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