NSW Syllabuses

# Mathematics Standard Stage 6 - Year 12 Standard 2 - Networks MS-N3 Critical Path Analysis

## Outcomes

#### A student:

• MS2-12-8

solves problems using networks to model decision-making in practical problems

• MS2-12-9

chooses and uses appropriate technology effectively in a range of contexts, and applies critical thinking to recognise appropriate times and methods for such use

• MS2-12-10

uses mathematical argument and reasoning to evaluate conclusions, communicating a position clearly to others and justifying a response

Related Life Skills outcomes: MALS6-11, MALS6-12, MALS6-13, MALS6-14

• ## Subtopic Focus

• The principal focus of this subtopic is to use critical path analysis in the optimisation of real-life problems.
• Students develop awareness that critical path analysis is a useful tool in project planning, management and logistics.
• ## Content

• Students:
• construct a network to represent the duration and interdependencies of activities that must be completed during a particular project, for example a student schedule, or preparing a meal
• given activity charts, prepare network diagrams and use critical path analysis to determine the minimum time for a project to be completed
• use forward and backward scanning to determine the earliest starting time (EST) and latest starting time (LST) for each activity in a project (ACMGM105)
• understand why the EST for an activity could be zero, and in what circumstances it would be greater than zero
• calculate float times of non-critical activities (ACMGM108)
• understand what is meant by critical path
• use ESTs and LSTs to locate the critical path(s) for the project (ACMGM106)
• solve small-scale network flow problems, including the use of the &lsquo;maximum-flow minimum-cut&rsquo; theorem, for example determining the maximum volume of oil that can flow through a network of pipes from an oil storage tank (the source) to a terminal (the sink) (ACMGM109)
• convert information presented in a table into a network diagram
• determine the flow capacity of a network and whether the flow is sufficient to meet the demand in various contexts