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FARE$3310-$ Fal$1$: Assignment $1$

$(30$ points$)$ An advertising agency CEO has gathered the activity information for a new advertising campaign as shown in the accompanying table.

$\backslash$table$[[$Activity$,$Time estimate weeks$],[$Optimistic$,$Most Likely,Pessimistic,$\backslash$table$[[$Immediate$],[$Predecessors$]]],[$A$,2,5,8,-],[$B$,2,6,7,-],[$C$,3,3,6,$B$],[$D$,7,14,15,$A$],[$E$,3,6,12,$A$,$C$],[$F$,6,8,16,$B$],[$G$,2,6,7,$E$,$F$]]$

a$)$ Draw the network diagram. What is the expected completion time $($state it explicitly$)?$ What is the variance of project completion time?

b$)$ The deadline is $23$ weeks. What is the probability of completing it on time? What is the probability of the project missing the deadline?

c$)$ As project manager, you will be paid a bonus if you finish the project in $19$ weeks. What is the probability of achieving the bonus?

d$)$ What is the probability of finishing between $19$ and $23$ weeks?

e$)$ What is the timeline that would achieve a $60\%$ probability of finishing?