Practical Management Science
Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
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I need help for number 12, please.

Based on question number 11, which I already know the answer, find number 12. First image is the answer for number 11.

11. Building a backyard swimming pool consists of nine major activities. The activities and their immediate predecessors are shown. Develop the project network.

For number 12, see the second image

12. Assume that the activity time estimates (in days) for the swimming pool construction project in Problem 11 are as follows: 

a. What are the critical activities? 

b. What is the expected time to complete the project? 

c. Based only on the critical path, what is the estimated probability that the project can be completed in 25 or fewer days? 

This table represents the time estimates for different activities within a project, using three-point estimation. Each activity has three estimates: Optimistic, Most Probable, and Pessimistic.

| Activity | Optimistic | Most Probable | Pessimistic |
|----------|------------|---------------|-------------|
| A        | 3          | 5             | 6           |
| B        | 2          | 4             | 6           |
| C        | 5          | 6             | 7           |
| D        | 7          | 9             | 10          |
| E        | 2          | 4             | 6           |
| F        | 1          | 2             | 3           |
| G        | 5          | 8             | 10          |
| H        | 6          | 8             | 10          |
| I        | 3          | 4             | 5           |

**Explanation:**

- **Optimistic Estimate**: The minimum time required to complete an activity, assuming everything proceeds better than expected.
- **Most Probable Estimate**: The best guess for the time required to complete the activity under normal circumstances.
- **Pessimistic Estimate**: The maximum time required to complete the activity, assuming unfavorable conditions. 

These estimates are used in project management to provide a more accurate prediction of project timelines by considering uncertainty and variability.
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Transcribed Image Text:This table represents the time estimates for different activities within a project, using three-point estimation. Each activity has three estimates: Optimistic, Most Probable, and Pessimistic. | Activity | Optimistic | Most Probable | Pessimistic | |----------|------------|---------------|-------------| | A | 3 | 5 | 6 | | B | 2 | 4 | 6 | | C | 5 | 6 | 7 | | D | 7 | 9 | 10 | | E | 2 | 4 | 6 | | F | 1 | 2 | 3 | | G | 5 | 8 | 10 | | H | 6 | 8 | 10 | | I | 3 | 4 | 5 | **Explanation:** - **Optimistic Estimate**: The minimum time required to complete an activity, assuming everything proceeds better than expected. - **Most Probable Estimate**: The best guess for the time required to complete the activity under normal circumstances. - **Pessimistic Estimate**: The maximum time required to complete the activity, assuming unfavorable conditions. These estimates are used in project management to provide a more accurate prediction of project timelines by considering uncertainty and variability.
The image depicts a directed graph with nine nodes labeled from A to I. This graph illustrates the connections or pathways between these nodes. Here's a detailed explanation:

- Nodes: A, B, C, D, E, F, G, H, and I.
- Edges: Directed connections between nodes.

### Description of Connections:

- **Node A** is connected to Nodes C, D, and G.
- **Node B** is connected to Nodes C, E, and H.
- **Node C** is connected to Nodes D and F.
- **Node D** is connected to Node G.
- **Node E** is connected to Node H.
- **Node F** is connected to Node H.
- **Node G** is connected to Node I.
- **Node H** is connected to Node I.

### Purpose:

Graphs like this are used to model relationships and flows in various fields such as networking, social sciences, algorithm design, and more. Each edge indicates a possible path or a directional flow from one node to another, which helps in understanding how information or resources traverse through the network.
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Transcribed Image Text:The image depicts a directed graph with nine nodes labeled from A to I. This graph illustrates the connections or pathways between these nodes. Here's a detailed explanation: - Nodes: A, B, C, D, E, F, G, H, and I. - Edges: Directed connections between nodes. ### Description of Connections: - **Node A** is connected to Nodes C, D, and G. - **Node B** is connected to Nodes C, E, and H. - **Node C** is connected to Nodes D and F. - **Node D** is connected to Node G. - **Node E** is connected to Node H. - **Node F** is connected to Node H. - **Node G** is connected to Node I. - **Node H** is connected to Node I. ### Purpose: Graphs like this are used to model relationships and flows in various fields such as networking, social sciences, algorithm design, and more. Each edge indicates a possible path or a directional flow from one node to another, which helps in understanding how information or resources traverse through the network.
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