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