
- Contribution = \(0.60 \times 70 = 42\)

- Weak Demand:
- Probability = 40% = 0.40
- Value = $15
- Contribution = \(0.40 \times 15 = 6\)

- Total Expected Value before Cost:
\[
42 + 6 = 48
\]

- Subtract Initial Cost:
\[
48 - 70 = -22
\]

So, the Expected Net Value for Upgrading the Plant is:
\[
-22
\]

#### Step 4: Compare the Expected Net Values
- Build New Plant: Expected Net Value = \(-55.75\)
- Upgrade Plant: Expected Net Value = \(-22\)

Since \(-22\) is greater than \(-55.75\), the Upgrade Plant option has a higher expected net value.

Final Answer:

\[
\boxed{\text{Upgrade Plant}}
\]