It was mid-July 2022. Professor Frank Hill, the Admissions Chairman realized that he should start thinking about conducting the New Admissions Test (NAT) for admitting students to Seneca business schools, as it was just a few months away. He began by examining the activities involved in conducting the NAT:

Table 1 - Required activities and durations.

Not being familiar with Project Management, Frank walked over to his friend Professor Manoj's office. Manoj taught a course in Project Management. Responding to Frank's request to help in planning for NAT, Manoj asked Frank to describe in his own words as to how the various activities were related to each other. "Why do you need that?" asked Frank. "That will help in developing what is known as 'Precedence Restrictions' in Project Management," replied Manoj. "That is also required to identify the critical activities that would need your attention," continued Manoj. "Would I also know how long it will take to get everything organized?" asked Frank. "Yes, it would be possible to determine what is known as the Critical Path. This path is the one that will determine the time you would need to execute your plan," said Manoj.

The next day, Frank sat down in his office and started constructing statements that described the relationships among the various activities pertaining to CAT. He realized that though he had been in charge of admissions for a while, it was not easy to make the required assertions. After about two hours of effort, he finally produced the following statements on how the activities were related to each other:

1. The collation of the test paper cannot be carried out until the questions for the three sections, namely, verbal, quantitative and data analysis have been decided.

2. The scrutiny of the test papers can be performed only after the collation of the questions is completed.

3. The application forms cannot be printed until the test centres are finalized.

4. The printing of test papers cannot be undertaken until the printers are identified for printing and the test papers scrutinized.

5. The list of successful applicants cannot be prepared until the application forms are received.

6. The admission cards cannot be despatched until the list of successful applicants is readied.

7. The test papers cannot be despatched unless the test centres are chosen, and the test papers are printed.

8. The test papers cannot be printed until the test centres are chosen.

9. The test cannot be conducted until the admission cards are despatched to the candidates and the test papers despatched to the centres.

Manoj sat down with the stat