Question

KNAPSACK Optimization Problem using Greedy
Method

Problem 1:

Item Weight Value

1 14 20

2 6 16

3 10 8

4 5 10

5 4 12

Allowed weight = 24 Kg

Problem 2:

Item Weight Value

1 6 30

2 8 40

3 15 45

4 22 88

5 25 80

Allowed weight = 60 Kg

Problem 3:

Item Weight Value

1 6 30

2 8 40

3 15 45

4 22 88

5 25 80

Allowed weight = 60 Kg

Answer #1

Solution 1:-

Item | Value | Weight | Value/Weight |

1 | 20 | 14 | 1.42 |

2 | 16 | 6 | 2.66 |

3 | 8 | 10 | 0.8 |

4 | 10 | 5 | 2 |

5 | 12 | 4 | 3 |

Arranging items in decreasing order of Value/Weight: 5 , 2 , 4 , 1 , 3. Now the items will be put in the bag in this order.

Allowed weight = 24 kg

Items put in the bag | Value | Weight in the bag |

5 | 12 | 4 |

2 | 16 | 6 |

4 | 10 | 5 |

1 | 9 * 20/14 | 9 |

Total value = 50.85

Solution 2:-

Items | Value | Weight | Value/Weight |

1 | 30 | 6 | 5 |

2 | 40 | 8 | 5 |

3 | 45 | 15 | 3 |

4 | 88 | 22 | 4 |

5 | 80 | 25 | 3.2 |

Decreasing order of Value/Weight : 1,2,4,5,3

Allowed weight = 60 kg

Items put in the bag | Value | Weight in the bag |

1 | 30 | 6 |

2 | 40 | 8 |

4 | 88 | 22 |

5 | 24*3.2 | 24 |

Total value= 234.8

Solution 3:-

It has same values as that of Problem 2 so the solution is also same.

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