Problem $4(15$ Points$).$

The complete diagram for the following PERT problem is shown below.

$\backslash$table$[[$Activity$,\backslash$table$[[$Predecess$],[$ors$]],$Optimistic,$\backslash$table$[[$Most$],[$Likely$]],\backslash$table$[[$Pessimisti$],[$c$]],\backslash$table$[[$Expected$],[$Time$],[$Weeks$)]],\backslash$table$[[$Variances$],[$ Weeks$^2)]]],[$A$,--,4,7,10,,],[$B$,$A$,2,8,20,,],[$C$,$A$,8,12,16,,],[$D$,$B$,1,2,3,,],[$E$,$D$,$ C$,6,8,22,,],[$F$,$C$,2,3,4,,],[$G$,$F$,2,2,2,,],[$H$,$F$,6,8,10,,],[$I$,$E$,$ G$,$ H$,4,8,12,,],[$J$,$I,$1,2,3,,],[,,,,,,]]$

a$.$ Calculate the expected times and variances in the above table.

b$.$ Draw a network and determine the critical path based on the expected completion times.

c$.$ What is the expected completion time of the project,

What is the total variance with critical path of the project,

What is the standard deviation with critical path of the project,

d$.$ Determine the probability of finishing the project,

i$.$ Less than $42$ weeks

ii$.$ Greater than $35$ weeks

iii. Between $42$ to $44$ weeks

iii. Greater than $40$ weeks

$\backslash$table$[[$