An automobile manufacturer is considering mechanical design changes in one of its top-selling cars to reduce the weight of the car by at least 420 pounds to improve its fuel efficiency. Design engineers have identified 10 changes that could be made in the car to make it lighter (e.g., using composite body pieces rather than metal). The weight saved by each design change and the estimated costs of implementing each change are summarized in the following table. Design Change 1 2 3 4 5 6 8 9 10 Weight Saved (Ibs) 50 75 25 150 60 95 200 40 80 30 Cost (in $1,000s) 150 350 50 650 | 90 35 450 75 110 30 Changes 4 and 7 represent alternate ways of modifying the engine block and, therefore, only one of these options could be selected. The company wants to determine which changes to make in order to reduce the total weight of the car by at least 420 pounds in the least costly manner. (a) Formulate an ILP model for this problem to minimize cost (in thousands of dollars). (Let X, = 1 if design change i is implemented and 0 otherwise. In your changes 4 and 7 constraint, only use coefficients of 1 or -1.) MIN: Subject to: total reduced weight changes 4 and 7 constraint X, binary (b) Create a spreadsheet model for this problem and solve it. What is the optimal solution?

An automobile manufacturer is considering mechanical design changes in one of its top-selling cars to reduce the weight of the car by at least 420 pounds to improve its fuel efficiency. Design engineers have identified 10 changes that could be made in the car to make it lighter (e.g., using composite body pieces rather than metal). The weight saved by each design change and the estimated costs of implementing each change are summarized in the following table. Design Change 1 2 3 4 5 6 8 9 10 Weight Saved (Ibs) 50 75 25 150 60 95 200 40 80 30 Cost (in $1,000s) 150 350 50 650 | 90 35 450 75 110 30 Changes 4 and 7 represent alternate ways of modifying the engine block and, therefore, only one of these options could be selected. The company wants to determine which changes to make in order to reduce the total weight of the car by at least 420 pounds in the least costly manner. (a) Formulate an ILP model for this problem to minimize cost (in thousands of dollars). (Let X, = 1 if design change i is implemented and 0 otherwise. In your changes 4 and 7 constraint, only use coefficients of 1 or -1.) MIN: Subject to: total reduced weight changes 4 and 7 constraint X, binary (b) Create a spreadsheet model for this problem and solve it. What is the optimal solution?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 25EQ

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