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6 marksGraph Theory and Critical Path Analysis

CAPE Applied Mathematics Unit 2 · 2018 · Paper 2 · Question 1(a)(i)

A table provides activities, durations, and precedence relations for a project.

Determine the earliest and latest start times for EACH activity, in order for the project to be completed in the minimum time. Write your answers in the relevant spaces in the table.

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Other parts of this question

  1. 1(a)(ii)Identify the critical path.[2 marks]
  2. 1(a)(iii)Determine the minimum time for completion of the project.[1 mark]
  3. 1(a)(iv)Draw a fully labelled activity network to represent these activities and their precedence.[4 marks]
  4. 1(a)(v)Assume that the duration of Activity C is increased to 6 days. Determine which activities are now critical, and the new minimum time for completion of the…[4 marks]
  5. 1(b)(i)Use a truth table to show that for any propositions, p and q, p \Rightarrow q \Leftrightarrow \sim p \vee q.[3 marks]
  6. 1(b)(ii)Using the laws of Boolean algebra, show that for any two propositions, p and q, \sim(p \vee \sim(p \wedge q)) is a contradiction.[5 marks]

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