Question 1
A conference needs to schedule 5 sessions across 3 time slots and 3 rooms. Each room can hold one session per slot. The constraints are:
- Dr. Smith can only speak at 9:00-10:00
- Machine Learning and Data Science cannot be in the same time slot
- Prof. Garcia and Dr. Lee must speak in consecutive time slots
- Robotics must be in Hall A
Which speaker presents the Machine Learning session?
Step-by-step solution:
Scheduling Grid Analysis:
1. Fix direct constraints:
- Dr. Smith at 9:00-10:00
- Robotics in Hall A
2. Apply consecutive constraint: Prof. Garcia and Dr. Lee in consecutive slots
3. Apply conflict constraint: Machine Learning and Data Science not together
4. Final Schedule:
9:00-10:00:
- Hall A: IoT by Dr. Smith
- Hall B: AI Ethics by Dr. Lee
- Hall C: Data Science by Prof. Garcia
10:00-11:00:
- Hall A: Robotics by Dr. Taylor
- Hall B: Machine Learning by Prof. Jones
- Hall C: (empty)
11:00-12:00:
- Hall A: (empty)
- Hall B: (empty)
- Hall C: (empty)
Answer: Prof. Jones presents Machine Learning
Key Strategy: Use a grid to solve the assignment problem and satisfy all constraints sequentially.
Scheduling Grid Analysis:
1. Fix direct constraints:
- Dr. Smith at 9:00-10:00
- Robotics in Hall A
2. Apply consecutive constraint: Prof. Garcia and Dr. Lee in consecutive slots
3. Apply conflict constraint: Machine Learning and Data Science not together
4. Final Schedule:
9:00-10:00:
- Hall A: IoT by Dr. Smith
- Hall B: AI Ethics by Dr. Lee
- Hall C: Data Science by Prof. Garcia
10:00-11:00:
- Hall A: Robotics by Dr. Taylor
- Hall B: Machine Learning by Prof. Jones
- Hall C: (empty)
11:00-12:00:
- Hall A: (empty)
- Hall B: (empty)
- Hall C: (empty)
Answer: Prof. Jones presents Machine Learning
Key Strategy: Use a grid to solve the assignment problem and satisfy all constraints sequentially.