In a multi-component engineering system, the strength requirements for various materials (steel,concrete, wood) are interconnected. The strengths of the materials are given by the followingsystem of equations:3x−y+2z=15002x+2y−z=1200x+3y+2z=1600Additionally, there is a cost factor associated with each material. The costs per ton are: Steel: $5000 Concrete: $2000 Wood: $1000The total cost of the materials is represented by the dot product of the material amounts vector[x, y, z]and the cost vector.1. Use any matrix method to find the optimal combination of materials that meets the strengthrequirements while minimizing the cost.2. Validate the solution using a computer software (Matlab, python)
In a multi-component engineering system, the strength requirements for various materials (steel,concrete, wood) are interconnected. The strengths of the materials are given by the followingsystem of equations:3x−y+2z=15002x+2y−z=1200x+3y+2z=1600Additionally, there is a cost factor associated with each material. The costs per ton are: Steel: $5000 Concrete: $2000 Wood: $1000The total cost of the materials is represented by the dot product of the material amounts vector[x, y, z]and the cost vector.1. Use any matrix method to find the optimal combination of materials that meets the strengthrequirements while minimizing the cost.2. Validate the solution using a computer software (Matlab, python)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.7: Solving Systems Of Linear And Quadratic Equations
Problem 6CYU
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In a multi-component engineering system, the strength requirements for various materials (steel,
concrete, wood) are interconnected. The strengths of the materials are given by the following
system of equations:
3x−y+2z=1500
2x+2y−z=1200
x+3y+2z=1600
Additionally, there is a cost factor associated with each material. The costs per ton are:
Steel: $5000
Concrete: $2000
Wood: $1000
The total cost of the materials is represented by the dot product of the material amounts
[x, y, z]and the cost vector.
1. Use any matrix method to find the optimal combination of materials that meets the strength
requirements while minimizing the cost.
2. Validate the solution using a computer software (Matlab, python)
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