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.