Kathleen Taylor is a freshman at Roanoke College, and she wants to develop her schedule for the spring semester. Courses are o ered with class periods either on Monday and Wednesday or Tuesday and Thursday for 1 hour and 15 minutes duration, with 15 minutes between class periods. For example, a course designated as 8M meets on Monday and Wednesday from 8:00 a. m. to 9:15 a. m.; the next class on Monday and Wednesday (9M) meets from 9:30 a. m. to 10:45 a. m.; the next class (11M) is from 11:00 a. m. to 12:15 p. m.; and so on. Kathleen wants to take the following six freshman courses, with the available sections shown in order of her preference, based on the professor who's teaching the course and the time:

Course Sections Available

Math 11T, 12T, 9T, 11M, 12M, 9M, 8T, 8M
History 11T, 11M, 14T, 14M, 8T, 8M
English 9T, 11T, 14T, 11M, 12T, 14M, 12M, 9M
Biology 14T, 11M, 12M, 14M, 9M, 8T, 8M
Spanish 9T, 11M, 12M, 8T
Psychology 14T, 11T, 12T, 9T, 14M, 8M

For example, there are eight sections of math offered, and Kathleen's first preference is the 11T section, her second choice is the 12T section, and so forth.
a. Determine a class schedule for Kathleen that most closely meets her preferences.
b. Determine a class schedule for Kathleen if she wants to leave 11:00 a. m. to noon open for lunch every day.
c. Suppose Kathleen wants all her classes on two days, either Monday and Wednesday or Tuesday and Thursday.
Determine schedules for each and indicate which most closely matches her preferences.