Critical paths and floatEdexcel International A Level Maths: Subtopic test

1. 1
   A project is modelled by an activity network with start event 1 and finish event 6. The activities are: A from event 1 to 2 (3 days); B from 1 to 3 (5 days); C from 2 to 4 (6 days); D from 3 to 4 (2 days); E from 3 to 5 (4 days); F from 4 to 6 (3 days); G from 5 to 6 (5 days).

   (a)

   Carry out a forward pass. What is the earliest event time at event 4?

   [1 mark]

   • A7 days
   • B11 days
   • C14 days
   • D9 days

   (b)

   The minimum project duration is 14 days. Carry out a backward pass. What is the latest event time at event 2?

   [1 mark]

   • A5 days
   • B3 days
   • C8 days
   • D9 days

   (c)

   Calculate the total float on activity D.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A project is modelled by an activity network with start event 1 and finish event 5. The activities are: A from event 1 to 2 (6 days); B from 1 to 3 (4 days); C from 2 to 4 (3 days); a dummy from 2 to 3; D from 3 to 4 (7 days); E from 4 to 5 (5 days); F from 3 to 5 (9 days).

   (a)

   Which of these is the critical path?

   [1 mark]

   • AA, C, E
   • BA, dummy, D, E
   • CB, D, E
   • DA, dummy, F

   (b)

   What is the latest start time of activity C, relative to the start of the project?

   [1 mark]

   • A6 days
   • B9 days
   • C10 days
   • D13 days

   (c)

   Find the earliest finish time and the latest finish time of activity B, and hence its total float.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A project is modelled by an activity network with start event 1 and finish event 5. The activities are: A from event 1 to 2 (5 days); B from 1 to 3 (7 days); C from 2 to 4 (6 days); D from 3 to 4 (5 days); E from 3 to 5 (8 days); F from 4 to 5 (3 days).

   (a)

   Carry out a forward pass and state the minimum project duration.

   [3 marks]

   (b)

   Carry out a backward pass, and hence find all the critical paths.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A project is modelled by an activity network with start event 1 and finish event 6. The activities are: A from event 1 to 2 (4 days); B from 1 to 3 (6 days); C from 2 to 4 (7 days); D from 3 to 4 (3 days); E from 2 to 5 (6 days); F from 3 to 5 (5 days); G from 4 to 6 (6 days); H from 5 to 6 (4 days).

   (a)

   Find the minimum project duration, the critical path, and the total float on activity E.

   [6 marks]

   (b)

   Extra staff can reduce the duration of C by up to 3 days. Find the minimum project duration if C is reduced by 3 days, and explain why the project duration is not reduced by 3 days.

   [6 marks]

   Total for question 4: 12 marks

End of questions