## Answers

Since each machine is given a rank in each criteria in order of 1 to 4 where 1 is the best rank and 4 is the worst

Furhter, each criteria is given an importance rating where higher the rating is better

To align the ratings, we will reverse the rankings to arrive at overall score where rank 1 means score of 4, rank 2 means score of 3, rank 3 means score of 2 and rank 4 means score of 1

Hence the overall scores matrix with importance rating is given below:

Scores | Criteria A | Criteria B | Criteria C |

Machine1 | 4 | 2 | 1 |

Machine2 | 3 | 3 | 3 |

Machine3 | 2 | 1 | 4 |

Machine4 | 1 | 4 | 2 |

Importance | 3 | 2 | 5 |

Now weighted average scores for each machine is calculated by summing products of each criteria by their importance rating as shown:

Hence overall score for Machine 1 = 4X3 + 2X2 + 1X5 = 12 + 4 + 5 = 23

Overall score for Machine 2 = 3X3 + 3X2 + 3X5 = 9 + 6 + 15 = 30

Score for machine 3 = 2X3 + 1X2 + 4X5 = 6 + 2 + 20 = 28

Score for machine 4 = 1X3 + 4X2 + 2X5 = 3 + 8 + 10 = 21

Now the machines in order of score are

Rank 1 -> Machine 2 with score of 30

Rank 2 -> Machine 3 with score of 28

Rank 3 -> Machine 1 with score of 23

Rank 4 : Machine 4 with score of 21

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