Problem 3: You have the task of scheduling several courses. There is a total of 5 courses, and there are 3 professors who you will assign to teach the various courses. Each course will be taught by a single professor. A given professor can teach more than one course, as long as the courses do not overlap in terms of meeting time. The courses and professors are listed below. The courses are as follows: Course 1 meeting time is 9:00 - 10:00 am Course 2 meeting time is 9:30 - 10:30 am Course 3 meeting time is 10:15 - 11:15 am Course 4 meeting time is 10:15 - 11:15 am Course 5 meeting time is 10:45 - 11:45 am The professors are as follows: Professor X, who is available to teach Courses 1, 2, 3, 4, 5. Professor Y, who is available to teach Courses 2, 3, 4, 5. Professor Z, who is available to teach Courses 3, 4. (a) Formulate this as a constraint satisfaction problem. That is, define the variables, the domains, and the constraints. Let the variables be the courses. (b) Draw the corresponding constraint graph