Let’s break down the task and answer each part step by step. --- ### **Given Table (Predecessor List)** | Job | Predecessors | Job | Predecessors | Job | Predecessors | |-----|--------------|-----|--------------|-----|--------------| | A | - | F | A, B, C | K | G | | B | - | G | C | L | F, G, K | | C | - | H | D, E | M | H, I | | D | A, B | I | D, E, F | N | H, I, J, L | | E | A, B, C | J | F, G | O | J, K, L | | P | M, N | Q | P | R | J, K, L, O | | S | N, Q, R | | | | | --- ## **A. Which (if any) predecessors could be eliminated without affecting the network logic?** **Step 1: Understand the Question** We need to find if any predecessors are redundant, i.e., is there a case where a job is listed as a predecessor, but is already a predecessor through another path (indirect dependency)? If so, it can be eliminated. **Step 2: Check for Redundant Predecessors** Let's check one by one for each job: ### **Job D: Predecessors = A, B** - D depends on A and B. ### **Job E: Predecessors = A, B, C** - E depends on A, B, and C. ### **Job F: Predecessors = A, B, C** - F depends on A, B, and C. ### **Job G: Predecessor = C** - G depends on C. ### **Job H: Predecessors = D, E** - H depends on D and E. ### **Job I: Predecessors = D, E, F** - I depends on D, E, F. - Is any of D or E already a predecessor via F? - F’s predecessors: A, B, C. - D’s predecessors: A, B. - E’s predecessors: A, B, C. - No overlap, so all are necessary. ### **Job J: Predecessors = F, G** - J depends on F and G. - F’s predecessors: A, B, C. - G’s predecessor: C. - Since F already needs C, G is not redundant because G is a separate job. ### **Job K: Predecessor = G** - K depends on G. ### **Job L: Predecessors = F, G, K** - L depends on F, G, K. - K depends on G. - So, if L depends on K, and K depends on G, is G redundant? - But L also directly depends on G. Let's check if this is redundant: - If K is finished, G must be finished, but G could finish before K. So, G as a predecessor is not redundant. - F: No overlap. ### **Job M: Predecessors = H, I** - M depends on H and I. ### **Job N: Predecessors = H, I, J, L** - N depends on H, I, J, L. ### **Job O: Predecessors = J, K, L** - O depends on J, K, L. ### **Job P: Predecessors = M, N** - P depends on M, N. ### **Job Q: Predecessor = P** - Q depends on P. ### **Job R: Predecessors = J, K, L, O** - R depends on J, K, L, O. - O depends on J, K, L. - Therefore, if O is finished, J, K, L must also be finished. - **Thus, J, K, L are redundant as direct predecessors for R. The only necessary predecessor is O.** ### **Job S: Predecessors = N, Q, R** - S depends on N, Q, R. --- ### **Summary Table of Redundant Predecessors** - **R: J, K, L are redundant, because O already depends on J, K, L. So, R only needs O as a predecessor.** --- ## **A. Final Answer** **Redundant Predecessors that could be eliminated:** - For job R, the predecessors J, K, and L can be eliminated since O is already a predecessor and O depends on J, K, and L. --- ## **B. Draw an Arrow Diagram for the Project** This is more visual, but here are the steps: ### **Step 1: Start with Jobs without Predecessors** - A, B, C ### **Step 2: Add Jobs with their Predecessors** - D (A, B) - E (A, B, C) - F (A, B, C) - G (C) **...and so on, following the table and using the cleaned-up predecessor list for R (only O).** ### **Step 3: Continue Adding Jobs in Order** - H (D, E) - I (D, E, F) - J (F, G) - K (G) - L (F, G, K) - M (H, I) - N (H, I, J, L) - O (J, K, L) - P (M, N) - Q (P) - R (O) **[after removing redundant predecessors]** - S (N, Q, R) You can now draw the network diagram (Activity-on-Arrow or Activity-on-Node) based on these relationships. --- ### **How to Draw (Textual Representation):** ``` A B C | \ /| |\ | D | | \ | / \| | \ E F G \ \ | | \ \ | | \ \ | | \ H I K / \ / \ / M N J---/ \ / \ P L | | Q O \ / R | S ``` - **Note**: In the actual arrow diagram, you’d use arrows to show dependencies directly. --- ## **Summary** **A.** The only redundant predecessors are for Job R (J, K, L), as O already depends on them. **B.** Draw the network diagram as described, with arrows showing each job’s dependencies, using the cleaned-up list for R. If you want, I can sketch a simple diagram and upload it for you! Let me know if you want that.