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### Problem Statement: For the following problem, what would be the constraint that limits the capacity of Machine 1 considering that X1, X2, X3, and X4 are the number of units produced and sold of Products 1, 2, 3, and 4, respectively? ### Table: | Machine | Cost per hr ($) | | Manufacturing time (hr) per unit | | Capacity (hr) | |---------|-----------------|----------|--------------------|---------|------------| | | | Product 1 | Product 2 | Product 3 | Product 4 | | | 1 | 10 | 2 | 3 | 4 | 2 | 500 | | 2 | 5 | 3 | 2 | 1 | 2 | 380 | | 3 | 4 | 7 | 3 | 2 | 1 | 450 | **Unit selling price ($): 75, 70, 55, 45** ### Multiple Choice Answers: a. 75X1 + 70X2 + 55X3 + 45X4 b. **2X1 + 3X2 + 4X3 + 2X4 ≤ 500** c. 2X1 + 3X2 + 7X3 ≤ 75 d. 20X1 + 30X2 + 40X3 + 20X4 ≤ 500 ### Explanation: The table summarizes the manufacturing details for four different products across three machines. It contains the following information: - **Cost per hr ($)**: The cost of running each machine per hour. - **Manufacturing time (hr) per unit**: The time it takes each machine to manufacture each unit of the respective products. - **Capacity (hr)**: The maximum number of hours each machine can operate. The multiple-choice question defines possible constraints based on the machine and product data. In this context, "X1, X2, X3, and X4" denote the number of units produced and sold for Products 1, 2, 3, and 4, respectively. The goal is to determine the

### Problem Statement: For the following problem, what would be the constraint that limits the capacity of Machine 1 considering that X1, X2, X3, and X4 are the number of units produced and sold of Products 1, 2, 3, and 4, respectively? ### Table: | Machine | Cost per hr ($) | | Manufacturing time (hr) per unit | | Capacity (hr) | |---------|-----------------|----------|--------------------|---------|------------| | | | Product 1 | Product 2 | Product 3 | Product 4 | | | 1 | 10 | 2 | 3 | 4 | 2 | 500 | | 2 | 5 | 3 | 2 | 1 | 2 | 380 | | 3 | 4 | 7 | 3 | 2 | 1 | 450 | **Unit selling price ($): 75, 70, 55, 45** ### Multiple Choice Answers: a. 75X1 + 70X2 + 55X3 + 45X4 b. **2X1 + 3X2 + 4X3 + 2X4 ≤ 500** c. 2X1 + 3X2 + 7X3 ≤ 75 d. 20X1 + 30X2 + 40X3 + 20X4 ≤ 500 ### Explanation: The table summarizes the manufacturing details for four different products across three machines. It contains the following information: - **Cost per hr ($)**: The cost of running each machine per hour. - **Manufacturing time (hr) per unit**: The time it takes each machine to manufacture each unit of the respective products. - **Capacity (hr)**: The maximum number of hours each machine can operate. The multiple-choice question defines possible constraints based on the machine and product data. In this context, "X1, X2, X3, and X4" denote the number of units produced and sold for Products 1, 2, 3, and 4, respectively. The goal is to determine the

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter5: Network Models
Section5.5: Shortest Path Models
Problem 30P
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### Problem Statement: For the following problem, what would be the constraint that limits the capacity of Machine 1 considering that X1, X2, X3, and X4 are the number of units produced and sold of Products 1, 2, 3, and 4, respectively? ### Table: | Machine | Cost per hr ($) | | Manufacturing time (hr) per unit | | Capacity (hr) | |---------|-----------------|----------|--------------------|---------|------------| | | | Product 1 | Product 2 | Product 3 | Product 4 | | | 1 | 10 | 2 | 3 | 4 | 2 | 500 | | 2 | 5 | 3 | 2 | 1 | 2 | 380 | | 3 | 4 | 7 | 3 | 2 | 1 | 450 | **Unit selling price ($): 75, 70, 55, 45** ### Multiple Choice Answers: a. 75X1 + 70X2 + 55X3 + 45X4 b. **2X1 + 3X2 + 4X3 + 2X4 ≤ 500** c. 2X1 + 3X2 + 7X3 ≤ 75 d. 20X1 + 30X2 + 40X3 + 20X4 ≤ 500 ### Explanation: The table summarizes the manufacturing details for four different products across three machines. It contains the following information: - **Cost per hr ($)**: The cost of running each machine per hour. - **Manufacturing time (hr) per unit**: The time it takes each machine to manufacture each unit of the respective products. - **Capacity (hr)**: The maximum number of hours each machine can operate. The multiple-choice question defines possible constraints based on the machine and product data. In this context, "X1, X2, X3, and X4" denote the number of units produced and sold for Products 1, 2, 3, and 4, respectively. The goal is to determine the
Transcribed Image Text:### Problem Statement: For the following problem, what would be the constraint that limits the capacity of Machine 1 considering that X1, X2, X3, and X4 are the number of units produced and sold of Products 1, 2, 3, and 4, respectively? ### Table: | Machine | Cost per hr ($) | | Manufacturing time (hr) per unit | | Capacity (hr) | |---------|-----------------|----------|--------------------|---------|------------| | | | Product 1 | Product 2 | Product 3 | Product 4 | | | 1 | 10 | 2 | 3 | 4 | 2 | 500 | | 2 | 5 | 3 | 2 | 1 | 2 | 380 | | 3 | 4 | 7 | 3 | 2 | 1 | 450 | **Unit selling price ($): 75, 70, 55, 45** ### Multiple Choice Answers: a. 75X1 + 70X2 + 55X3 + 45X4 b. **2X1 + 3X2 + 4X3 + 2X4 ≤ 500** c. 2X1 + 3X2 + 7X3 ≤ 75 d. 20X1 + 30X2 + 40X3 + 20X4 ≤ 500 ### Explanation: The table summarizes the manufacturing details for four different products across three machines. It contains the following information: - **Cost per hr ($)**: The cost of running each machine per hour. - **Manufacturing time (hr) per unit**: The time it takes each machine to manufacture each unit of the respective products. - **Capacity (hr)**: The maximum number of hours each machine can operate. The multiple-choice question defines possible constraints based on the machine and product data. In this context, "X1, X2, X3, and X4" denote the number of units produced and sold for Products 1, 2, 3, and 4, respectively. The goal is to determine the
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