The Chief Operations Officer $($COO$)$ of a firm that moves earth in preparation for the construction in Abbotsford has identified the activities and their durations for each stage of an operation to prepare a difficult stretch of motorway $($see Table $1$ below$).$ The COO needs to know how long the project will take and which are the critical activities.

a$)$ Identify the three goals of a project and describe how the project manager achieves them.

b$)$ Draw the network diagram for the motorway project.

c$)$ Calculate the latest and earliest event times for the project activities.

d$)$ Show the critical path of the project and indicate the total days to complete the project.

e$)$ Develop the Gantt Chart for the project.

Table $1$

Activity Duration Preceding Activities

A $5---$

B $10---$

C $1---$

D $8$ B

E $10$ B

F $9$ B

G $3$ A$,$D

H $7$ A$,$D

I $4$ F

J $3$ F

K $5$ C$,$J

L $8$ H$,$E$,$I,K

M $3$ C$,$J