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