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.
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.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter6: Systems Of Linear Equations And Inequalities
Section6.1: Graphing Systems Of Equations
Problem 59PFA
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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 vector
[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.
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