MHB Some works can be done simultaneously

[evinda]

Hello! (Wave)

The nodes $A,B,C,D,E,F,G,H,I$ are given and are related as follows:View attachment 5084

The nodes $B,C,D,E,F,G,H,I$ are tasks that are done so that a work is completed , for example a building, and the cost $p(a,b)$ are the days that are needed so that the work $b$ finishes if the work $a$ has already finished.
For example, $p(A,B)=22$: 22 days are needed so that the work B is done.
$p(B,E)$: 16 days are needed so that the work E is done if the work B has finished.

Of course, some works can be done simultaneously.

Find the minimum time needed so that the building gets finished.How do we use the fact that some works can be done simultaneously?

 

[I like Serena]

Hey evinda! (Smile)

Suppose we would only need $A,B,C$.
How much time would that take? (Wondering)

 

[evinda]

Hey evinda! (Smile)

Suppose we would only need $A,B,C$.
How much time would that take? (Wondering)

22 days? (Thinking)

 

[I like Serena]

22 days? (Thinking)

Exactly!
So how long will it take to complete $D, E$ additionally? (Wondering)

 

[evinda]

Exactly!
So how long will it take to complete $D, E$ additionally? (Wondering)

So in this case do we have to complete all the works $B, C, \dots, I$ so that the whole work is completed?

If so, then don't we make $B, C, D$ simultaneously and if we have completed for example $D$ we start with one of $G$ or $F$ ? (Thinking)

 

[I like Serena]

So in this case do we have to complete all the works $B, C, \dots, I$ so that the whole work is completed?

If so, then don't we make $B, C, D$ simultaneously and if we have completed for example $D$ we start with one of $G$ or $F$ ? (Thinking)

How so?
Can't we complete just $B,C,D,E$? (Wondering)

And yes, we should indeed complete $B, C, D$ simultaneously.

 

[evinda]

How so?
Can't we complete just $B,C,D,E$? (Wondering)

Don't we have to reach at $J$ , which is the last work?

 

[I like Serena]

Don't we have to reach at $J$ , which is the last work?

Yes... we're building up to that...
We can create a timeline and keep track of the earliest time that each part can be completed. (Thinking)