# Shirley Hopkins Critical Path Exercise with 7 ActivitiesCritical Path Example - CPM Method

### Problem Data

It is required to calculate the critical path of the project, using the CPM method according to the following data:

- Number of Activities
- 7
- Time Unit
- Days
- Chart Type
- Activities-on-Nodes
- Description
**Shirley Hopkins Critical Path Exercise with 7 Activities**Shirley Hopkins is developing a program in leadership training for middle-level managers. Shirley has listed a number of activities that must be completed before a training program of this nature could be conducted. The activities, immediate predecessors, and times appear in the accompanying table. (a) Develop an AON network for this problem. (b) What is the critical path? (c) What is the total project completion time? (d) What is the slack time for each individual activity?- Table of Activities
Activity Immediate Predecessor(s) Time (Days) A 2 B 5 C 1 D B 10 E A,D 3 F C 6 G E,F 8

## Solution

The following are the calculations and detailed graphs to obtain the **critical path** according to the data provided:

### Step 1: Evaluation of the relationships between activities

In order to be able to plot the Network diagram (Activity-on-node), it is necessary to know the precedence and descent relationships of each activity; that is why the following table shows the relationships of each activity so that we can create our graph. Two fictitious “Start” and “End” activities are included.

Predecessor | Activity | Successor |
---|---|---|

Start → A | A | A → E |

Start → B | B | B → D |

Start → C | C | C → F |

B → D | D | D → E |

A → ED → E | E | E → G |

C → F | F | F → G |

E → GF → G | G | G → End |

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