Suppose that a citizens group is planning an Earth Day program consisting of a series of seminars dealing with topics such as recycling, alternative energy sources, and solid waste management. A local university has agreed to allow the use of their classrooms to conduct a total of 14 seminars that can begin at 8:00a.m, but must conclude by 5:00p.m. No seminars are scheduled to run during the lunch hour (12:00- 1:00p.m.), leaving eight one-hour time blocks available. The seminar coordinators have requested specific blocks of time during the day for each of their sessions. These are shown below:

For example, seminar A has been requested to run during period 2 (i.e. from 9-10:00 a.m) whereas seminar K needs to run for two consecutive periods (from 2:00-4:00p.m., etc.

Now the problem. The university would like to have as few rooms as possible used and they have given you five rooms thus far. Is this enough to schedule all of the seminars in their desired periods? What if only four rooms are allocated?