Question $2$:

A partially solved PERT problem is detailed in the table below. Times are given in weeks.

$\backslash$table$[[$Activity$],[$Areceding Time,,$],[$A$,--,9\mathrm{.}5],[$B$,$A$,3],[$C$,$A$,12],[$D$,$A$,5\mathrm{.}5],[$E$,$B$,6],[$F$,$B$,8],[$G$,$C$,$ F$,3],[$H$,$D$,3],[$I$,$H$,9],[$J$,$G$,$ I,$7],[$K$,$E$,$ J$,2\mathrm{.}5]]$

Activity Preceding Optimistic Probable Pessimistic Expected Variance

$\backslash$table$[[,,$Time,Time,Time,Time,$],[$A$,--,7,9,14,,1\mathrm{.}361],[$B$,$A$,2,2,8,0,],[$C$,$A$,8,12,16,,0],[$D$,$A$,3,5,10,1\mathrm{.}361,],[$E$,$B$,4,6,8,0,],[$F$,$B$,6,8,10,0,],[$G$,$C$,$ F$,2,3,4,0,],[$H$,$D$,2,2,8,1\mathrm{.}000,],[$I$,$H$,6,8,16,2\mathrm{.}778,],[$J$,$G$,$ I,$4,6,14,2\mathrm{.}778,],[$K$,$E$,$ J$,2,2,5,0\mathrm{.}250,]]$

a$.$ Draw the network diagram.

b$.$ Calculate the ES$,$ EF$,$ LS$,$ LF$,$ and Slack for each activity.

c$.$ Which activities form the critical path?

d$.$ What is the estimated time of the critical path?

e$.$ Calculate the expected time for each activity. Enter these values in the appropriate column in the table above.

f$.$ Given the variance for each activity, what are the project variance and the standard deviation?

g$.$ What is the probability of completion of the project before week $40?$