You are tasked with designing a timetable for a university's final exams. The university has three exam slots $($morning$,$ afternoon, evening$)$ and four courses $($Math$,$ Physics, Chemistry, Computer Science$).$ The constraints are as follows:

$$ No student should have two exams at the same time.

$$ Math and Physics should not be scheduled consecutively.

$$ Computer Science must be scheduled in the morning slot.

$1.$ Formulate this problem as a CSP$.$ Define the variables, domains, and constraints clearly.

$2.$ Use the backtracking algorithm with constraint propagation $($e$.$g$.,$ forward checking$)$ to solve this problem. Provide a step$-$by$-$step trace of how the algorithm would assign slots to the courses.

$3.$ Suppose there is an additional requirement to minimize the number of students who have more than one exam on the same day. Describe how you would modify the CSP to handle this optimization criterion.