Jay Gatsby categorizes wines into one of three clusters. The centroids of these clusters, describing the average characteristics of a wine in each cluster, are listed in the following table. Characteristic Cluster 1 Cluster 2 Cluster 3 Alcohol 0.819 0.164 -0.937 MalicAcid -0.329 0.869 -0.368 Ash 0.248 0.186 -0.393 Alcalinity -0.677 0.523 0.249 Magnesium 0.643 -0.075 -0.573 Phenols 0.825 0.977 -0.034 Flavanoids 0.896 -0.212 0.083 Nonflavanoids -0.595 0.724 0.009 Proanthocyanins 0.619 -0.778 0.010 ColorIntensity 0.135 0.939 -0.881 Hue 0.497 -1.162 0.437 Dilution 0.744 -1.289 0.295 Proline 1.117 -0.406 -0.776 Jay has recently discovered a new wine from the Piedmont region of Italy with the following characteristics. In which cluster of wines should he place this new wine? Justify your choice with appropriate calculations. Characteristic Alcohol -1.023 MalicAcid -0.480 Ash 0.049 Alcalinity 0.600 Magnesium -1.242 Phenols 1.094 Flavanoids 0.001 Nonflavanoids 0.548 Proanthocyanins -0.229 ColorIntensity -0.797 Hue 0.711 Dilution -0.425 Proline 0.010 Hint: Compute the Euclidian distance from the new wine’s characteristics to each of the three cluster centers to serve as guide in answering the question.

Jay Gatsby categorizes wines into one of three clusters. The centroids of these clusters, describing the average characteristics of a wine in each cluster, are listed in the following table. Characteristic Cluster 1 Cluster 2 Cluster 3 Alcohol 0.819 0.164 -0.937 MalicAcid -0.329 0.869 -0.368 Ash 0.248 0.186 -0.393 Alcalinity -0.677 0.523 0.249 Magnesium 0.643 -0.075 -0.573 Phenols 0.825 0.977 -0.034 Flavanoids 0.896 -0.212 0.083 Nonflavanoids -0.595 0.724 0.009 Proanthocyanins 0.619 -0.778 0.010 ColorIntensity 0.135 0.939 -0.881 Hue 0.497 -1.162 0.437 Dilution 0.744 -1.289 0.295 Proline 1.117 -0.406 -0.776 Jay has recently discovered a new wine from the Piedmont region of Italy with the following characteristics. In which cluster of wines should he place this new wine? Justify your choice with appropriate calculations. Characteristic Alcohol -1.023 MalicAcid -0.480 Ash 0.049 Alcalinity 0.600 Magnesium -1.242 Phenols 1.094 Flavanoids 0.001 Nonflavanoids 0.548 Proanthocyanins -0.229 ColorIntensity -0.797 Hue 0.711 Dilution -0.425 Proline 0.010 Hint: Compute the Euclidian distance from the new wine’s characteristics to each of the three cluster centers to serve as guide in answering the question.

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section: Chapter Questions

Problem 63P

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Jay Gatsby categorizes wines into one of three clusters. The centroids of these clusters, describing the average characteristics of a wine in each cluster, are listed in the following table.

Characteristic Cluster 1 Cluster 2 Cluster 3

Alcohol 0.819 0.164 -0.937

MalicAcid -0.329 0.869 -0.368

Ash 0.248 0.186 -0.393

Alcalinity -0.677 0.523 0.249

Magnesium 0.643 -0.075 -0.573

Phenols 0.825 0.977 -0.034

Flavanoids 0.896 -0.212 0.083

Nonflavanoids -0.595 0.724 0.009

Proanthocyanins 0.619 -0.778 0.010

ColorIntensity 0.135 0.939 -0.881

Hue 0.497 -1.162 0.437

Dilution 0.744 -1.289 0.295

Proline 1.117 -0.406 -0.776

Jay has recently discovered a new wine from the Piedmont region of Italy with the following characteristics. In which cluster of wines should he place this new wine? Justify your choice with appropriate calculations.

Characteristic

Alcohol -1.023

MalicAcid -0.480

Ash 0.049

Alcalinity 0.600

Magnesium -1.242

Phenols 1.094

Flavanoids 0.001

Nonflavanoids 0.548

Proanthocyanins -0.229

ColorIntensity -0.797

Hue 0.711

Dilution -0.425

Proline 0.010

Hint: Compute the Euclidian distance from the new wine’s characteristics to each of the three cluster centers to serve as guide in answering the question.

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