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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
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 $15$.
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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