Question 1
A conference needs to schedule 6 sessions across 3 time slots and 3 rooms. Each room can hold one session per slot. The constraints are:
- Dr. Lee can only speak at 9:00-10:00
- IoT and Blockchain cannot be in the same time slot
- Dr. Taylor and Prof. Wilson must speak in consecutive time slots
- Machine Learning must be in Hall C
Which speaker presents the IoT session?
Step-by-step solution:
Scheduling Grid Analysis:
1. Fix direct constraints:
- Dr. Lee at 9:00-10:00
- Machine Learning in Hall C
2. Apply consecutive constraint: Dr. Taylor and Prof. Wilson in consecutive slots
3. Apply conflict constraint: IoT and Blockchain not together
4. Final Schedule:
9:00-10:00:
- Hall A: AI Ethics by Prof. Wilson
- Hall B: Cybersecurity by Prof. Jones
- Hall C: Blockchain by Dr. Lee
10:00-11:00:
- Hall A: IoT by Dr. Chen
- Hall B: Data Science by Dr. Taylor
- Hall C: Machine Learning by Dr. Smith
11:00-12:00:
- Hall A: (empty)
- Hall B: (empty)
- Hall C: (empty)
Answer: Dr. Chen presents IoT
Key Strategy: Use a grid to solve the assignment problem and satisfy all constraints sequentially.
Scheduling Grid Analysis:
1. Fix direct constraints:
- Dr. Lee at 9:00-10:00
- Machine Learning in Hall C
2. Apply consecutive constraint: Dr. Taylor and Prof. Wilson in consecutive slots
3. Apply conflict constraint: IoT and Blockchain not together
4. Final Schedule:
9:00-10:00:
- Hall A: AI Ethics by Prof. Wilson
- Hall B: Cybersecurity by Prof. Jones
- Hall C: Blockchain by Dr. Lee
10:00-11:00:
- Hall A: IoT by Dr. Chen
- Hall B: Data Science by Dr. Taylor
- Hall C: Machine Learning by Dr. Smith
11:00-12:00:
- Hall A: (empty)
- Hall B: (empty)
- Hall C: (empty)
Answer: Dr. Chen presents IoT
Key Strategy: Use a grid to solve the assignment problem and satisfy all constraints sequentially.