Gantt charts and schedulingEdexcel International A Level Maths: Subtopic test

1. 1
   A project has seven activities. Their durations in days and immediate predecessors are: A (4 days, none); B (3 days, none); C (5 days, A); D (6 days, A); E (4 days, B and C); F (2 days, D); G (3 days, E and F). A cascade (Gantt) chart is to be drawn with every activity starting at its earliest start time.

   (a)

   What is the earliest start time of activity E?

   [1 mark]

   • A4 days
   • B10 days
   • C9 days
   • D13 days

   (b)

   The minimum completion time is 16 days. What is the total float of activity B?

   [1 mark]

   • A3 days
   • B9 days
   • C0 days
   • D6 days

   (c)

   Calculate the total float of activity D, and state the latest time at which D can start without delaying the project.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A project has six activities. Their durations in days and immediate predecessors are: P (5 days, none); Q (3 days, none); R (4 days, P); S (5 days, P); T (2 days, Q and R); U (3 days, S and T). Every activity starts at its earliest start time, and the minimum completion time is 14 days.

   (a)

   With every activity starting at its earliest time, which activities are in progress at time 7 days?

   [1 mark]

   • AP and Q
   • BR and S
   • CR, S and T
   • DS and T

   (b)

   Activity S starts 2 days later than its earliest start time. By how much is the completion of the project delayed?

   [1 mark]

   • A1 day
   • B0 days
   • C2 days
   • D3 days

   (c)

   Show that at least 2 workers are needed to complete the project in the minimum time.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A workshop job has six tasks. Their durations in hours and immediate predecessors are: A (3 hours, none); B (5 hours, none); C (4 hours, A); D (6 hours, B); E (2 hours, A and B); F (3 hours, C, D and E). Each task is done by one worker without interruption, and a worker can do only one task at a time.

   (a)

   Find the minimum time in which the job can be completed with as many workers as are needed, and a lower bound for the number of workers needed to complete it in that time.

   [3 marks]

   (b)

   Show that 2 workers can complete the job in the minimum time by giving the tasks each worker does and when they start.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A project has eight activities. Their durations in days and immediate predecessors are: A (5 days, none); B (4 days, none); C (6 days, A); D (3 days, A); E (7 days, B); F (4 days, C and D); G (2 days, E); H (5 days, F and G). Workers can each do one activity at a time, and an activity cannot be interrupted.

   (a)

   Find the minimum completion time of the project and the critical activities, the total float on D and on G, and a lower bound for the number of workers needed to complete the project in the minimum time.

   [6 marks]

   (b)

   Show that 2 workers cannot complete the project in 20 days, but that 3 workers can, by giving a schedule for 3 workers.

   [6 marks]

   Total for question 4: 12 marks

End of questions