Bin packing First-fit algorithm. 1 2 3 6 2 3 5 3 A B C D E F 4 Each block will be fitted into the first bin that has room for it. Bin packing First-fit.

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Presentation transcript:

Bin packing First-fit algorithm

A B C D E F 4 Each block will be fitted into the first bin that has room for it. Bin packing First-fit algorithm

A B C D E F 4 The first block fits into the first bin Bin packing First-fit algorithm

A B C D E F 4 The second block fits into the first bin Bin packing First-fit algorithm

A B C D E F 4 The third block will not fit in the first bin But there is room in the second bin. Bin packing First-fit algorithm

The third bin is the first one the 5 will fit into. A B C D E F Bin packing First-fit algorithm

The second bin has room for the 3. Bin packing First-fit algorithm A B C D E F

The fourth bin is the first one with room for the 2. Bin packing First-fit algorithm A B C D E F

The 3 also fits into the fourth bin. Bin packing First-fit algorithm A B C D E F

No room until the fifth bin for the 6. Bin packing First-fit algorithm A B C D E F

The 3 has to start a new bin Bin packing First-fit algorithm A B C D E F Total usage is 6 bins.

Bin Packing Examples of first-fit algorithm

Example 1 Pack the following items into bins of size 20: 11, 7, 3, 4, 3, 5, 1, 8, 9 How many bins are required?

11, 7, 3, 4, 3, 5, 1, 8, 9 Bin size Bins 11

11, 7, 3, 4, 3, 5, 1, 8, 9 Bin size Bins 11

11, 7, 3, 4, 3, 5, 1, 8, 9 Bin size Bins 11

11, 7, 3, 4, 3, 5, 1, 8, 9 Bin size Bins 11

11, 7, 3, 4, 3, 5, 1, 8, 9 Bin size Bins 11

11, 7, 3, 4, 3, 5, 1, 8, 9 Bin size Bins 11

11, 7, 3, 4, 3, 5, 1, 8, 9 Bin size Bins 11

11, 7, 3, 4, 3, 5, 1, 8, 9 Bin size Bins 11

11, 7, 3, 4, 3, 5, 1, 8, 9 Bin size Bins 11

11, 7, 3, 4, 3, 5, 1, 8, 9 Bin size Bins 11

11, 7, 3, 4, 3, 5, 1, 8, 9 Bin size Bins 11

11, 7, 3, 4, 3, 5, 1, 8, 9 Bin size Bins 11 We need 3 bins.

Example 2 Pack the following items into bins of size 20: 5, 8, 12, 4, 11, 17, 7, 9, 7 How many bins are required?

5, 8, 12, 4, 11, 17, 7, 9, 7 Bin size Bins 5

5, 8, 12, 4, 11, 17, 7, 9, 7 Bin size Bins 5

5, 8, 12, 4, 11, 17, 7, 9, 7 Bin size Bins 5

5, 8, 12, 4, 11, 17, 7, 9, 7 Bin size Bins 5

5, 8, 12, 4, 11, 17, 7, 9, 7 Bin size Bins 5

5, 8, 12, 4, 11, 17, 7, 9, 7 Bin size Bins 5

5, 8, 12, 4, 11, 17, 7, 9, 7 Bin size Bins 5

5, 8, 12, 4, 11, 17, 7, 9, 7 Bin size Bins 5

5, 8, 12, 4, 11, 17, 7, 9, 7 Bin size Bins 5

5, 8, 12, 4, 11, 17, 7, 9, 7 Bin size Bins 5

5, 8, 12, 4, 11, 17, 7, 9, 7 Bin size Bins 5

5, 8, 12, 4, 11, 17, 7, 9, 7 Bin size Bins 5

5, 8, 12, 4, 11, 17, 7, 9, 7 Bin size Bins 5 We need 5 bins.

Example 3 A wholesale greengrocer is packing the following items into crates that will carry 24 kg: ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181 How many crates will the greengrocer need?

Crates (24 kg) ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

Crates (24 kg) 9 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

Crates (24 kg) 9 kg, 6 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

Crates (24 kg) 9 kg, 6 kg, 6 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

Crates (24 kg) 9 kg, 6 kg, 6 kg, 7 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

Crates (24 kg) 9 kg, 6 kg, 6 kg 7 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg, 20 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg 20 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg, 10 kg 20 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg 20 kg, 10 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg 20 kg 10 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg, 6 kg 20 kg 10 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg 20 kg, 6 kg 10 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg 20 kg 10 kg, 6 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg, 8 kg 20 kg 10 kg, 6 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg 20 kg, 8 kg 10 kg, 6 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg 20 kg 10 kg, 6 kg, 8 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg 20 kg 10 kg, 6 kg, 8 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg, 5 kg 20 kg 10 kg, 6 kg, 8 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg 20 kg, 5 kg 10 kg, 6 kg, 8 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg 20 kg 10 kg, 6 kg, 8 kg 5 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg 20 kg 10 kg, 6 kg, 8 kg 5 kg, 5 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg 20 kg 10 kg, 6 kg, 8 kg 5 kg, 5 kg, 5 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg, 2 kg 20 kg 10 kg, 6 kg, 8 kg 5 kg, 5 kg, 5 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg, 2 kg, 18 kg 20 kg 10 kg, 6 kg, 8 kg 5 kg, 5 kg, 5 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg, 2 kg 20 kg, 18 kg 10 kg, 6 kg, 8 kg 5 kg, 5 kg, 5 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg, 2 kg 20 kg 10 kg, 6 kg, 8 kg 5 kg, 5 kg, 5 kg, 18 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg, 2 kg 20 kg 10 kg, 6 kg, 8 kg 5 kg, 5 kg, 5 kg 18 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181

Crates (24 kg) 9 kg, 6 kg, 6 kg, 3 kg 7 kg, 14 kg, 2 kg 20 kg 10 kg, 6 kg, 8 kg 5 kg, 5 kg, 5 kg 18 kg ItemWeight of item (kg)Number of items required Carrots91 Apples62 Pears71 Courgettes31 Cauliflowers141 Potatoes201 Oranges101 Leeks61 Bananas81 Tomatoes53 Grapes21 Onions181 So the greengrocer needs 6 crates.

Example 4 Pack the following items into bins of size 16: 14, 2, 7, 3, 1, 9, 12, 4, 6 How many bins are required?

14, 2, 7, 3, 1, 9, 12, 4, 6 Bin size Bins 14

14, 2, 7, 3, 1, 9, 12, 4, 6 Bin size Bins 14

14, 2, 7, 3, 1, 9, 12, 4, 6 Bin size Bins 14

14, 2, 7, 3, 1, 9, 12, 4, 6 Bin size Bins 14

14, 2, 7, 3, 1, 9, 12, 4, 6 Bin size Bins 14

14, 2, 7, 3, 1, 9, 12, 4, 6 Bin size Bins 14

14, 2, 7, 3, 1, 9, 12, 4, 6 Bin size Bins 14

14, 2, 7, 3, 1, 9, 12, 4, 6 Bin size Bins 14

14, 2, 7, 3, 1, 9, 12, 4, 6 Bin size Bins 14

14, 2, 7, 3, 1, 9, 12, 4, 6 Bin size Bins 14

14, 2, 7, 3, 1, 9, 12, 4, 6 Bin size Bins 14

14, 2, 7, 3, 1, 9, 12, 4, 6 Bin size Bins 14

14, 2, 7, 3, 1, 9, 12, 4, 6 Bin size Bins 14

14, 2, 7, 3, 1, 9, 12, 4, 6 Bin size Bins 14 We need 4 bins.

Example 5 A music store is ordering musical instruments. They are packed into boxes and delivered by a lorry. Each box can hold 20 kg. InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12 How many boxes will be needed to deliver all the instruments?

Boxes (20 kg) InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 15 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg 15 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg 15 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg, 2 kg 15 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg 15 kg, 2 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg 15 kg, 2 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg, 7 kg 15 kg, 2 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg 15 kg, 2 kg, 7 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg 15 kg, 2 kg 7 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg 15 kg, 2 kg 7 kg, 7 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg 15 kg, 2 kg 7 kg, 7 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 15 kg, 2 kg 7 kg, 7 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 15 kg, 2 kg 7 kg, 7 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 15 kg, 2 kg 7 kg, 7 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 15 kg, 2 kg, 2 kg 7 kg, 7 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 15 kg, 2 kg, 2 kg, 2 kg 7 kg, 7 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 15 kg, 2 kg, 2 kg 7 kg, 7 kg, 2 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 15 kg, 2 kg, 2 kg 7 kg, 7 kg, 2 kg, 2 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 15 kg, 2 kg, 2 kg 7 kg, 7 kg, 2 kg, 2 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg, 1 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg, 1 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg, 1 kg, 4 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg, 1 kg 4 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg, 1 kg 4 kg, 4 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg, 1 kg 4 kg, 4 kg, 4 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg, 1 kg 4 kg, 4 kg, 4 kg, 4 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg, 1 kg 4 kg, 4 kg, 4 kg, 4 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg, 1 kg, 18 kg 4 kg, 4 kg, 4 kg, 4 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg, 1 kg 4 kg, 4 kg, 18 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg, 1 kg 4 kg, 4 kg, 4 kg, 4 kg 18 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg, 1 kg, 1 kg 4 kg, 4 kg, 4 kg, 4 kg 18 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg, 1 kg, 1 kg 4 kg, 4 kg, 4 kg, 4 kg 18 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg, 1 kg, 1 kg 4 kg, 4 kg, 1 kg 18 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12

Boxes (20 kg) 15 kg, 2 kg, 2 kg, 1 kg 7 kg, 7 kg, 2 kg, 2 kg, 1 kg, 1 kg 4 kg, 4 kg, 1 kg 18 kg InstrumentWeight of instrument (kg) Number of each instrument ordered Guitars152 Trumpets23 Saxophones72 Violins11 Trombones23 Flutes12 Bassoons44 Tubas181 Cymbals12 5 boxes are needed.