The strength requirements for various materials (steel, concrete, wood) in a multi-component system are interconnected. The strengths of the materials are given by the following equations: 3x−y+2z=1500 2x+2y−z=1200 4x-2y+z=1600 Additionally, there is a cost factor associated with each material. The costs per ton are: Steel: $4000 Concrete: $1500 Wood: $1000 Use a matrix method to find the optimal combination of materials that meets the strength requirements while minimizing the cost. The total cost of the materials is represented by the dot product of the material amounts vector [x, y, z]and the cost vector.
The strength requirements for various materials (steel, concrete, wood) in a multi-component system are interconnected. The strengths of the materials are given by the following equations: 3x−y+2z=1500 2x+2y−z=1200 4x-2y+z=1600 Additionally, there is a cost factor associated with each material. The costs per ton are: Steel: $4000 Concrete: $1500 Wood: $1000 Use a matrix method to find the optimal combination of materials that meets the strength requirements while minimizing the cost. The total cost of the materials is represented by the dot product of the material amounts vector [x, y, z]and the cost vector.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The strength requirements for various materials (steel, concrete,
wood) in a multi-component system are interconnected. The strengths of the materials are given by the following equations:
3x−y+2z=1500
2x+2y−z=1200
4x-2y+z=1600
Additionally, there is a cost factor associated with each material. The costs per ton are:
Steel: $4000
Concrete: $1500
Wood: $1000
The total cost of the materials is represented by the dot product of the material amounts vector [x, y, z]and the
cost vector.
wood) in a multi-component system are interconnected. The strengths of the materials are given by the following equations:
3x−y+2z=1500
2x+2y−z=1200
4x-2y+z=1600
Additionally, there is a cost factor associated with each material. The costs per ton are:
Steel: $4000
Concrete: $1500
Wood: $1000
Use a matrix method to find the optimal combination of materials that meets the strength
requirements while minimizing the cost.
cost vector.
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