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?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text: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
6
7
8
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.)
IN:
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?
(X1, X2, X3, X4, X5, X6, X7, Xg, X9, X10) =
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