refer to the project described by the project digraph shown on the right. complete (a) through (d)…

Explanation:

Step1: Initialize END time

The END vertex has a critical - time of 0. Let $T_{END}=0$.

Step2: Calculate G time

Since G points to END and the weight of the edge from G to END is 6, $T_G=T_{END}-6 = 0 - 6=-6$.

Step3: Calculate E time

Since E points to G and the weight of the edge from E to G is 2, $T_E=T_G - 2=-6 - 2=-8$.

Step4: Calculate C time

Since C points to E and the weight of the edge from C to E is 5, $T_C=T_E - 5=-8 - 5=-13$.

Step5: Calculate F time

Since F points to END and the weight of the edge from F to END is 7, $T_F=T_{END}-7 = 0 - 7=-7$.

Step6: Calculate D time

Since D has two outgoing edges to F and END. We consider the maximum of the time - calculations based on these edges. The time from D to F gives $T_{F}-3=-7 - 3=-10$ and the time from D to END is not relevant as it's not the maximum. So $T_D=-10$.

Step7: Calculate B time

Since B points to D and the weight of the edge from B to D is 13, $T_B=T_D - 13=-10 - 13=-23$.

Step8: Calculate A time

Since A points to B and the weight of the edge from A to B is 9, $T_A=T_B - 9=-23 - 9=-32$.

Step9: Calculate START time

Since START has outgoing edges to A, B and C. We consider the maximum of the time - calculations based on these edges. For the edge to A: $T_A=-32$, for the edge to B: $T_B=-23$, for the edge to C: $T_C=-13$. So $T_{START}=\max{-32,-23,-13}=-13$.

Answer:

Vertex	Critical Time	Vertex	Critical Time
START	- 13	E	- 8
A	- 32	F	- 7
B	- 23	G	- 6
C	- 13	END	0
D	- 10