You're a consultant charging $500/hour. A client asks you to find the optimal solution to a complex problem. You estimate: - A quick solution (1 hour) has 60% chance of being optimal - More analysis (5 hours) has 90% chance of being optimal - The optimal solution saves the client $50,000 vs. the suboptimal one 1. How much analysis should you do? 2. How would your answer change if you charged $1000/hour? 3. What if you were doing this for yourself (no billing)? 4. Generalize: derive a formula for optimal thinking time given problem stakes and thinking cost