# In-Class Exercise: The Carpenter's Dilemma

**Time Limit:** 15 Minutes

**Tools Allowed:** Pen & Paper, Excel, Calculator, Python, AI, or Guesswork.

### The Scenario

You are the production manager of a boutique furniture workshop. You produce two high-end products: **Oak Tables** and **Oak Chairs**.

Your goal is to determine the weekly production plan that maximizes your **Total Profit**.

### The Data

**1. Financials**

- **Tables:** Profit is **\$100.00** per unit.

- **Chairs:** Profit is **\$30.00** per unit.

2\. Resource Constraints

You have limited supplies for this week:

- **Wood:** You have **200 board-feet** of oak available.

  - One Table uses **20** board-feet.

  - One Chair uses **5** board-feet.

- **Labor:** You have **40 hours** of skilled labor available.

  - One Table takes **5** hours to build.

  - One Chair takes **2** hours to build.

3\. The "Marketing" Constraint (Read Carefully)

Because customers typically buy dining sets, you have a strict policy:

- For every **1 Table** you produce, you must produce **at least 4 Chairs**.

- *Note:* You are allowed to produce extra chairs (spare chairs are sold individually), but you cannot produce fewer than 4 chairs per table.

**4. The "Physical" Constraint**

- You cannot sell half a table or half a chair. All production numbers must be **whole numbers (Integers)**.

### Your Task

Answer the following questions:

1.  **The Plan:** How many Tables and how many Chairs should you make?

2.  **The Result:** What is your maximum Total Profit?

3.  **The Logic:** If you used a tool (like AI or Excel), did it give you a valid answer? If you guessed, how did you verify your answer is actually feasible?