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Widgetco is making a prototype of a new product. The product consists of two subassemblies. Before building either subassembly, the firm must purchase raw materials and train workers. Before the subassemblies can be combined, subassembly 2 must be inspected. The following table describes the project: Activity Description Requires Duration (Days) A Train workers 6 B Purchase materials 9 C Make subassembly 1 A,B 8 D Make subassembly 2 A,B 7 E Inspect subassembly 2 D 10 F Combine subassemblies C, E 12 G Subassembly 2 safety report E 6 How quickly can Widgetco complete this project? (a) Define decision variables. (b) Write a suitable LP problem formulation.

Widgetco is making a prototype of a new product. The product consists of two subassemblies. Before building either subassembly, the firm must purchase raw materials and train workers. Before the subassemblies can be combined, subassembly 2 must be inspected. The following table describes the project: Activity Description Requires Duration (Days) A Train workers 6 B Purchase materials 9 C Make subassembly 1 A,B 8 D Make subassembly 2 A,B 7 E Inspect subassembly 2 D 10 F Combine subassemblies C, E 12 G Subassembly 2 safety report E 6 How quickly can Widgetco complete this project? (a) Define decision variables. (b) Write a suitable LP problem formulation.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Widgetco is making a prototype of a new product. The product
consists of two subassemblies. Before building either subassembly, the firm must purchase
raw materials and train workers. Before the subassemblies can be combined, subassembly
2 must be inspected. The following table describes the project:
Activity Description Requires Duration (Days)
A Train workers 6
B Purchase materials 9
C Make subassembly 1 A,B 8
D Make subassembly 2 A,B 7
E Inspect subassembly 2 D 10
F Combine subassemblies C, E 12
G Subassembly 2 safety report E 6
How quickly can Widgetco complete this project?
(a) Define decision variables.
(b) Write a suitable LP problem formulation.

**Project Description:** Widgetco is developing a prototype for a new product that consists of two subassemblies. The initial steps involve purchasing raw materials and training workers. Before the subassemblies can be combined into the final product, Subassembly 2 must be inspected. **Activity Table:** | Activity | Description | Requires | Duration (Days) | |----------|----------------------------|----------|-----------------| | A | Train workers | | 6 | | B | Purchase materials | | 9 | | C | Make subassembly 1 | A, B | 8 | | D | Make subassembly 2 | A, B | 7 | | E | Inspect subassembly 2 | D | 10 | | F | Combine subassemblies | C, E | 12 | | G | Subassembly 2 safety report| E | 6 | **Questions:** 1. **How quickly can Widgetco complete this project?** - **(a) Define decision variables.** - **(b) Write a suitable Linear Programming (LP) problem formulation.** **Explanation:** To complete the project, one must determine the earliest completion time using project management techniques such as Critical Path Method (CPM). By defining the decision variables, we can structure an LP problem to optimize the project timeline, considering the dependencies and durations of each task outlined in the table.
Transcribed Image Text:**Project Description:** Widgetco is developing a prototype for a new product that consists of two subassemblies. The initial steps involve purchasing raw materials and training workers. Before the subassemblies can be combined into the final product, Subassembly 2 must be inspected. **Activity Table:** | Activity | Description | Requires | Duration (Days) | |----------|----------------------------|----------|-----------------| | A | Train workers | | 6 | | B | Purchase materials | | 9 | | C | Make subassembly 1 | A, B | 8 | | D | Make subassembly 2 | A, B | 7 | | E | Inspect subassembly 2 | D | 10 | | F | Combine subassemblies | C, E | 12 | | G | Subassembly 2 safety report| E | 6 | **Questions:** 1. **How quickly can Widgetco complete this project?** - **(a) Define decision variables.** - **(b) Write a suitable Linear Programming (LP) problem formulation.** **Explanation:** To complete the project, one must determine the earliest completion time using project management techniques such as Critical Path Method (CPM). By defining the decision variables, we can structure an LP problem to optimize the project timeline, considering the dependencies and durations of each task outlined in the table.
**Widgetco Project Prototype Planning** **Project Overview:** Widgetco is developing a prototype for a new product consisting of two subassemblies. The production process requires specific sequential activities: 1. **Initial Preparations:** - Purchase raw materials. - Train workers. 2. **Subassembly Construction:** - Construct subassembly 1. - Construct subassembly 2, followed by inspection. 3. **Final Assembly:** - Combine both subassemblies. **Activity Breakdown:** | **Activity** | **Description** | **Requires** | **Duration (Days)** | |--------------|--------------------------------|--------------|---------------------| | A | Train workers | | 6 | | B | Purchase materials | | 9 | | C | Make subassembly 1 | A, B | 8 | | D | Make subassembly 2 | A, B | 7 | | E | Inspect subassembly 2 | D | 10 | | F | Combine subassemblies | C, E | 12 | | G | Subassembly 2 safety report | E | 6 | **Project Completion Questions:** **(a) Decision Variables Definition:** Define variables representing the start times of each project activity to determine the optimal sequence and timing of tasks for efficient project completion. **(b) Linear Programming (LP) Problem Formulation:** Develop an LP model to minimize the project completion time while respecting all precedence requirements and durations for each activity. The formulation should encompass constraints for the order of activities based on their dependencies, ensuring tasks commence only when all prerequisite activities are finished.
Transcribed Image Text:**Widgetco Project Prototype Planning** **Project Overview:** Widgetco is developing a prototype for a new product consisting of two subassemblies. The production process requires specific sequential activities: 1. **Initial Preparations:** - Purchase raw materials. - Train workers. 2. **Subassembly Construction:** - Construct subassembly 1. - Construct subassembly 2, followed by inspection. 3. **Final Assembly:** - Combine both subassemblies. **Activity Breakdown:** | **Activity** | **Description** | **Requires** | **Duration (Days)** | |--------------|--------------------------------|--------------|---------------------| | A | Train workers | | 6 | | B | Purchase materials | | 9 | | C | Make subassembly 1 | A, B | 8 | | D | Make subassembly 2 | A, B | 7 | | E | Inspect subassembly 2 | D | 10 | | F | Combine subassemblies | C, E | 12 | | G | Subassembly 2 safety report | E | 6 | **Project Completion Questions:** **(a) Decision Variables Definition:** Define variables representing the start times of each project activity to determine the optimal sequence and timing of tasks for efficient project completion. **(b) Linear Programming (LP) Problem Formulation:** Develop an LP model to minimize the project completion time while respecting all precedence requirements and durations for each activity. The formulation should encompass constraints for the order of activities based on their dependencies, ensuring tasks commence only when all prerequisite activities are finished.
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