Question $1$

The following table represents a schedule of activities for the completion of four new Spanish Hotels in Jamaica:

$\backslash$table$[[$ACTIVITY$,\backslash$table$[[$PREDECESSO$],[$R$]],$OPTIMISTIC,MOST LIKELY,PESSIMISTIC$],[$A$,-,3,4,5],[$B$,$A$,2,3,4],[$C$,$A$,4,5,6],[$D$,$B$,4,4,4],[$E$,$B$,2,5,6],[$F$,$C$,$D$,$E$,2,4,5],[$G$,$F$,2,4,6],[$H$,$F$,4,6,7],[$I$,$G$,$ H$,4,6,8]]$

NB: Time periods are in months.

A$.$ Draw the activity network for this problem.

B$.$ Determine the Expected Time and Variance for each activity.

C$.$ Show the activity schedule $($EST$,$ EFT, LST$,$ LFT$)$ as well as slack. You may work in the network but please show the results in a table.

D$.$ Determine and state the critical path for this project. $($This must be based on your work in c$)$ and not by inspection.

E$.$ What are the expected time and the variance of the project?

F$.$ What is the probability the project will be finished within $30$ months?