LeBron Woods is responsible for developing a leadership$-$training program for

his organization. The following table describes the relationships between the

activities that need to be completed.

Activity

Days

Immediate Predecessors a m b

A $3714$

B $51015$

C $3510$ A$,$ B

D $51213$ C

E $258$ C

F $2514$ E

G $5811$ F

H $61014$ D

I $348$ F$,$ H

J $4710$ G$,$ I

$436$Chapter $7$:$$Project Management

$($a$)$ Determine the expected times and variances for each activity.

$($b$)$ Construct a project network for this problem.

$($c$)$ Determine the EST, EFT, LST$,$ LFT$,$ and slack for each activity. Also determine the critical path and project completion time.

$($d$)$ What is the probability that the project will be finished in less than $49$

days?

$($e$)$ What is the probability that the project will need at least $54$ days