Knapsack problem

Question

5.Consider the Knapsack instance with 5 objects and a capacity M=11, profit P=(5,4,7,2,3) and
weight W=(4,3,6,2,2.). Solve it using dynamic programming approach.

Comments

$14$ is the correct answer Using Dynamic Programming $(0/1)$ Knapsack Problem. And $13.5$ Using Greedy Algorithm, Fractional knapsack problem.

Answer 1

 

                                

0	0	0	0	0	0	0	0	0	0	0	0
0	0	0	0	5	5	5	5	5	5	5	5
0	0	0	4	5	5	5	9	9	9	9	9
0	0	0	4	5	5	7	9	9	9	9	9
0	0	2	4	5	6	7	9	9	11	12	13
0	0	3	4	5	7	8	9	10	12	12	14

 

 

Columns w represents weights <0, 1, 2, 3, ........11>

Rows i represent Item number <0, 1, 2, 3, 4, 5>

cell <i, w> indicates total profit P by "including any/some/all of the first i items in knapsack having combined weight w"

verify it !!