A blood bank wants to determine the least expensive way to transport available blood donations from Pittsburgh and Staunton to hospitals in Charleston, Roanoke, Richmond, Norfolk, and Suffolk. The supply and demand for donated blood is shown in the figure along with the unit cost of shipping along each possible arc. Provide the complete linear programing formulation. Clearly specify decision variables, objective function and constraints.Build a model in Excel and paste a screenshot here. Use “FORMULATEXT” in your model to show calculations.According to Excel Solver, what is the optimal transportation plan for blood bank? What is the minimum total shipping cost? The image is a flow network diagram depicting transportation or distribution routes between seven nodes, which are labeled 1 through 7. These nodes possibly represent cities or distribution centers, and they are connected by directed edges with associated numbers that likely denote capacities, costs, or flow rates.### Nodes:- **1 (Pittsburgh)**- **2 (Staunton)**- **3 (Charleston)**- **4 (Roanoke)**- **5 (Richmond)**- **6 (Norfolk)**- **7 (Suffolk)**### Node Capacities:- Node 1: -1,300- Node 2: -1,200- Node 3: 300- Node 4: 200- Node 5: 800- Node 6: 700- Node 7: 400### Directed Edges and Capacities:- 1 to 3: 3- 1 to 4: 4- 2 to 3: 4- 2 to 4: 4- 3 to 4: 7- 3 to 5: 9- 4 to 5: 7- 4 to 6: 8- 5 to 7: 3- 6 to 7: 2### Explanation of the Diagram:The diagram likely illustrates the flow of goods or resources between various points. Each node has a capacity indicating either supply, demand, or some constraint. The directed edges dictate the permissible direction of flow, with attached numbers showing the strength or limit of each connection. For instance, there is a flow from Pittsburgh (Node 1) to Charleston (Node 3) with a capacity of 3.### Possible Uses:This flow network could be analyzed using algorithms to determine maximum flow, minimum cost flow, or to optimize logistics in transportation networks. Understanding the balance and flow between these nodes can be crucial for efficient supply chain management.

Solution : (a and b) According to the provided details , the networking problem has two supply nodes…

Answered: A blood bank wants to determine the…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

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A blood bank wants to determine the least expensive way to transport available blood donations from Pittsburgh and Staunton to hospitals in Charleston, Roanoke, Richmond, Norfolk, and Suffolk. The supply and demand for donated blood is shown in the figure along with the unit cost of shipping along each possible arc.

Provide the complete linear programing formulation. Clearly specify decision variables, objective function and constraints.
Build a model in Excel and paste a screenshot here. Use “FORMULATEXT” in your model to show calculations.
According to Excel Solver, what is the optimal transportation plan for blood bank? What is the minimum total shipping cost?

The image is a flow network diagram depicting transportation or distribution routes between seven nodes, which are labeled 1 through 7. These nodes possibly represent cities or distribution centers, and they are connected by directed edges with associated numbers that likely denote capacities, costs, or flow rates.

### Nodes:
- **1 (Pittsburgh)**
- **2 (Staunton)**
- **3 (Charleston)**
- **4 (Roanoke)**
- **5 (Richmond)**
- **6 (Norfolk)**
- **7 (Suffolk)**

### Node Capacities:
- Node 1: -1,300
- Node 2: -1,200
- Node 3: 300
- Node 4: 200
- Node 5: 800
- Node 6: 700
- Node 7: 400

### Directed Edges and Capacities:
- 1 to 3: 3
- 1 to 4: 4
- 2 to 3: 4
- 2 to 4: 4
- 3 to 4: 7
- 3 to 5: 9
- 4 to 5: 7
- 4 to 6: 8
- 5 to 7: 3
- 6 to 7: 2

### Explanation of the Diagram:
The diagram likely illustrates the flow of goods or resources between various points. Each node has a capacity indicating either supply, demand, or some constraint. The directed edges dictate the permissible direction of flow, with attached numbers showing the strength or limit of each connection. For instance, there is a flow from Pittsburgh (Node 1) to Charleston (Node 3) with a capacity of 3.

### Possible Uses:
This flow network could be analyzed using algorithms to determine maximum flow, minimum cost flow, or to optimize logistics in transportation networks. Understanding the balance and flow between these nodes can be crucial for efficient supply chain management.

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