QUESTION $25(10$ points$)-$ Critical Path Method $($CPM$)$ with Crashing

The film The Lord of the Rings: The Return of the King, the last installment of The Lord of the

Rings trilogy, was directed by Peter Jackson and released on December $172003$ in the U$.$S$.$ with

huge successes. Eventually, the film won $11$ Oscars for all of its nominations. The film's box

office was $$1\mathrm{.}12$ billion. In the film, there are long sequences where the main characters split up

in different directions. And, there are big scenes where all the characters reunited. Reflecting

upon the film making, we can hypothetically break down the entire cinematic project into the

following aggregate activities: $($We assume away all the complexities in shooting the three

installments at the same time and other production details.$)$

A $-$ Plan, screenplay, finance, cast, film crew, location

B $-$ Construction of movie sets

C $-$ Shooting of sequence $1$

D $-$ Shooting of sequence $2$

$E-$ Shooting of sequence $3$

$F-$ Shooting of the big scene sequence

G $-$ Post$-$production & finalization before release

We have the following hypothetical data on time in months and costs in millions of dollars:

Note: IP $=$ Immediate Predecessor; $T=$ Normal Time; ES $=$ Earliest Start; EF $=$ Earliest Finish;

LS $=$ Latest Start; LF $=$ Latest Finish; ST $=$ Slack Time; & NC $=$ Normal Cost.

$($a$)[1]$ Based on the table, draw an AON project network: circles$/$nodes for activities and

arrows$/$arcs for the precedence relationships between activities. Above each node, put a

number to represent the activity's normal time.

$($b$)[1]$ Draw a Gantt chart in Excel to represent the project schedule with earliest times, and

make a printout. Make sure to show all arrows for the precedence relationships.

$($c$)[1]$ By looking at the chart in part $($a$),$ find all possible paths through the network with their

corresponding path times. Based on these path times, determine the critical path and its length.

$($d$)[2]$ Based on part $($a$),$ draw a boxed AON project network: nodes are boxes with data. By

using the forward and backward passes, fill your calculations for ES$,$ EF$,$ LS$,$ LF$,$ and ST in the

appropriate cells.

$($e$)[1]$ Based on part $($d$),$ find the critical path by going through the activities with no slack time.

Compare this result with the critical path found in part $($c$).$

$($f$)[2]$ Independently fill in the columns ES$,$ EF$,$ LS$,$ LF$,$ and ST of the table. Use arrows to explain

how you got the values. If you have difficulties, refer to part $($d$).$ Find the activity with the most

slack time. Based on the table alone, find the critical path. Compare this result with the critical

path found in part $($c$).$

$(g)[2]$ Find the total normal cost of the film. Find the normal cost on the original critical path.

Compute the cost proportion of the critical path in the film's budget.