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:
The Plan: How many Tables and how many Chairs should you make?
The Result: What is your maximum Total Profit?
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?