Question

fractional Knopsack [0,1], W=8 ob; 1112131415161 wi 12 4 1556 Vi 20/24 9 15 25 36 optimal solution?

Answer 1

> For solving fractional knapsnack there is always 3 option for select the items. We try every option and get total value and which option give max total value we take it answer as a optimal solution Options: 1.Select By minimum weight 2.Select By maximum value 3.Select By max Vi/wi.

option 1:

obj 2 3 4 Wi 2 4 5 5 6. Vi 20 24 15 25 36 1.Minimum weight > In this solution first we select the minimum value weight first. > So, First we select full obj 3 so remaining weight is w=8-1=7. > Than we select full obj 1 with weight 2 so remaining weight is w=7-2=5 > Than we select full ob. 2 with weight 4 so remaining weight is w=5-4=1 > Than we select 0.2 ob. 5 with weight 4 so remaining weight is w=1-(5*0.2)=0. Total value obj 2 3 4 5 4 1 5 Wi 20 24 9 15 25 Vi 36 20+24+9+(0.2*25)=58 Min 0.2 | weight

option 2:

obj 2 3 4 5 Wi 2 4 5 5 6. Vi 20 24 9. 15 25 36 2.Maximum value > In this solution first we select the maximum value object first. > So, First we select full obj 6 so remaining weight is w=8-6=2. > Than we select 0.4 ob. 5 with weight 4 so remaining weight is w=2-(5*0.4)=0. obj Total value 3 4 Wi 2 5 6. 20 24 9 15 25 Vi 36 Min 36+(0.4*25)=46 0.4 weight

option 3:

obj Wi 2 2 4 4 6. Vi 20 24 15 25 36 Vi/wi 10 9. 3 6.

3.Maximum vi/wi > In this solution first we select the maximum vi/wi object first. > So, First we select full obj 1 so remaining weight is w=8-2=6. > Than we select full ob. 3 with weight 3 so remaining weight is w=6-1=5. > Here obj 6 and obj 2 both are same so you can select any of them. We select full obj 3 with weight 4 so remaining weight is=6-5=1. > Now last we select 0.16 obj 6 with weight 6 so remaining weight is =1-(0.16*6)=0 obj Total value 2 3 4 5 Wi 4 5 5 20 24 9 15 25 Vi 36 Vi/wi 10 6 3 5 0.16 20+24+9+(0.16*36)=58.76 Min weight In this we get a maximum value so this is a optimal solution for your problem and solution is take obj as per above table for getting maximum value.

answer:

Answer Obj 1=1 Obj 2=1 Obj 3=1 Obj 6=0.16 Take object by this than you will get max value