This business/management problem is solved step by step below, with detailed explanations to help you understand the method and arrive at the correct answer.
ScanSolve AI Answer
You're on a roll — Here are the calculations for the project activities: i. The Early Start, Early Finish, Late Start, Late Finish and the slack for all the activities Step 1: Perform a forward pass to calculate Early Start (ES) and Early Finish (EF) for each activity. ES_successor = (EF_predecessors) EF = ES + Duration Step 2: Perform a backward pass to calculate Late Finish (LF) and Late Start (LS) for each activity. The project completion time is the maximum EF of all final activities. LF_predecessor = (LS_successors) LS = LF - Duration Step 3: Calculate Slack (Total Float) for each activity. Slack = LF - EF = LS - ES The calculated values are as follows: | Activity | Duration | Predecessor | ES | EF | LS | LF | Slack | |:---|:---:|:---:|:---:|:---:|:---:|:---:|:---:| | A | 2 | - | 0 | 2 | 0 | 2 | 0 | | B | 5 | A | 2 | 7 | 17 | 22 | 15 | | C | 8 | A | 2 | 10 | 5 | 13 | 3 | | D | 6 | A | 2 | 8 | 2 | 8 | 0 | | E | 8 | A | 2 | 10 | 16 | 24 | 14 | | F | 9 | B | 7 | 16 | 23 | 32 | 7 | | G | 10 | B | 7 | 17 | 22 | 32 | 5 | | H | 8 | C | 10 | 18 | 24 | 32 | 6 | | I | 17 | C | 10 | 27 | 13 | 30 | 3 | | J | 22 | D | 8 | 30 | 8 | 30 | 0 | | K | 6 | E | 10 | 16 | 24 | 30 | 8 | | L | 8 | F, G, H | 18 | 26 | 32 | 40 | 6 | | M | 10 | I, J, K | 30 | 40 | 30 | 40 | 0 | | N | 12 | L, M | 40 | 52 | 40 | 52 | 0 | ii. Draw a network and determine the Critical Path A network diagram (Activity-On-Node) shows activities as nodes and precedence relationships as arrows. Due to the text-based format, a visual diagram cannot be drawn here. However, the critical path can be determined from the activities with zero slack. The critical path is the longest path through the network, representing the minimum time required to complete the project. Activities on the critical path have zero slack. The activities with zero slack are A, D, J, M, N. The Critical Path is: A D J M N The project completion time is 52 units. iii. Estimate the project schedules with the Gantt Chart A Gantt chart visually represents the project schedule, showing the start and end times for each activity. Critical activities are typically highlighted. Below is the data required to construct the Gantt chart, using the Early Start (ES) and Early Finish (EF) times. | Activity | Duration | ES | EF | Critical Path | |:---|:---:|:---:|:---:|:---:| | A | 2 | 0 | 2 | Yes | | B | 5 | 2 | 7 | No | | C | 8 | 2 | 10 | No | | D | 6 | 2 | 8 | Yes | | E | 8 | 2 | 10 | No | | F | 9 | 7 | 16 | No | | G | 10 | 7 | 17 | No | | H | 8 | 10 | 18 | No | | I | 17 | 10 | 27 | No | | J | 22 | 8 | 30 | Yes | | K | 6 | 10 | 16 | No | | L | 8 | 18 | 26 | No |