# Decision Tree Analysis for "2C" Decision Let's break down your problem step-by-step, as if you are a complete beginner, and solve it logically like a software engineer and tutor. --- ## 1. **Summarize Briefly** You are given a decision tree for "2C" with options and outcomes. You need to calculate: - Total expected profit (for "2C") - Net profit (for "2C") - Total operation profit for "2C" - "Decision 2F" value after comparing the outcome of "2C" and "2D". --- ## 2. **Explain Like I'm a Beginner** ### **What is a Decision Tree?** A decision tree is a tool to help you choose between different options by mapping out each possible outcome and its probability. ### **What are Expected Value and Profit?** - **Expected Value (EV):** The sum of all possible outcomes, each multiplied by its probability. - **Profit:** The revenue minus the cost. --- ## 3. **Step-by-Step Solution** ### **Step 1: Diagram Details** From your image: #### **2C: Expand Now (Cost: 200,000)** - **High Response (P=.6):** $700,000 profit - **Low Response (P=.4):** $300,000 profit #### **2D: No Expand (Cost: )** - **High Response (P=.6):** $400,000 profit - **Low Response (P=.4):** $100,000 profit --- ### **Step 2: Calculate Expected Profit for "2C"** **Expected Profit = (Probability * Profit) for each outcome, then sum** \[ \text{Expected Profit for 2C} = (.6 \times 700,000) + (.4 \times 300,000) \] \[ = 420,000 + 120,000 = 540,000 \] --- ### **Step 3: Net Profit for "2C"** Subtract the cost from the expected profit. \[ \text{Net Profit for 2C} = \text{Expected Profit for 2C} - \text{Cost} \] \[ = 540,000 - 200,000 = 340,000 \] --- ### **Step 4: Total Operation Profit for "2C"** Total operation profit is the sum of possible profits weighted by their probabilities (already calculated as expected profit above). \[ \text{Total Operation Profit for 2C} = 540,000 \] --- ### **Step 5: Decision 2F (Best Option Outcome)** Now, compare "2C" and "2D" to choose the best: #### **Expected Profit for 2D:** \[ = (.6 \times 400,000) + (.4 \times 100,000) = 240,000 + 40,000 = 280,000 \] Since "2D" has no cost, net profit is also \$280,000. #### **Best Option ("Decision 2F"):** Choose the higher net profit: - "2C": \$340,000 - "2D": \$280,000 **So, Decision 2F = \$340,000** (from "2C") --- ## 4. **Logic Explanation (Problem Solver Approach)** 1. **Identify choices and outcomes.** 2. **Calculate expected profits using probabilities.** 3. **Subtract costs to get net profit.** 4. **Compare net profits to choose the best decision.** --- ## 5. **Code Example (Python)** ```python # Probabilities p_high = .6 p_low = .4 # Profits profit_2C_high = 700000 profit_2C_low = 300000 cost_2C = 200000 profit_2D_high = 400000 profit_2D_low = 100000 cost_2D = # Expected Profits expected_2C = p_high * profit_2C_high + p_low * profit_2C_low net_2C = expected_2C - cost_2C expected_2D = p_high * profit_2D_high + p_low * profit_2D_low net_2D = expected_2D - cost_2D # Best Decision decision_2F = max(net_2C, net_2D) print(f"Expected Profit for 2C: {expected_2C}") print(f"Net Profit for 2C: {net_2C}") print(f"Total Operation Profit for 2C: {expected_2C}") print(f"Decision 2F (Best): {decision_2F}") ``` --- ## 6. **Final Answers** - **Expected Profit for 2C:** \$540,000 - **Net Profit for 2C:** \$340,000 - **Total Operation Profit for 2C:** \$540,000 - **Decision 2F:** \$340,000 (Choose "2C" over "2D" since it gives higher profit) --- ## 7. **Summary Table** | Calculation | Value | |------------------------------|-----------| | Expected Profit for 2C | \$540,000 | | Net Profit for 2C | \$340,000 | | Total Operation Profit for 2C| \$540,000 | | Decision 2F (Best Option) | \$340,000 | --- **Let me know if you need further clarification on any step!**