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UGC NET Computer Science Dec 2022 Shift I (Paper II)

For a knapsack problem, $P$ and $W$ are profits and weights for a set of $7$ items as given below:

$P={9,5,2,7,6,16,9}$

$W={2,5,6,11,1,9,3}$
Find the optimal solution for fractional knapsack problem when its maximum capacity is $15$.

Solution

$P={9,5,2,7,6,16,9}$

$W={2,5,6,11,1,9,3}$

Find profit by weight ratio:

Item 5: $\frac{6}{1}=6$

Item 1: $\frac{9}{2}=4.5$

Item 7: $\frac{9}{3}=3$

Item 6: $\frac{16}{9}=1.77$

Now take items in decreasing ratio:

Total weight $=1+2+3+9=15$

Total profit $=6+9+9+16=40$

Correct option is:

$\boxed{(b)\ 40}$

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