Gantt charts, resource histograms and levellingAQA A-Level Further Maths: Subtopic test

1. 1
   A project has seven activities. Activity A takes 4 days and has no predecessor. B takes 3 days and has no predecessor. C takes 5 days and follows A. D takes 2 days and follows both A and B. E takes 6 days and follows C. F takes 3 days and follows D. G takes 2 days and follows both E and F.

   (a)

   What is the minimum time in which the project can be completed?

   [1 mark]

   • A25 days
   • B15 days
   • C17 days
   • D10 days

   (b)

   What is the total float on activity B?

   [1 mark]

   • A7 days
   • B3 days
   • C10 days
   • D4 days

   (c)

   A cascade (Gantt) diagram is drawn with every activity starting as early as possible. For activity F, state the day on which its bar ends and the length of the float drawn after it.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A project is planned with every activity starting at its earliest time. P runs from day 0 to day 3 and needs 2 workers. Q runs from day 0 to day 4 and needs 3 workers. R runs from day 3 to day 5 and needs 2 workers. S runs from day 4 to day 7 and needs 4 workers. T runs from day 5 to day 7 and needs 2 workers. Each worker is paid for every day on which they are needed.

   (a)

   What is the largest number of workers needed on any one day?

   [1 mark]

   • A4
   • B5
   • C7
   • D6

   (b)

   What is the total number of worker-days needed for the whole project?

   [1 mark]

   • A14
   • B13
   • C38
   • D42

   (c)

   The firm employs only 5 workers. State the period during which the schedule needs more than 5 workers, and by how many it is short.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A project consists of seven activities, each needing one worker. Durations are in days. A takes 5 days and has no predecessor. B takes 3 days and has no predecessor. C takes 4 days and follows A. D takes 6 days and follows A. E takes 2 days and follows B. F takes 3 days and follows both C and E. G takes 4 days and follows both D and F.

   (a)

   Find the minimum completion time and list the critical activities.

   [3 marks]

   (b)

   Find a lower bound for the number of workers needed to finish in the minimum time, and give a schedule showing that this number of workers is enough.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A building project has seven activities. A takes 4 days, needs 3 workers and has no predecessor. B takes 3 days, needs 2 workers and has no predecessor. C takes 5 days, needs 2 workers and follows A. D takes 4 days, needs 3 workers and follows B. E takes 3 days, needs 2 workers and follows both A and B. F takes 4 days, needs 3 workers and follows both C and D. G takes 2 days, needs 2 workers and follows both E and F. Once started, an activity cannot be interrupted.

   (a)

   Carry out a forward and backward pass to find the minimum completion time, the critical activities and the floats of B, D and E.

   [6 marks]

   (b)

   Only 5 workers are available. Show that the schedule with every activity starting at its earliest time needs more than 5 workers, and describe a schedule that stays within 5 workers and still finishes in the minimum time.

   [6 marks]

   Total for question 4: 12 marks

End of questions