Answered: 1. Please model the following two…

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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Related questions

Question

answer

1. Please model the following two problems
and provide the corresponding mathematical
expressions.
1.1 A certain car requires one each of three
types of axles, labeled A, B, and C. The
specifications for these axles are 1.5, 1, and
0.7 meters, respectively. These axles are made
from the same type of circular steel rod, which
has a length of 4 meters. Now, the goal is to
manufacture 1000 cars. What is the minimum
amount of circular steel rod required to
produce these axles?

Expert Solution

Step 1: Introduction to the problem and concepts used

Given: A certain car requires each of three types of axles, labeled A, B, and C. The specifications for these axles are 1.5, 1, and 0.7 meters respectively. These axles are made from the same type of circular steel rod, which has a length of 4 meters. Now the goal is to manufacture 1,000 cars,

The aim is to model the problem and provide the corresponding mathematical expressions for the minimum amount of circular steel rod required to produce these axles.

Concepts used:

Linear programming: LP is a mathematical optimization method for finding the best solution to a problem in which there are a set of linear constraints and an objective function to be maximized or minimized.
Decision variables: These are the variables that are used to represent the possible solutions to the problem. In this problem, the decision variables are x, y, and z.
Objective function: This is a mathematical expression that represents the goal of the optimization problem. In this problem, the objective function is to minimize the total length of the circular steel rod required.