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