Consider the network described in the table below. Summarize your answers in the table below. Show all your work otherwise no credit given. Ten points $($network $2$ points, part a$+$b$-6$ points, part c$-2$ points$).$ If using software as evidence of your work please provide relevant software output data.

$\backslash$table$[[$Activity$,\backslash$table$[[$Immediate$],[$Predecessor$($s$)]],$Pessimistic,Probable,Optimistic$],[$A$,-,12,10,8],[$B$,--,9,8,7],[$C$,$A$,10,6,5],[$D$,$A$,9,8,4],[$E$,$B$,$D$,9,5,1],[$F$,$B$,$D$,13,7,4],[$G$,$C$,$E$,11,8,3]]$

a$.$ Calculate the expected duration of each activity.

b$.$ Calculate the expected duration and variance of the critical path.

c$.$ Calculate the probability that the project will be completed in fewer than $30$ time units.

ANSWERS:

Part a and b$.$

$\backslash$table$[[$Task$,$Early Start,$\backslash$table$[[$Early$],[$Finish$]],$Late Start,$\backslash$table$[[$Late$],[$Finish$]],$Slack,$\backslash$table$[[$Expected$],[$time$]],\backslash$table$[[$Activity$],[$Variance$]]],[$A$,,,,,,,],[$B$,,,,,,,],[$C$,,,,,,,],[$D$,,,,,,,],[$E$,,,,,,,],[$F$,,,,,,,],[$G$,,,,,,,],[,,,,,,\backslash$table$[[$Project Expected$],[$duration$]],],[,,,,,,,]]$