# OCR A Level: Decision 2 - Critical Path Analysis [January 2012 Q2]

$$(\text{i})$$ Draw an activity network, using activity on arc, to represent this project. Your network will require a dummy activity.

$$(\text{ii})$$ Carry out a forward and backward pass through the network, showing the early and late event times at each vertex. State the minimum project completion time and list the critical activities.

$$(\text{iii})$$ Draw a resource histogram to show the number of workers required at each time when each activity begins at its earliest possible start time.

Suppose that there is only one worker available at the start of the project, but another two workers are available later.

$$(\text{iv})$$ Find the latest possible start time for the other workers to start and still have the project completed on time. Which activities could happen at the same time as painting the ceiling if the other two workers arrive at this time?

Input the latest possible start time for the other workers, in minutes, as your answer.

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