Consider a simplified scheduling problem for a new postgraduate course as follows. All students of a new postgraduate course will take exactly the same n modules. Each module has two lectures, and each lecture requires a 1 hour time slot. We need to schedule these lectures to non-clashing time slots and lecture theatres. The University has m lecture theatres, and lectures can be booked between 9:00 and 18:00, Monday to Friday. The size of the cohort is not large, because this is the first time that this course is provided. So, any lecture theatre has enough capacity for the cohort. As some of the students live far, we would like to reduce the number of days that students need to come to the University. However, the availability of time slots and lecture theatres is limited, due to other courses that have already been scheduled. So, only a smaller subset of the total number of lecture theatres and time slots is available.

Formulate this problem as a search problem by specifying the following:

Initial state. Explain why you consider your initial state to be adequate.

Goal state(s). Explain why you consider your goal state(s) to be adequate.

Possible actions and their effect on states. Explain why you consider your proposed actions to be adequate.

Cost function. Explain why you consider your cost function to be adequate.

When writing your problem formulation, you may or may not need to make assumptions about the problem, given the information provided in the first paragraph of this coursework. If you need to make any assumptions, please ensure that you explain these assumptions in your answer.