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Home/Questions/Q 22557
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Minni
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Minni
Asked: October 17, 20222022-10-17T09:37:59+05:30 2022-10-17T09:37:59+05:30In: Data Science

Solve using fractional knapsack: M=20, n=4 P= (3, 10, 15, …

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Solve using fractional knapsack:

M=20, n=4

P= (3, 10, 15, 5)

W= (5, 13, 12, 8).

101213155) w= (58).design and analysis of algorithmsn=4 p= (3solve using fractional knapsack: m=20
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    1. Saurav kumar
      2022-10-17T18:23:31+05:30Added an answer on October 17, 2022 at 6:23 pm

      M=20 (total capacity of bag)

      N=4 (no of items)

      Let’s find Pi/Wi (profit/weight) for each items:

      P1/W1=3/5 = 0.60 (O1)

      P2/W2=10/13= 0.76(O2)

      P3/W3= 15/12 = 1.25 (O3)

      P4/W4 = 5/8 = 0.62 (O4)

      Where O is object no

       

      Let’s arrange them in order: 1.25 >> 0.76 >> 0.62 >> 0.60

       

      Object taken

      profit

      weight

      Remaining weight

      O3

      15

      12

      8

      O2

      10

      13

      0

      O4

      5

      8

      0

      O1

      3

      5

      0

       

      Now,

      • Knapsack weight left to be filled is 8 kg but item-2 has a weight of 13 kg.
      • Since in fractional knapsack problem, even the fraction of any item can be taken.
      • So, knapsack will contain the following items-

      < O3,(8/13)O2 >

       

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