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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:
$P={9,5,2,7,6,16,9}$
$W={2,5,6,11,1,9,3}$
What is the maximum value of items you can carry if maximum weight allowed is $25$ with a fractional knapsack?
Solution
Take items in decreasing profit by weight ratio:
Item 5: weight $1$, profit $6$
Item 1: weight $2$, profit $9$
Item 7: weight $3$, profit $9$
Item 6: weight $9$, profit $16$
Item 2: weight $5$, profit $5$
Total weight used:
$1+2+3+9+5=20$
Total profit:
$6+9+9+16+5=45$
Remaining capacity:
$25-20=5$
Next best item is item 4 with profit $7$ and weight $11$.
Fractional profit:
$5\times \frac{7}{11}=\frac{35}{11}=3.18$
Maximum profit:
$45+3.18=48.18\approx 48.1$
Correct option is:
$\boxed{(a)\ 48.1}$
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