Consider the following instances of knap-sack problem:

Item	Weight(in Kgs)	Value(in $)
1	3	10
2	2	25
3	2	20
4	5	15
5	7	40
6	4	36

Maximum weight of knapsack is 10 Kg. What will be the maximum profit with the optimal solution of the 0/1 knapsack problem?

(A) 101
(B) 96
(C) 92.42
(D) 81


Answer: (D)

Explanation: Knapsack Instance with value / weight:

Item	Weight	Value	Value / weight
1	3	10	3.33
2	2	25	12.5
3	2	20	10
4	5	15	3
5	7	40	5.71
6	4	36	9

Decrersing order of value/weight:

Item	Weight	Value	Value / weight
2	2	25	12.5
3	2	20	10
6	4	36	9
5	7	40	5.71
1	3	10	3.33
4	5	15	3

Now start filling the sack-
item 2 fully:
left weight = 10 – 2 = 8
item 3 fully:
left weight = 8 – 2 = 6
item 6 fully:
left weight = 6 – 4 = 2
So, only P2, P3, and P6 are chosen. Now no other item can be filled in because it is a 0/1 knap sack.
Total profit = 25 + 20 + 36 = 81.

So, option (D) is correct.

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